Patrick Weber

Hans Steinhart

Angelika Paschke
email: angelika.paschke@uni-hamburg.de

Characterization, Antigenicity, and Detection of Fish 1 Gelatine and Isinglass used as Processing Aids in Wines 2

Keywords: Chromatography -electrophoresis, Immunoassays Additives/Contaminants: Allergens, Residues Food Types: Animal, Fish and fish products, Wine Fish gelatine, isinglass, fish collagen, wine, bentonite, ELISA, food allergy 35

Fish gelatine (FG) and isinglass (IG) are widely used in the pharmaceutical industry and as 16 ingredients or processing aids in the food production. Both products are the focus of interest 17 since several nations, particularly the member states of the EU and Japan, USA, Australia, 18 and New Zealand, have introduced special labelling regulations for allergenic foodstuffs, such 19 as fish and products thereof. Thus, there is a demand for a reliable and sensitive method for 20 the detection of FG and IG in foodstuffs. In this study, the characterization of various FGs 21 and IGs, polyclonal antibodies raised against fish collagen and the development of a sensitive 22 indirect ELISA for the detection of FG and IG is described. The ELISA method detected ≤ 23 0.11 µg ml -1 from all FGs and IGs tested. The indirect ELISA was applied to various 24 experimental wines where FG and IG had been used as processing aids and to several 25

INTRODUCTION 36

Fish gelatine (FG) and isinglass (IG) are widely used in the food industry and are important 37 for the production of beverages, such as wine, beer, juice, cider, and mead [START_REF] Taylor | Fish allergy: Fish and products thereof[END_REF] consumption of foods nor after the administration of pharmaceuticals containing FG or fish 62 collagen. No adverse reactions were observed in a double-blind placebo-controlled food 63 challenge (DBPCFC) with FG performed by Andre et al. (2003) and only one mild, subjective 64 symptom occurred in a DBPCFC performed by [START_REF] Hansen | A randomized, double-blinded placebo-controlled oral challenge 519 study to evaluate the allergenicity of commercial, food-grade fish gelatin[END_REF] on 30 fish allergic 65 patients after the consumption of a cumulative dosage of 7.6 g of FG. Positive skin prick tests 66 and positive histamine release tests, though, were obtained against FG in some fish allergic 67 patients [START_REF] Hansen | A randomized, double-blinded placebo-controlled oral challenge 519 study to evaluate the allergenicity of commercial, food-grade fish gelatin[END_REF]. Published cases of allergic reactions to gelatine-containing 68 foods are rare and were referred to as mammalian gelatine [START_REF] Sakaguchi | Food allergy to gelatine in children with 539 systemic immediate-type reactions, including anaphylaxis, to vaccines[END_REF] or to 69 gelatine with uncharacterized origin [START_REF] Sakaguchi | IgE antibody to gelatine in children with immediate-537 type reactions to measles and mumps vaccines[END_REF][START_REF] Kelso | Anaphylaxis to measles, mumps, and rubella 525 vaccine mediated by IgE to gelatin[END_REF], Wang et al. 70 2005;[START_REF] Wahl | IgE-mediated allergic reactions to fruit gums and investigation 560 of cross-reactivity between gelatine and modified gelatine-containing products[END_REF]. That also applies to pharmaceuticals where known cases of allergic 71 reactions were referred to as mammalian gelatine [START_REF] Sakaguchi | Reactivity of the 545 immunoglobulin E in bovine gelatine-sensitive children to gelatins from various animals[END_REF], Sakaguchi et al. 72 1996[START_REF] Nakayama | Gelatin allergy[END_REF][START_REF] Sakaguchi | Anaphylaxis to gelatine-containing rectal suppositories[END_REF] or to gelatine with uncharacterized origin 73 [START_REF] Sakaguchi | IgE antibody to gelatine in children with immediate-537 type reactions to measles and mumps vaccines[END_REF][START_REF] Nakayama | A clinical analysis of gelatine allergy and 531 determination of its causal relationship to the previous administration of gelatin-containing 532 acellular pertussis vaccine combined with diphtheria and tetanus toxoids[END_REF][START_REF] Sakaguchi | Development of IgE 542 antibody to gelatine in children with systemic immediate-type reactions to vaccines[END_REF]) that were not 74 administered by the oral route. The latter three studies referred to vaccines from Japan which 75 are usually produced with mammalian gelatine [START_REF] Sakaguchi | Reactivity of the 545 immunoglobulin E in bovine gelatine-sensitive children to gelatins from various animals[END_REF]. Differentiation 76 between mammalian gelatine, FG, and fish collagen is very important since in vitro cross-77 reactivities were not observed [START_REF] André | Gelatin prepared from tuna skin: a risk factor for fish 501 allergy or sensitization?[END_REF][START_REF] Hamada | Identification of collagen as a new fish allergen[END_REF] or rather weak 78 (Sakaguchi et al. 2000a, Sakaguchi et al. 2000b[START_REF] Sakaguchi | Reactivity of the 545 immunoglobulin E in bovine gelatine-sensitive children to gelatins from various animals[END_REF][START_REF] Kelso | Anaphylaxis to measles, mumps, and rubella 525 vaccine mediated by IgE to gelatin[END_REF]. 79

Based on these facts, an allergic potential of FG and the fish collagen protein was not proven. 80 However, there is the risk that allergic reactions are not referred to the consumption of FG or 81 fish collagen containing foods or pharmaceuticals. Many foodstuffs or pharmaceuticals are 82 prepared by the usage of these substances but they are usually not considered to contain fish 83 proteins by the fish allergic consumer, e. g. due to improper labelling. Furthermore, the 84 adherence of fish muscle tissue, including the major fish allergen parvalbumin, must be 85 considered in FG and IG even though the information does not exist. Apart from this, 86 vegetarians and vegans wish to abstain from any animal substances. In conclusion, there is a demand for a reliable and sensitive method in detecting FG and IG in 88 order to assure an adequate labelling of foodstuffs and to detect contamination of foods and 89 pharmaceuticals for consumer protection. A common method for the determination of protein 90 traces is the enzyme-linked immunosorbent assay (ELISA). 91 92In this study, the characterization of polyclonal antibodies raised against fish collagen and the 93 development of a sensitive indirect ELISA for the determination of FG and IG is described. 94 This includes the characterization of various FGs and IGs by SDS-PAGE and the 95 investigation of their affinity to the polyclonal antibodies by Western blot. Furthermore, the 96 application of the ELISA for the investigation of wines is demonstrated. FG and IG are used 97 in wine production to reduce the polyphenol and protein content as described previously 98 [START_REF] Weber | Investiation of the allergenic potential of wines fined 565 with various proteinogenic fining agents by ELISA[END_REF]. The treatment contributes to the organoleptic properties of the wine and 99 to the prevention of proteinogenic haze. A range of experimental and commercial wines were 100 investigated for the presence of FG and IG residues. Bentonite treatment -an important fining 101 step in the winery process, which reduces the protein content in wines -was considered in the 102 production of experimental wines. 103

104

MATERIALS & METHODS 105

Food-grade gelatines and collagens 106

A total of seven commercially available FG and IG samples were collected from four 107 different suppliers (Erbslöh GmbH, Germany; Begerow GmbH, Germany; Norland Products 108 Inc., USA; Sigma Aldrich Co., USA): Three FGs A -C (derived from fish skin and provided 109 as yellow powders), two acid-hydrolyzed IG A and B (provided as acidic gel with 2 % IG 110 derived from swim bladder collagen), one hydrolyzed FG A (provided as white powder 111 derived from acidic and enzymatic hydrolysis from fish skin collagen), and one native IG 112 (derived from swim bladder and provided as yellow sheets). Three mammalian gelatines were purchased as yellow powders from local markets or 114 pharmacies: One mammalian gelatine composed of porcine and bovine gelatine, one porcine 115 gelatine, and one bovine gelatine. Protein contents were measured by the Kjeldahl method as 116 published earlier (Mattisek et al. 1992). 117 118

Polyclonal antibodies against fish collagen 119

Primary antibodies against fish collagen were produced in New Zealand white rabbits in 120 accordance with institutional guidelines (Eurogentec SA, Belgium). Briefly, 100 µg of acid-121 hydrolyzed IG A was mixed with 400 µl saline (0.9%) and 500 µl of complete Freund's 122 adjuvant and were injected intradermally to three rabbits each. Injection was repeated three 123 times with the incomplete Freund's adjuvant in four-week intervals. Blood samples were 124 taken 10 days after the second, third and fourth injection and the serum was obtained by 125 centrifugation. The third serum sample (~ 60 ml) was purified by affinity chromatography 126 using 10 mg hydrolyzed IG A immobilized at CNBr Sepharose. The column was washed with 127 10 ml elution buffer (100 mM glycin, pH 2.5) and 15 ml phosphate-buffered saline (PBS). 128 Afterwards, the serum was loaded with a flow rate of 0.5 -1 ml/min and the column was 129 washed thoroughly with PBS. Then, antibodies were eluted with elution buffer and 130 neutralized immediately with a solution of 1.5 M Tris(hydroxymethyl)-aminomethan (Tris), 131 pH 8.5. After dialysis against PBS over night, the final solution consisted of 15.2 mg 132 antibodies in 8 ml of PBS. hydrolyzed IG A, hydrolyzed IG B and the native IG, respectively. This process is described 152 elsewhere [START_REF] Weber | Investiation of the allergenic potential of wines fined 565 with various proteinogenic fining agents by ELISA[END_REF]) in which "isinglass 1" corresponds to hydrolyzed IG A, 153 "isinglass 2" to hydrolyzed IG B, "isinglass 3" to the native IG and "fish gelatine" to FG B. 154 Additionally, wines without bentonite treatment were prepared to evaluate the impact onto 155 residual amounts of FG and IG. Therefore, wines were bottled directly after separation from 156 the fining precipitate and, thus, lacked of the final cross-flow and membrane filtration. 157 158

Reagents and buffers 159

All chemicals used were of analytical grade. 160 Urea solution was prepared from 8 M urea and 2 % cyclohexylaminopropane sulfonic acid in 161 double distilled water. 162 Colloidal Coomassie Brilliant Blue (CBB) staining solution was prepared by dissolving 1 g of 163 CBB G250 in 20 ml double distilled water (solution 1). Then, 16 ml of solution 1 was added 164 to 16 ml o-phosphoric acid (85%), 80 g ammonium sulphate, and 768 ml double distilled 165 water. 200 ml of methanol was slowly added immediately before use. 166

Electrode solutions for the Western blot were composed as follows: Cathode solution (pH 7.6) 167 was prepared with 2.6 g 6-aminohexanoic acid, 0.05 g SDS, 0.05 g sodium azide, and 100 ml 168 ethanol, filled to 500 ml with double distilled water. Anode I solution (pH 10.4) consisted of 169 18.15 g Tris, 0.05 g sodium azide, and 100 ml ethanol, which was filled to 500 ml with 170 double distilled water. The anode II solution (pH 10.4) contained 1.52 g of Tris, 0.05 g 171 sodium azide, and 100 ml ethanol, filled to 500 ml with double distilled water. 172 173 For immunostaining, the following solutions were prepared: The Tris solution contained 50 174 mM Tris, 150 mM NaCl, and 0.5 % polyethylene-sorbitan monolaurate (Tween 20) in double 175 distilled water [START_REF] Szepfalusi | 555 Detection of IgE antibodies specific for allergens in cow milk and cow dander[END_REF]. The TMB solution consisted of 12 mg 3,3',5,5'-176 tetramethylbenzidine (TMB) and 40 mg dioctylsodiumsulfosuccinate dissolved in 10 ml 177 ethanol. Citric buffer (pH 5.0) was prepared with 9.4 g of citric acid and 18.2 g of Na 2 HPO 4 * 178 2 H 2 O dissolved in 1 l double distilled water. The substrate solution for immunostaining was 179 carefully mixed from 5 ml TMB solution, 15 ml citric buffer and 10 µl of H 2 O 2 (30%). Re-180 buffer solution was prepared with 121.2 mg Tris, filled up to 80 ml with double distilled 181 water, then adjusted to pH 6.0 with 4 M hydrochloric acid and finally filled up to 100 ml with 182 double distilled water. Ponceau red solution was prepared from 2 % Ponceau red and 3 % 183 trichloroacetic acid in double distilled water. 184 185 Goat anti-rabbit horseradish peroxidase (HRP) immunoglobulins were purchased from Dako 186 (order no. P0448, Dako GmbH, Germany). 187 Carbonate buffer for ELISA was prepared from 75 mM Na 2 CO 3 and 175 mM NaHCO 3 in 188 double distilled water (pH 9.5). The washing solution, substrate solution, and stop solution for 189 ELISA were prepared according to Weber et al. (2007). 190 191 Preparation of FG and IG solutions 192 FGs and hydrolyzed FG A were completely soluble in double distilled water. The urea 193 solution was added to the insoluble IGs, giving a concentration of approximately 200 µg ml -1 . 194

The suspension was stirred at room temperature and repeatedly heated at 80 °C until the 195 collagen was dissolved (24-72 h). Samples soluted in urea were diluted at least 20-fold with 196 the carbonate buffer to allow renaturation for the indirect ELISA. 197 198 Preparation of fish extracts 199 An amount of 2.4 g thawed fish muscle was homogenized for 2 min with 20 ml of the urea 200 solution using an Ultra-Turrax with 8000 rpm. Then, the homogenate was extracted for 2 h 201 The gel was then laid onto the cloth pile. Afterwards, the nitrocellulose transfer membrane 227 was soaked with anode solution II and was transferred onto the gel. Areas where no transfer 228 was desired were covered up with plastic slides. Two layers of cloth were soaked with the 229 anode buffer II and were put onto the blot membrane. After that, four layers of cloth were 230 soaked with the anode solution I and were transferred onto the pile. Finally, the graphite 231 anode was put onto the pile and the blotting was performed for one gel for 80 min at 60 mA. 232

Afterwards, the air-dried membrane was blocked two times with Tris solution for 1 h each 233 and was incubated for 1.5 h with polyclonal antibodies against fish collagen (1:500 diluted in 234 Tris solution). Then, washing was done three times with the Tris solution for 5 min each and 235 the membrane was incubated for 1.5 h with goat anti-rabbit HRP immunoglobulins (diluted 236 1:2000 in Tris solution). The membrane was washed four times with the Tris solution and for 237 For the indirect ELISA assay, standard solutions were prepared in carbonate buffer and wine 245 samples were diluted 1:10 with the carbonate buffer. 150 µl of these solutions were loaded in 246 the wells of a polystyrene microtiter plate (Maxisorb F96, certified, Nunc, Denmark). The 247 plate was incubated for 16 h at 8-9 °C and washed three times with 200 µl/well of the 248 washing solution. Afterwards, free binding sites of the wells were blocked with 250 µl/well 249 washing solution for 2 h at room temperature. The plate was washed three times with 250 µl 250 washing solution and the ELISA was proceeded by addition of 150 µl/well polyclonal 251 antibodies against fish collagen (diluted 1:2000 in washing solution). After 1.5 h of 252 incubation at room temperature, the plate was washed three times with 200 µl/well washing 253 solution. Thereafter, 150 µl/well of goat anti-rabbit HRP immunoglobulins (diluted 1:2500 in 254 washing solution) were added and incubated for 1.5 h at room temperature. After four 255 washing steps with 250µl/well washing solution, 150 µl/well substrate solution was added and 256 reacted for exactly 9 min in darkness, at 8-9 °C. The enzymatic colorimetric reaction was 257 stopped by adding 75 µl stop solution. The optical density (OD) was measured at 450 nm 258 against a reference wavelength of 630 nm using a microtiter plate reader (MRX, Dynex 259 Technologies, USA). 260 261The attained ODs were plotted against the logarithm of the protein concentration. Quantitative 262 evaluations were performed by AssayZap Software (Biosoft, United Kingdom) using 4-263 parametric regression. All ODs were reduced by the mean blank OD. Thus, the limit of values) was defined as zero plus 3-fold the standard deviation of the blank OD and the limit 266 of detection (LOD; 99.8% probability that the measured values are larger than the spread of 267 the blank values) was defined as zero plus 6-fold the standard deviation of the blank OD 268 [START_REF] Einax | Chemometrics in Environmental Analysis[END_REF][START_REF] Doerffel | Statistik in der analytischen Chemie[END_REF]. 269 270 Intraassay variation coefficients were calculated from five independent standard curves on the 271 same microtiter plate whereas interassay variation coefficients were calculated from five 272 independent standard curves on five different microtiter plates and on five different days. 273

The effect of heating and urea treatment during the preparation of the IG solutions to the 274 antigenicity was mathematically considered. Porcine and the mammalian gelatine had a similar composition to FGs, indicating proteins 297 and many fragments between ~ 250 -30 kDa. Distinct bands were visible for porcine gelatine 298 at ~240, 120, 117 and 60 kDa. However, bovine gelatine showed considerable differences to 299 fish and other mammalian gelatines. MWs were determined between 50 -8 kDa for bovine 300 gelatine. Thus, this bovine gelatine has a character rather similar to hydrolyzed IG or 301 hydrolyzed FG than to FG. This indicated that the bovine gelatine had been comprehensively 302 processed. 303 304

Characterization of the polyclonal antibody's specificity by semidry Western blot and 305

immunostaining. 306 Specificity of the polyclonal antibody was initially evaluated by various fish and mammalian 307 gelatines and IG (Figure 2). Proteins were detected in all FGs and IGs. FGs bound antibodies 308 to proteins and their fragments between MWs of approximately 460 -40 kDa. Smaller 309 proteins, despite being detected by CBB staining, were not detected by this antibody. Binding 310 to the hydrolyzed IG and FG was, with the exception of hydrolyzed IG A, considerably 311 weaker compared to FGs. Hydrolyzed IG B revealed a weak antibody binding to MWs 312 between 100 -38 kDa whereas hydrolyzed FG A showed a single immunostained protein 313 fragment at 14 kDa. On the contrary, hydrolyzed IG A, which had been used for the antibody 314 production, was well recognized by the antibody in the range of 460 -8 kDa. 315 Bovine and mammalian gelatine were not recognized by the antibody whereas porcine 316 gelatine revealed a slight antibody binding in the range between 400 -120 kDa. 317 318 Furthermore, the specificity of the polyclonal antibody to fish collagen was assessed by the 319 investigation of various fish muscle extracts (Figure 3). Colloidal CBB showed proteins 320 between > 200 -8 kDa for all fish species except for tuna. Binding of the primary antibody by 321 immuno-staining occurred almost exclusively to proteins with MWs ≥ 120 kDa. Detection of 322 these proteins can be expected as they represent the major collagen fractions (see Figure 3, 323 lane 6). Only weak staining occurred in proteins of ~ 55 and ~ 36 kDa. Major fish proteins 324 with MWs lower than collagen, e. g. definite bands between 50 -36 kDa, were barely 325 detected. 326 327

Indirect ELISA evaluation 328

The indirect ELISA standard curves were derived by serial dilution of gelatine and IG 329 samples in the range of 0.001 -10 µg ml -1 protein. Figure 4 shows a significant difference in 330 the slopes of the various products. The relative reactivity of FGs and IGs related to FG A had 331 values between 70 -13 % within the steepest range of 0.3 -3 µg ml -1 . Calculation of 332 recovery rates was not possible for hydrolyzed IG A because of a greater sensitivity. LODCs 333 were calculated in the range of 0.001 -0.11 µg ml -1 and LOD were calculated in the range of 334 0.002 -0.18 µg ml -1 for all FGs and IGs (Table 1). 335 336 Gelatines from mammals displayed higher LODCs and LODs of 0.14 -0.8 µg ml -1 and 0.27 -337 2.05 µg ml -1 , respectively. Bovine gelatine was not detectable by indirect ELISA. Relative 338 reactivities related to FG A were between 30 -1% and thus, were lower compared to FG and 339 IG. Intra-assay and inter-assay variation coefficients were calculated for FG A. Intra-assay 340 variation coefficients were less than 10 % (1.1 -6.3 %) and inter-assay variation coefficients were less than 25 % (3.6 -21.5 %) for concentrations between 0.1 -10 µg ml -1 . Matrix 342 effects were assessed by spiking experiments with all four experimental wines by spiking 343 with FG A and hydrolyzed IG A, respectively (Table 2). Considering the 10-fold dilution, 344 recovery rates for FG A were between 73 -125 % within the steepest range of 3 -20 µg ml -1 . 345 Thus, the limit of quantification (LOQ) was found to be 3 µg ml -1 , which resulted in a 346 practical working range of 3 -20 µg ml -1 for the white wines. The LODCs were calculated 347 between 0.5 -0.6 µg ml -1 and the LODs between 0.7 -0.9 µg ml -1 for all spiked wines. 348

Consequently, LODC and LOD of FG A were only insignificantly affected by the wine 349 matrix. 350 351 Hydrolyzed IG A was detected in 10-fold diluted experimental wines with recovery rates 352 between 69 -113 % in the range of 0.03 -1 µg ml -1 . The LOQ was found to be 0.03 µg ml -1 , 353 establishing a practical working range of 0.03 -1 µg ml -1 . The LODCs were calculated 354 between 0.01 -0.02 µg ml -1 and the LOD result was 0.02 µg ml -1 for all investigated wines. 355 Thus, the LODC and LOD of hydrolyzed IG A were also not significantly affected by the 356 wine matrix. 357 358

Determination of fish gelatine and isinglass in wines by indirect ELISA 359

Of the 60 commercial white wine samples none were found to give signals significantly 360 different from the blank OD. This included two wines with the known treatment of fish skin 361 gelatine. All signals were significantly lower than the LODC. Based on the LODC values that 362 were achieved for the various FG and IG (Table 1), the amounts of FG or IG were considered 363 lower than 1.1 µg ml -1 in these wines. 364 365 Investigation of the experimental wines fined with FG and various IGs revealed negative 366 results for all wines fined with FG B, hydrolyzed IG B and native IG. This result was wines fined with hydrolyzed IG A. Quantification was performed against a standard curve 369 prepared with hydrolyzed IG A. Detected residues were up to the level of 0.33 µg ml -1 in 370 wines not treated with bentonite (Table 3). Thereof, amounts in wines treated with usual 371 dosages of hydrolyzed IG A were up to the level of 0.09 µg ml -1 while treatment with an 372 excessive dosage led to residues between 0.04 -0.33 µg ml -1 . Negative results were obtained 373 for all wines treated with hydrolyzed IG A and bentonite. Thus, amounts of hydrolyzed IG A 374 were lower than 0.01 µg ml -1 in these wines. 375 376 DISCUSSION 377 FGs and IGs are produced from various fish species and by various methods. Methods for the 378 FG production include heating, acidic extraction, and further acidic and/or enzymatic 379 hydrolysis depending on the required properties [START_REF] Baziwane | Gelatin: The paramount food additive[END_REF]. IG is produced from 380 swim bladders by washing and cleaning, conditioning in hot water, and the removal of muscle 381 layers and blood vessels [START_REF] Koochekian | Production of isin glass from the swim bladder 527 of sturgeons[END_REF][START_REF] Efsa | Opinion of the scientific panel on dietetic products, nutrition and allergies on a 509 request from the commission related to a notification from DWV and VINIFLHOR on fish 510 gelatine or isinglass used as fining agent in wine pursuant to article 6 paragraph 11 of 511 Directive 2000/13/EC -for permanent exemption from labelling[END_REF]. Thus, the final products vary 382 in their species composition and alterations in their collagen structure. This may interfere with 383 the detection of various FGs and IGs with only a single method. In this regard, Figure 1 384 illustrates the highly heterogeneous composition of various FGs and IGs. Depending on the 385 degree of hydrolysis, their constitutions range from native products with the characteristic α-, 386 β-, and γ-collagens with MWs larger than 117 kDa to highly hydrolyzed products with MWs 387 lower than 40 kDa. However, all products bound to the primary antibody as displayed by 388 Western blot in Figure 2. As previously assumed, a strong impact of processing could be 389 demonstrated to the primary antibody's binding. Highly hydrolyzed products such as 390 hydrolyzed IG B and hydrolyzed FG A were less detected by the primary antibody raised 391 against fish collagen. Other products with their various native and fragmented proteins 392 showed good affinity to the antibody. Consequently, the detection of FG and IG by indirect IGs. Hydrolyzed IG A showed the highest affinity to the antibody. This can be simply 401 explained as the product had been used for the antibody production. If hydrolyzed IG A is 402 ignored, the three FGs showed the highest antigenicity. Hydrolyzed IG B and hydrolyzed FG 403 A, which had been further hydrolyzed by acidic and/or enzymatic digestion, revealed the 404 lowest antigenicity. Interestingly, native IG indicated an antigenicity between FG and 405 hydrolyzed IG. The complex tertiary and quaternary structure of native IG could be 406 considered as a possible factor for the masking of epitopes since the product had not been 407

processed. These structures are destroyed during the production of FG, resulting in a higher 408 antigenicity. In conclusion, the antibody binding occurs seemingly in a processing dependent 409 manner with the lowest affinity belonging to highly processed hydrolyzed IGs and the highest 410 affinity to moderately processed FGs. However, differences in the affinity of FGs and IGs to 411 the microtiter plate must also be considered for some products demonstrated by competitive 412 ELISA (results not shown). Furthermore, sequential differences of collagens from various fish 413 species must be kept in mind since the sequential information is currently inaccessible, 414 therefore, differences or conformities in the amino acid sequences are unknown. 415

416

The ELISA results showed that cross-reactivities between various FGs and IGs are rather 417 unacceptable for a reliable quantification if the used product is unknown. 418 as demonstrated by the relative reactivity related to FG A, were between 13-70 % if (results not shown). Furthermore, the effects were mathematically considered as explained in 425 the introduction. 426 427 Cross-reactivity between fish and mammalian gelatine was demonstrated as weak by SDS-428 PAGE (Figure 2) and indirect ELISA (Table 1). Thus, bovine gelatine was not detected by the 429 primary antibody. This is most likely due to high sequential differences and also due to 430 different hydrolysis levels. The SDS-PAGE (Figure 1) indicated a stronger hydrolysis of the 431 used bovine gelatine compared to the fish, porcine, and mammalian gelatines. However, the 432 observation of low cross-reactivity between fish and mammalian gelatine is in accordance 433 with the published findings described in the introduction. This allows the fish and bovine 434 gelatine traces to differentiate, but not the fish and porcine gelatine traces by indirect ELISA. 435

In conclusion, the indirect ELISA can be used for the sensitive qualitative detection of minute 436 amounts of ≤ 0.11 µg ml -1 rather than as a quantitative method for the detection of FGs and 437

IGs. The possibility of differentiation between fish and mammalian products is limited. 438

439

The extent of the use of FG and IG within wine production is barely known and largely 440 depends on grape variety, vintage, region, and the winemaker's practice. It is estimated that 441 about 16% of French and 7% of German wines have been fined with products composed of 442 fish collagen (personal communication: Deutscher Weinbauverband, Germany, and Union des 443 Fabricants, des Laboratoires et des Industries Oenologiques, France, 2006). The appliance of 444 this indirect ELISA to white wines indiacted only minor effects of the wine's matrix to the powder or egg white powder, led to unacceptable results (results not shown). Thus, the 452 analysis of wines was focused on white wines. 453 454 Residues of FG or IG were not detected in any of the 60 commercial white wine samples 455 including the two samples known to be fined with FG. Experimental wines were found to 456 contain traces of hydrolyzed IG A, less than 0.33 µg ml -1 , when these wines were not treated 457 with bentonite and lacked of the successive cross-flow and membrane filtration (Table 3). 458

Bentonite is an important substance for the stabilization of white wines as previously 459 mentioned. Thus, it should be applied to most white wines. No traces of FG or IG were 460 detected in any of the experimental wines treated with bentonite and successive cross-flow 461 and membrane filtration, indicating amounts of < 0.02 µg ml -1 . 462 463 Bentonite treatment of red wines is a critical step because it can reduce the red colour of the 464 wine. Furthermore, red wines are more stable against protein clouding because of their natural 465 protein precipitating properties, which is due to their high polyphenol content. Thus, bentonite 466 is frequently avoided in red wine production. However, residues of foreign proteins, such as 467 FG and IG, can be expected to be considerably lower in those untreated red wines compared 468 to the untreated white wines as earlier demonstrated [START_REF] Weber | Lysozyme in wine: A 567 risk evaluation for consumers allergic to hen's egg[END_REF]. This is most likely 469 due to the high content of polyphenols. 470 Overall, no residues of FG and IG could be detected in wines if good manufacturing practices 471 were used combined with thorough filtration. The lack of bentonite usage and additional 472 filtration can result in minute amounts of IG in white wines. However, there is no evidence 473 that FG or IG can present a risk to human health. Combining this lack of evidence with the 474 results of detectable residues as from little to none, fining of wines with FG and IG seemed to 475 be of no risk for the consumers allergic to fish. This conclusion is in accordance with Taylor 476 et al. (2004). Labelling of FG and IG on wines for the purpose of protection of fish allergic 477 developed. This method is suitable to detect ≤ 0.11 µg ml -1 independent of the analyte's 482 composition and processing stage. Involving a 10-fold dilution, this method can be directly 483 applied to the investigation of white wines. No residues of FG and IG were found in 484 commercially available wines and in experimental wines treated with bentonite, a strong 485 adsorbent for proteins, and successive cross-flow and membrane filtration. Only ≤ 0.33 µg ml - 486 1 were found in some white wines not treated with bentonite or with successive cross-flow 487 and membrane filtration. 488

ACKNOWLEDGEMENTS 490

We would like to thank Mrs. Annelie Damerau and Mrs. Svenja Schloß for their assistance in 491 this study. Furthermore, we would like to thank Eurogentec S.A., Belgium, for the antibody 492 production, DLR-Mosel (especially Mr. Bach and Mr. Scholten), Germany, for the 493 experimental wine production, Mr. Goertges and Mr. Meinl from Erbslöh Geisenheim AG, 494 Germany, Mr. Norland from Norland Products Inc., USA,and SIHA Begerow AG,Germany,495 for their support. Finally, we would like to thank Deutsche Weinakademie GmbH (especially

  through continuous shaking and centrifuged for 15 min at 6700 g. The clear supernatant was 202 removed and used for SDS-PAGE analysis. Spare extracts were stored at -24 °C. 203 204 SDS-PAGE 205 SDS-PAGE was performed on Invitrogen equipment (Invitrogen Corp., USA). Samples were 206 separated between 200 -3.5 kDa at 200 V for 45-50 min with 1mm thick pre-cast NuPAGE 207 Novex Bis-Tris 12-well gels with 12% acrylamide (Invitrogen Corp.), NuPAGE MES SDS 208 running buffer as electrolyte (Invitrogen Corp.), and were calibrated against the Serva Mark12 209 molecular weight (MW) ladder (Invitrogen Corp.). Proteins with MWs between 460 -31 kDa 210 were separated at 150 V for 70 min on 1mm thick pre-cast NuPAGE Novex Tris-Acetate 10-211 well gels with 3-8% acrylamide (Invitrogen Corp.), NuPAGE Tris-Acetate SDS running 212 Corp.), and were calibrated against the pre-stained HiMark MW ladder 213 (Invitrogen Corp.). 214 background was decolorized through incubation in double distilled water with soaked paper 218 tissues. 219 220 Semidry Western blot and immunostaining (Immunoblot) 221 Semidry Western blot was performed on a LKB Bromma 2117 Multiphor II blotting 222 apparatus with Pharmacia Biotech Nova Blot graphite electrodes (Pharmacia Biotech, USA) 223 and a Powerease 500 power supply (Invitrogen Corp.) onto nitrocellulose transfer membranes 224 with a 0.2 µm pore size (Whatman PROTRAN, Whatman GmbH, Germany). 225 Initially, four layers of thin cloth were soaked with cathode solution and put on the cathode. 226

  immunostaining until the desired color intensity was obtained. The 239 reaction was stopped by washing with double distilled water. The Serva Mark12 MW ladder 240 was stained by the addition of 50 ml Ponceau red solution for 1.5 h followed by a thorough 241 washing with double distilled water. 242 243 Indirect ELISA Procedure 244

  ; 50% probability that the measured values lie within the spread of the blank 265

  Figure1shows the heterogeneous composition of various gelatines and IGs. FGs showled 284

  agent dosage and bentonite usage. Positive results were obtained for 368

  FGs and IG products would lead to such a method. 398 399 The indirect ELISA revealed different affinities of the primary antibody to various FGs and 400

  or by masking the polyphenols by adding other proteins, like skim milk 451

  persons has been exempted within the EU by the initiation of the EU-Directive 2007/68/EC in 478 November 2007. 479 480 In conclusion, an indirect ELISA method for the sensitive detection of FG and IG has been 481

Figure 1 Figure 2 Figure 4

 124 FIGURE CAPTION 584

4Figure 1

 1 Figure 1 SDS-PAGE with colloidal Coomassie Brillant Blue staining of various gelatines and collagen products derived from fish and mammals.

Figure 2 Figure 3 Figure 4

 234 Figure 1 subtitle A: MW between 460 -31 kDa; B: MW between 200 -3.5 kDa; M: MW marker; 1: Fish gelatine A; 2: Fish gelatine B, 3: Fish gelatine C; 4: Hydrolyzed isinglass A; 5: Hydrolyzed isinglass B; 6: Hydrolyzed fish gelatine A; 7: Native isinglass; 8: Bovine gelatine; 9: Mammalian gelatine; 10: Porcine gelatine. 160x222mm (300 x 300 DPI)

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	O n l
	y

  Five fish muscle samples from species important to FG and IG production were purchased 138 filleted and frozen from local markets; cod (Gadus ssp.), pollock (Pollochius virens), tuna 139 (Thunnus ssp.), sturgeon (Acipenser ssp.) and tilapia (Oreochromis ssp.).

	140
	141
	142	Wine samples
	143	Sixty commercial white wine samples were purchased from local stores. The selection pattern
	144 145	F was restricted to the country of origin (23 German wines, 18 French wines and 19 Italian o r wines) and to important European grape varieties (Chardonnay, Pinot gris, Pinot blanc,
	146 147	Riesling, Sauvignon blanc and Silvaner). Fining with fish skin gelatine was known for two of P e these commercial white wine samples whereas fining was not known for the remaining 58
	148 149	samples.	e r
	150	R Experimental wines were prepared from four grape varieties (Riesling Mosel, Riesling
	151	e Rheingau, Pinot blanc and Pinot gris) by treatment with two different dosages of FG B,
			v i e
			w
	133		The antibody purity was greater than 85 %, estimated by SDS-O n l y
	134	PAGE. 0.1% bovine serum albumin and 0.01 % Thimerosal was added for stabilization and
	135	the purified serum was stored at -80 °C.
	136
	137	Fish samples

Table 1 :

 1 LODC, LOD, and relative reactivities of various gelatines and IGs determined by 572

	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y

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Table 2 :

 2 LODC, LOD, and recovery rates of FG A and hydrolyzed IG A in various wines 575

	Page 25 of 35		Food Additives and Contaminants
	576	determined by indirect ELISA.
		Grape variety	LODC [µg ml -1 ]	LOD [µg ml -1 ]	Recovery [%]
			FG A Hydrol. IG	FG A Hydrol. IG A FG A	Hydrol. IG
				A			(3-20 µg ml -	A (0.03 -1
							1 )	µg ml -1 )
		Riesling	0.6	0.02	0.9	0.02	80 -121	83 -116
		Mosel
		Riesling	0.6	0.01	0.9	0.02	78 -83	69 -93
		Rheingau
		Pinot blanc	0.5	0.01	0.7	0.02	87 -118	70 -107
		Pinot gris	0.6	0.01	0.7	0.02	73 -125	82 -113
	577

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Table 3 :

 3 Fining agent contents in white wines fined with hydrolyzed IG A and not treated 578 with bentonite. Results were acquired by indirect ELISA with a standard curve prepared of 579

	580	hydrolyzed IG A.
		Wine	Fining agent content for a	Fining agent content for an
			common fining agent dosage	excessive fining agent
			of 50 ml/hl [µg ml -1 ]	dosage of 250 ml/hl [µg ml -
				1 ]
		Riesling Mosel	0.09 ± 0.00	0.33 ± 0.01
		Riesling Rheingau	LODC	0.04 ± 0.01
		Pinot blanc	0.08 ± 0.00	0.32 ± 0.01
		Pinot gris	LOD	0.23 ± 0.03
	581	LODC = value was significantly equal to the limit of decision (t-Test); LOD = value was
	582	significantly equal to the limit of detection (t-Test); variation values represent the standard
	583	deviation.

Table 1 :

 1 LODC, LOD, and relative reactivities of various gelatines and IGs determined by

	Page 29 of 35	Food Additives and Contaminants
	1
	2	indirect ELISA.
		Product	LODC [µg ml -1 ]	LOD [µg ml -1 ]	Relative	reactivity
					related to FG A [%]
		FG A	0.04	0.08	-
		FG B	0.04	0.06	45.8 -70.1
		FG C	0.03	0.04	36.2 -68.4
		Hydrolyzed IG A	0.001	0.002	-
		Hydrolyzed IG B	0.11	0.18	16.7 -53.3
		Hydrolyzed FG A	0.11	0.13	13.4 -30.5
		Native IG	0.02	0.04	23.7 -70.0
		Porcine gelatine	0.14	0.27	6.4 -30.3 %
		Mammalian gelatine 0.80	2.05	0.6 -5.2 %
		Bovine gelatine	n. d.	n. d.	-

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Table 2 :

 2 LODC, LOD, and recovery rates of FG A and hydrolyzed IG A in various wines

				Food Additives and Contaminants		Page 30 of 35
	1
	2	determined by indirect ELISA.
		Grape variety	LODC [µg ml -1 ]	LOD [µg ml -1 ]	Recovery [%]
			FG A Hydrol. IG	FG A Hydrol. IG A FG A	Hydrol. IG
				A			(3-20 µg ml -	A (0.03 -1
							1 )	µg ml -1 )
		Riesling	0.6	0.02	0.9	0.02	80 -121	83 -116
		Mosel
		Riesling	0.6	0.01	0.9	0.02	78 -83	69 -93
		Rheingau
		Pinot blanc	0.5	0.01	0.7	0.02	87 -118	70 -107
		Pinot gris	0.6	0.01	0.7	0.02	73 -125	82 -113

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Table 3 :

 3 Fining agent contents in white wines fined with hydrolyzed IG A and not treated 1 with bentonite. Results were acquired by indirect ELISA with a standard curve prepared of

	2
	3	hydrolyzed IG A.
		Wine	Fining agent content for a	Fining agent content for an
			common fining agent dosage	excessive	fining	agent
			of 50 ml/hl [µg ml -1 ]	dosage of 250 ml/hl [µg ml -
				1 ]
		Riesling Mosel	0.09 ± 0.00	0.33 ± 0.01
		Riesling Rheingau	LODC	0.04 ± 0.01
		Pinot blanc	0.08 ± 0.00	0.32 ± 0.01
		Pinot gris	LOD	0.23 ± 0.03

LODC = value was significantly equal to the limit of decision (t-Test); LOD = value was

Colloidal CBB staining

Gels were stained with 50 ml of colloidal CBB staining solution for 16 h. After that, the

min each, was incubated for 1 min in re-buffer solution, and finally was incubated with

must be clarified. This is a very critical step because, sometimes, it is not clear which product

was used in the manufacturing process. Thus, a method predominantly independent from the

used product is needed. In the case of the ELISA, a high cross-reactivity among the various

the solubilization of some IGs was considered to have only a minor effect on these findings.

OD values in the steepest range between 0.3 -3 µg ml -1 were found to be between 104 % (0.3

µg ml -1 ) and 63 % (3 µg ml -1 ) of the respective untreated material as demonstrated with FG A

the investigation of red wines was impossible because of the strong impact of the red wine's

matrix. This led to an extremely high background noise causing false positive results.

Polyphenols are the main suspects as they strongly interact with proteins as previously stated

[START_REF] Weber | Investiation of the allergenic potential of wines fined 565 with various proteinogenic fining agents by ELISA[END_REF]. Separation of polyphenols by the use of solid-phase extraction, dialysis,

Mr. Nickenig), Germany, for co-founding.

peanut (Arachis hypogaea L.) protein in complex food matrixes. J Agric Food Chem. 47: 603-

http://mc.manuscriptcentral.com/tfac Email: fac@tandf.co.ukFood Additives and Contaminants


Waldo J De Boer
email: waldo.deboer@wur.nl

Hilko Van Der Voet

Polly E Boon

Bas G H Bokkers

Martine I Bakker

A comparison of two

Keywords: betabinomial and normal distribution, BBN, ISUF, transformation, dietary risk assessment, usual intake distribution

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The presence of substances in food, for example pesticide residues, contaminants or vitamins, can have positive or negative health impacts. The evaluation of dietary intake is an essential step in the risk or benefit/risk assessment of these substances. Health effects may be acute reactions to a short-term exposure (e.g. neurological effects of organophosphate pesticides), or may be of a chronic nature as a result of long-term exposure to relatively low concentrations (e.g. immune suppression due to mycotoxins). This paper addresses the assessment of long-term exposure, and specifically the question which of the available models can be used in specific cases.

When considering long-term exposure to substances in food it is not generally possible to specify the precise time period of interest. Therefore, this period is often left unspecified, and it is customary to consider usual intake, which is defined as the long-run average of daily intakes of a substance by an individual. Although usual intake is commonly expressed on a per-day basis it should not be confused with the daily intake data as calculated from the consumption and concentration information for each individual person-day. The estimation of the usual intake distribution is in one way less complex than that of acute intake distribution, because fluctuations in concentrations can often be assumed to average out in the long run.

Hence, one can ignore concentration variability, and only the mean concentration of the substance in the various foods is needed. A difficulty of usual intake estimation is that it is not practical to collect food consumption data of individuals over long periods of time. Typically, the available food surveys employ two to seven independent 24-hour dietary recalls (or records) per individual. As a consequence, the direct estimator (mean consumption over the available days per individual) suffers from large sampling error and the corresponding distribution of means over individuals is too wide in comparison to the distribution of true usual intakes.

Statistical models that separate the variation within persons from the variation between persons have proven very useful for the estimation of usual intake [START_REF] Hoffmann | Estimating the distribution of usual dietary intake by short-term measurements[END_REF], Dodd et al. 2006). The simpler models [START_REF] Slob | Modeling long-term exposure of the whole population to chemicals in food[END_REF][START_REF] Nusser | A semiparametric transformation approach to estimating usual daily intake distributions[END_REF][START_REF] Waijers | The potential of AGE MODE, an age-dependent model, to estimate usual intakes and prevalences of inadequate intakes in a population[END_REF] require that all individual-days in the dataset have a positive intake. In more advanced models [START_REF] Nusser | Estimating usual dietary intake distributions: adjusting for measurement error and nonnormality in 24-hour food intake data[END_REF][START_REF] Slob | Probabilistic dietary exposure assessment taking into account variability in both amount and frequency of consumption[END_REF], Tooze et al. 2006, Van der Voet et al. 2007) allowance is made for a non-negligible fraction of individual-days without intake (incidental or episodical intakes). This paper focuses on the latter category.

Consumed foods belong to one of two categories: A. foods with a positive mean concentration, and B. foods where the substance of interest has never been found. People who only eat from category B on a specific day will obviously have a zero intake of the substance.

The true intake on a specific day may still be zero even if foods from category A are consumed, since the concentration in a single food item may be zero even though the mean is positive. However, for the purpose of long-term intake modelling such days will be treated as positive-intake days.

Usual intake may be different for subgroups in the population and/or it may be correlated with person-specific variables such as age, sex and/or income. These phenomena can be efficiently taken into account by statistical models that estimate usual intake as a function of covariates (we use covariate as a general term for both categorical cofactors and continuous covariables).

In this paper, two models for usual intake that allow zero-intake days are compared. Both models are implemented in the Monte Carlo Risk Assessment (MCRA) program [START_REF] Boer | MCRA, Release 6, a web-based program for Monte Carlo Risk Assessment[END_REF], but also in other software, and have already gained some popularity of use [START_REF] Hoffmann | Estimating the distribution of usual dietary intake by short-term measurements[END_REF], Boon et al. 2009 in press). We illustrate their use and argue the appropriateness of each model in relation to data and model assumptions.

Material and methods

Models

The two models considered are based on the same principle of separately modelling intake frequencies and intake amounts, followed by an integration step. In this paper a positive intake refers to a day on which an individual consumes at least one food that has a positive average concentration of the substance considered. Modelling intake frequency is the modelling of frequencies of positive intake per individual, whereas modelling intake amount refers to the positive intake amounts themselves. One of the two models considered is called Statistical Exposure Model for Incidental Intakes (STEM.II) by [START_REF] Slob | Probabilistic dietary exposure assessment taking into account variability in both amount and frequency of consumption[END_REF], and betabinomial-normal (BBN) model by [START_REF] Boer | MCRA, Release 4, a web-based program for Monte Carlo Risk Assessment[END_REF], but they are essentially the same models, differing only in some details (see Table 1). The BBN model estimates the usual intake and allows for separate modeling of the effect of covariates for both the intake frequency and the intake amount model. The second model is developed at Iowa State University [START_REF] Dodd | A technical guide to C-SIDE[END_REF][START_REF] Nusser | Estimating usual dietary intake distributions: adjusting for measurement error and nonnormality in 24-hour food intake data[END_REF]. [START_REF] Dodd | Statistical methods for estimating usual intake of nutrients and foods: a review of the theory[END_REF] refer to this model as the Iowa State University Foods (ISUF) model, and we will follow that notation. The ISUF model estimates usual intake but without the option of taking covariates into account. For the calculations in this paper we have used the MCRA program, release 6 (De Boer and Van der Voet 2007).

In chronic risk assessment, the main interest is the fraction of individuals having a usual (daily) intake higher than a health based limit value such as the acceptable daily intake (ADI) or tolerable daily intake (TDI). Usually, food consumption data are available for individuals on two or more days. Although this is not an essential restriction, we only consider the case that for each individual an equal number of days is reported. Through the assumed independence of consumption data and compound concentration values (a most reasonable assumption) intake amounts of a substance by individual i on day j are calculated by multiplying the consumed amount per kg body weight by the mean concentration, and then summing over all food items. For calculation of the mean concentration, all available concentration measurements on a food are taken. Non-detect measurements were substituted by a suitable fraction of the limit of reporting (LOR). The calculated intake amounts are the basic data used in further modelling of the intake frequencies and intake amounts.

To assess the uncertainty of the outcomes, both the consumption data and the compound concentration values are resampled using the bootstrap method [START_REF] Efron | Bootstrap methods: another look at the jackknife[END_REF][START_REF] Efron | An introduction to the bootstrap[END_REF]. For each statistic under consideration, an uncertainty distribution is generated and the sampling error of the original dataset is quantified by a 95% uncertainty interval.

Betabinomial and normal (BBN) model

General description

The name of the BBN model refers to a betabinomial (BB) distribution used for modelling intake frequencies, and a normal (N) distribution used for modelling positive intake amounts.

Intake refers to a specific substance of interest. Intake frequency modelling concerns the number of days for which an intake is recorded, due to the consumption of foods that may contain the substance. This number of days is assumed to have a binomial distribution, with a binomial index equal to the total observed number of days, and with probability of intake p, which may itself vary between individual persons. In our model, individual probabilities p are assumed to follow a beta distribution. The beta distribution is commonly used for modelling probabilities and has domain (0, 1). The variability between individual intake probabilities is quantified by the so-called overdispersion parameter φ (where φ = 0 would indicate that all individuals have the same p, see Detailed description of BBN implementation in MCRA).

Intake amount modelling concerns the amount ingested of the substance on the days that intake of contaminated food takes place. The intake amount for an individual on a specific day (i.e. observed consumption multiplied by average concentration) is assumed to have an approximate normal distribution after a natural logarithmic or power (Box-Cox) transformation. Variation between and within persons is estimated by analysing the transformed positive intake amounts with a linear random effects model. The models for the intake frequencies and the transformed intake amounts can be extended with covariates, for example sex and/or age (such models are called mixed models because they include both random and fixed effects). After fitting the separate models for intake frequency and intake amount, the usual intake distribution is estimated by combining both models. In BBN this is and normal (usual intake amount) distribution (Monte Carlo integration). The BBN model assumes that the probability of consumption is unrelated to the individual's usual intake amount. See next section for details of the implementation.

In this paper we used the implementation of the BBN model in the MCRA program.

While MCRA and the implementation described in [START_REF] Slob | Probabilistic dietary exposure assessment taking into account variability in both amount and frequency of consumption[END_REF] will give very similar results in many cases, some differences exist in the details. The main differences are summarized in Table 1.

Detailed description of BBN implementation in MCRA Modelling the intake frequency distribution

Let n and npos be the total number of survey days per individual and the number of days with a positive intake, respectively. Then npos is modelled using a binomial distribution with binomial totals n and conditional on probabilities p. The probabilities p in turn are assumed to follow a beta distribution. The resulting distribution for npos is known as the betabinomial distribution. The mean and variance of a beta distribution are:

] ) 1 ( 1 )[ 1 ( ϕ π π - + - n
, respectively.

Note that the first part of the variance n ) 1 ( π πequals the binomial variance; the second part adds the effect of the so-called overdispersion, quantified by the overdispersion factor φ.

Fitting the beta-binomial model with maximum likelihood gives estimates πˆ and ϕˆ for the parameters π and φ. As regards notation, estimates are denoted by a hat (^). Backtransformation gives the following estimates for the standard Beta distribution parameters α and β:

F o r P e e r R e v i e w O n l y ϕ ϕ π α / ) 1 ( ˆ- = ϕ ϕ π β / ) 1 )( 1 ( ˆ-- =
The distribution of the probability that an individual has a positive intake on any single day is then modelled by Beta(α ˆ, β ˆ).

Modelling the positive intake amounts

First, to achieve a better normality, the positive intake amounts are transformed. ). The goodness-of-fit is determined by minimising the residual sum of squares:

∑ ⋅ - 2 ) ( ) ( ) ( pow i i ypos z
β of a regression of normal Blom scores on the power-transformed intake amounts. Normal Blom scores are [START_REF] Blom | Statistical estimates and transformed Beta-variables[END_REF]:

        + - Φ = - 4 1 8 3 1 ) ( n i z i
where i is the rank of the n th non-zero intake amount, n, the total number of non-zero intakes and ( ) ⋅ Φ -1 is the inverse of the standard normal cumulative distribution function.

The transformed positive intake amounts are modelled in a maximum likelihood analysis with random terms person and interaction person.day to estimate the between-and withinperson variance component:

transf(ypos ij )= µ + c i + u ij
where transf(ypos) is a transformed intake amount, and where c i and u ij are the betweenperson effect and within-person effect, respectively. These effects are assumed to be normally distributed with N(0, σ 2 B ) and N(0, σ 2 W ), respectively.

Calculating the usual daily intake distribution

The usual intake is defined as the expected intake amount per day (over both consumption and non-consumption days) of a random individual. The distribution is estimated by Monte Carlo integration, where a simulated intake from the distribution of positive intakes is multiplied by a simulated value from the distribution of individual intake probabilities.

First, a large number of positive intakes on the transformed scale are simulated as m + z i , where z i is a random value from the N(0, s 2 B ) distribution. Secondly, these values are backtransformed to the natural scale and a bias-correction is applied so that the values represent unbiased estimates of the expected value of positive intakes at the natural scale. For a logarithmic transformation there is an exact relation and the bias-corrected backtransformation is ( )

2 2 1 exp W i i s z m ypos + + =
For a power transformation with power pow a Taylor approximation for bias correction is used [START_REF] Dodd | Statistical methods for estimating usual intake of nutrients and foods: a review of the theory[END_REF] and the approximately bias-corrected backtransformation is:

( ) ( ) ( ) 2 2 1 1 1 W i i s z m ypos - + ⋅ + = λ λ λ
where λ = 1/pow is the inverse of the estimated power.

The distribution of ypos i obtained thus far represents values expected for positive intakes. An individual will not have a positive intake on all days but only on a fraction of days. For each value of ypos i a probability p i is drawn from the estimated Beta(α ˆ, β ˆ) distribution to represent this fraction, and these values are multiplied to obtain an estimate of the usual intake for this individual:

i i i ypos p y ⋅ =
Extended with a covariable and/or cofactor the regression model for intake frequencies can be written as: where π is the expected intake frequency, K is the number of levels of the cofactor, x 1 is the covariable, f is a spline or polynomial function and df the degrees of freedom of the spline or the degree of the polynomial. In the program the optimal degrees of freedom can be calculated by a backward or forward search.

cofactor: logit(π) = β 0k , k=1…K covariable: logit(π) = β 0 + β 1 f(x 1 ;df), cofactor + covariable: logit(π) = β 0k + β 1 f(x 1 ;df), k=1…K cofactor + covariable + interaction: logit(π) = β 0k + β 1k f(x 1 ;df), k=1…K
Also the positive intake amounts can be modelled to be dependent on a cofactor and/or covariable. The model for the transformed intake amount is then:

cofactor: transf(y ij ) = β 0k +c i + u ij , k=1…K covariable: transf(y ij ) = β 0 + β 1 f(x 1 ;df) +c i + u ij , cofactor + covariable: transf(y ij ) = β 0k + β 1 f(x 1 ;df) +c i + u ij , k=1…K cofactor + covariable + interaction: transf(y ij ) = β 0k + β 1k f(x 1 ;df) +c i + u ij , k=1…K
where transf() represents the chosen transformation function, with the same notation as used before.

Iowa State University Foods (ISUF) model

General decsription

The ISUF model is based on a model for estimating the usual intake distribution from data sets with positive intakes only, as described by [START_REF] Nusser | A semiparametric transformation approach to estimating usual daily intake distributions[END_REF]. Similarly to the BBN model, frequencies and amounts are independently modelled and variation between and within persons is estimated by analysing the transformed positive intake amounts with a linear random effects model. The difference is that, in addition to a logarithmic or power transformation, ISUF applies a spline transformation using grafted polynomials to meet the normality assumption (see Detailed description of ISUF implementation in MCRA for details). By increasing the number of parameters of the grafted polynomial, the procedure ensures that the adjusted positive intake values have a normal distribution. The modelling of the positive intake amounts via grafted polynomials also allows for heterogeneity of variance (in contrast to BBN), e.g. the concept that some individuals are more variable than others with respect to their consumption habits. [START_REF] Nusser | Estimating usual dietary intake distributions: adjusting for measurement error and nonnormality in 24-hour food intake data[END_REF] and [START_REF] Dodd | A technical guide to C-SIDE[END_REF] describe the estimation of usual intake from data sets with a substantial amount of zero intake days. They separately model zero intake on part or all of the days via the estimation of intake frequencies.

The ISUF model is available in the C-SIDE program [START_REF] Dodd | A technical guide to C-SIDE[END_REF] and the main features have been implemented with some differences in MCRA (De Boer andVan der Voet 2005, 2007). The implementation of the ISUF model in MCRA is described in more detail in the next section. In Table 2, the main differences in implementation of the ISUF model in MCRA and C-SIDE are described. The number of parameters to be estimated is usually higher than the number of possible outcomes for an individual (e.g. 3 when there are two days per individual), and therefore a smooth approximation is made using a modified minimum chi-squared estimator. See [START_REF] Dodd | A technical guide to C-SIDE[END_REF] for details. Only the fraction of non-consumers ( 0 θ ) is estimated separately with no restriction to be similar to the other m θ . It can be noted that the distribution of individual intake probabilities can be better estimated when the number of days per individual in the consumption survey becomes higher. With only 2 days per individual the procedure gives a rather artificial distribution, often with an estimated 0 θ of zero. This step can be timeconsuming. Therefore, the number of iterations in the estimation procedure can be limited by the user. In our experience it is not necessary to use 50,000 iterations as in [START_REF] Dodd | A technical guide to C-SIDE[END_REF] and we use 5000 (other value can be chosen by the user).

Modelling the positive intake amounts

Step 1: power or log transformation See description of the BBN model.

Step 2: spline fit

To achieve a better normality, a second transformation (optional) is performed:

a spline function ) (z g t =
is fitted to the logarithmically or power transformed data t as a function of the normal Blom scores. The spline function is a grafted polynomial consisting of cubic polynomials between p = 3 joint points (knots) and linear functions in the two outer regions.

The intake amounts are transformed by interpolating from t to

) ( 1 t g x - =
, using the fitted spline function.

After a successful transformation the intake amounts x will resemble Blom normal scores and their mean and total variance will therefore be approximately 0 and 1. The normality of the transformed values x is checked with the Anderson-Darling test. In the case of a spline Step 3: estimation of the parameters of the usual intake distribution Variance components for between and within-person information are fitted to the transformed non-zero intake amounts x using the model:

2 2 2 0 2 2 2 ) var( ; ) ( ); , 0 ( ); , ( ~W i i i ij B i ij i ij s s E s N u N x u x x σ σ σ µ = = + =
In this model the total variance of the intake amounts is divided into a between-person Further, a test statistic MA4 is calculated to test whether the heterogeneity of variances is significant (see [START_REF] Dodd | A technical guide to C-SIDE[END_REF] for details).

The estimate 2 B s of the between-person variance is the basis for the estimation of the distribution of usual intake. The distribution of usual intakes on non-zero intake days in the x scale is represented by a set of 400 normal Blom scores (which themselves represent the standard normal distribution) multiplied by s B :

) (i B i z s x =
. The same calculation is applied to user-requested percentiles

) ( 1 p z p - Φ = .
Step 4: back transformation and estimation of usual intake

The 400+ values x i are back-transformed to the original scale. This is simple if no spline function has been estimated. If a spline function has been used, then it is a rather complicated procedure, because the spline function g was developed for intake amounts, not usual intakes.

The following steps are made:

1. First the 400+ values x i are expanded in a set of 9 x 400 values representing the distribution of intake amounts around each of the 400 points; These 9 x 400+ values are back transformed using the functions g and f , and the sets of 9 values are then recombined by weighted averaging into 400 usual intake values y i . The precise amount of expansion and weighting takes into account the within-person variance component and the estimated heterogeneity of variances [START_REF] Dodd | A technical guide to C-SIDE[END_REF]. 3. Finally the usual intakes on non-zero intake days are represented by the backtransform using this improved function:

F
)) ( ( 1

1 i i x g f y - = .
The user-requested percentiles p y are the additional values (i > 400) in the 400+ set. The 400 y i values define the cumulative distribution function by:

4 1 8 3 400 ) ( + - = i y F i .
The distribution is adapted in order to account for days with zero intake of individuals (defined here as individuals who have a positive probability of intake on any day, and therefore a non-zero usual intake).

Modelling usual daily intake

The estimated distribution of individual intake probabilities ( M θ θ

,..., ˆ0

) is used to transform the distribution of usual intake on non-zero intake days ( y F ) to the distribution of usual intake for consumers ( C F ) and finally to the distribution of usual intake for the entire population ( U F ). These transformations are based on the relation:

∑ = + = M m m y m U p u F u F 1 0 ) ( ) ( θ θ
which basically says that to obtain a certain level of usual intake u we should consider a different level (u/p m ) for the class of consumers which consume only on a fraction p m of days.

See [START_REF] Dodd | A technical guide to C-SIDE[END_REF] for details of the computational procedure. Linear interpolation based on the 400 values of the y F distribution is then used to compute representations of the cumulative distribution functions for consumers only and the entire population.

Model adequacy

Both the BBN and ISUF model distinguish variation between individuals from variation between days of the same individual, and they assume normality of the between-individual term in order to derive usual intake percentiles. Departures from normality may give biased estimation of the model parameters and, hence, may give wrong inference about the usual intake distribution. So a check of model adequacy is necessary. There are three types of residuals that may be considered for checking model adequacy:

1) the set of best linear unbiased predictors (BLUPs, also called random effects, see e.g. [START_REF] Robinson | That BLUP is a good thing: the estimation of random effects[END_REF]), representing the individual deviations from the average, 2) the set of residuals on the level of days (conditional residuals), and 3) the sum of 1 and 2, which is the set of deviations per individual and day from the overall average (marginal residuals). See Testing for normality in mixed models for a more detailed description of the three types of residuals. [START_REF] Gurka | Extending the Box-Cox transformation to the linear mixed model[END_REF] showed that near-normality of the marginal residuals implies near-normality of both the random effects and the conditional residuals. MCRA provides diagnostic checks based on marginal residuals.

Formal normality tests are available to provide information about the adequacy of the model and/or the validity of its associated assumptions. The Anderson-Darling (AD) goodness-of-fit statistic [START_REF] Stephens | EDF statistics for goodness of fit and some comparisons[END_REF]) is especially sensitive towards deviations in the tail regions, and has been used more for tail risk applications [START_REF] Nusser | A semiparametric transformation approach to estimating usual daily intake distributions[END_REF]). An alternative is to consider graphical displays of residuals like the normal quantile-quantile (q-q) plot.

In the BBN model the intake amounts are transformed before analysis either logarithmically or by a power transformation. The choice of power is guided by the AD test statistic to approach normality of the positive intake amounts as well as possible. Nevertheless, the transformed data may still show considerable non-normality, and (visually) checking normality should be a standard diagnostic procedure.

The ISUF model has a more flexible data transformation than BBN, which increases in complexity in order to actually guarantee normality of the transformed values (on the guidance of AD tests). It is therefore questionable whether there is much purpose in checking normality after the full ISUF data transformation.

For intake amount distributions that show multimodal patterns, transformation to normality using the log or power transformation can be expected to fail. The multimodal pattern is a consequence of aggregation over multiple foods in circumstances where foods are not consumed on all days and/or foods have highly different average contamination levels.

The resulting intake amount distribution forms a mixture with various peaks related to the diverse foods. Multimodality may also be caused by different subpopulations with distinct consumption patterns.

Testing for normality in mixed models

The linear mixed model is: For the linear mixed model, three types of residuals are defined.

ij i i c ij y ε β α µ + + + =
Marginal residuals are:

ij i i c ij ij y ε β α µ ξ + = - - = ) ( , conditional residuals are: i i c ij ij y β α µ ε - - - = ) (
, and BLUPs or random effects: i β . [START_REF] Gurka | Extending the Box-Cox transformation to the linear mixed model[END_REF] show that, if the marginal error term after transformation results in near normality, then the random effects and conditional error term will have approximate Gaussian distributions. If normality is considered an acceptable assumption, then the usual intake distribution for category c is also a normal distribution with mean c α µ + and variance 2 B σ , which can be easily sampled (as done in the BBN method).

Case studies

We compare the methods by applying them to real data sets. Full validation of the results is not possible with real data because true usual intake distributions are unknown. Therefore the results of both models can only be compared to each other.

• Case 1 (acrylamide) represents intake data with few zeros. Covariates are not considered.

• Case 2 (glycoalkaloids) relates to intake amounts that are a function of a set of covariates, here age and sex.

• Case 3 (patulin) represents data with a bimodal intake distribution.

In all three studies, the uncertainty due to limited concentration and consumption data was quantified by a bootstrap uncertainty analysis using 500 re-sampled sets of the consumption and concentration data. Empirical 95% uncertainty intervals were used to describe the uncertainty in selected percentiles of the usual intake distribution. The purpose of this study is to compare models, not a detailed analysis of cases. Nondetects were in all studies assumed to be zero concentrations, although in a real risk assesment this could lead to an underestimation of the usual exposure.

Case 1: Acrylamide, approximate normality after power transformation

Acrylamide has been detected in foods since 2002 and is potentially genotoxic and carcinogenic in humans. It can be formed by heating of starchy foods, like French fries, biscuits and crisps. Consumption data of 1279 Dutch children aged two through six years, recorded on two non-consecutive days, were used [START_REF] Ocké | Dutch National Food Consumption Survey-Young Children 2005/2006[END_REF]). These food consumption data were combined with acrylamide levels as reported in Boon et al. (2009 in press) and obtained from the Dutch Food and Consumer Product Safety Authority (VWA).

We modelled the usual intake distribution of acrylamide using both the BBN and ISUF model, transforming intake amounts of acrylamide with a power transformation.

In the food consumption survey, 176 foods possibly containing acrylamide (these were the foods for which positive acrylamide concentrations have been measured) were recorded.

They were linked to 25 food groups. A total of 189 samples from each food group (e.g. cookies, crisps, chips and Dutch spice cake) were available with measured acrylamide concentrations, 13 of which were non-detects (samples with a level below the limit of reporting). For more details on the linkage between single foods and food groups, see Boon et al. (2009 in press) On 95% of the consumption days, at least one of the 176 foods was consumed. In more detail, 1172 (92%) out of 1279 children consumed at least one of the foods on both study days, 94 (7%) children on only one study day, and 13 (1%) children on none of the study days.

Food consumption per day was multiplied with the mean acrylamide level of that food, and summed over all foods to obtain a distribution of intake amounts (ng/kg bw/day). Data transformation (power 0.262) was necessary to obtain a reasonable normal distribution for the positive intake amounts (Figure 1a,1b). Based on the q-q plot (Figure 2a) the transformed data could be considered as reasonably normal, although normality was rejected in a formal test (AD = 1.76, p < 0.005). Normality was improved after the additional spline transformation of ISUF, see Figure 2b: AD = 0.57, p > 0.15).

Based on visual inspection of the q-q plots, we expect the relatively simple BBN model to give an adequate exposure assessment. It may be noted that a small deviation is seen in the lower part of the distribution, but in risk assessment the interest is in the upper part. The normality assumption of the underlying distributions seems reasonable and the more complex ISUF model may not be needed.

In Figure 3, the distributions for the intake frequencies (a) and positive intake amounts day was estimated as 0.953, with an overdispersion factor 0.178. These values imply a distribution of intake frequencies among individuals as shown in Figure 3a. Thus, most people consume foods containing acrylamide on a daily basis, but there are also some individuals who do so less frequently. The average transformed intake amount was estimated at 5.06 (s.e. 0.03), and the between and within individual variances at this scale were estimated at 0.27 and 1.95, indicating much more variation in acrylamide intake within individuals than between individuals.

Table 3 shows estimated percentiles of the usual intake of acrylamide for BBN after a power transformation, and ISUF after a power transformation with and without an additional spline transformation. As was expected, the three models give similar results, with for example p99 of usual intakes between 1317 and 1344 ng/kg bw/day. The percentiles relate to the usual intake distribution, and are much lower than those in Figure 1 due to the large variation within individuals

Case 2: Glycoalkaloids, covariate dependency of intake

In this example concerning glycoalkaloids, we demonstrate the ability to model usual intake of substances as a function of covariates, such as age and sex. We used the day food consumption patterns of 6187 persons aged 1 through 80 years and recorded on two consecutive days (DNFCS-3, [START_REF] Kistemaker | De consumptie van afzonderlijke producten door Nederlandse bevolkingsgroepen -Voedselconsumptiepeiling 1997-1998[END_REF], and combined it with glycoalkaloid concentrations in potatoes as obtained from [START_REF] Ruprich | Probabilistic modelling of exposure doses and implications for health risk characterization: glycoalkaloids from potatoes[END_REF].

Glycoalkaloids occur mainly in potato. Not only potatoes eaten as such were included but also potato as an ingredient of more complex dishes. This was done by the use of the Dutch food conversion model which converts foods as coded in the different Dutch food consumption surveys in their raw agricultural commodities, including weight fractions [START_REF] Van Dooren | Conversie van consumeerbare voedingsmiddelen naar primaire agrarische produkten (Conversion of consumed foods into raw agricultural commodities)[END_REF].

The glycoalkaloid intake from 62 foods was considered. In total, 372 positive glycoalkaloid concentrations and 67 non-detects were available, here quantified by the sum of solanin and chaconin concentrations. Concentrations were corrected for processing effects of cooking or frying [START_REF] Ruprich | Probabilistic modelling of exposure doses and implications for health risk characterization: glycoalkaloids from potatoes[END_REF]). Potato was consumed on 80% of the consumption days. Among the 6187 individuals, 4061 (66%) consumed potato on both study days, 1785 (29%) on only one of the days while 341 (6%) individuals did not record the consumption of potato during both study days.

The primary model used for these data was BBN, including an analysis of the effect of covariates age and sex on the usual intake. The intake frequency of glycoalkaloids was not found to depend on sex, while age dependency could be modelled with a spline function with 4 df. Intake frequencies were highly variable between persons, ranging from less than 50% to over 95% (see Figure 4a). A power of 0.339 was found to be optimal for approximating normality of the positive intake amounts. Intake amounts were dependent on both age and sex (see Figure 4b). For males, a slightly higher intake per kg body weight was found than for females. The age effect could be modelled with a spline with 4 df. The difference between males and females was not significant over the age range (no interaction term was necessary in the model). The between and within individual variances on the power-transformed scale were estimated at 0.30 and 1.92, indicating much more variation in glycoalkaloid intake within persons than between persons. A histogram of the marginal residual distribution after correcting for the covariates age and sex is shown in Figure 5a. In spite of the power transformation there was still a strong and significant deviation from normality (AD = 38.19, p<0.005), which casts doubt on the applicability of the BBN model to model the usual intake of glycoalkaloids. Some example results for the p99 of usual intake are shown in Table 4.

In order to make a comparison with ISUF, we ran both BBN and ISUF without those covariates (since ISUF has no facility for covariates). The AD test applied to the intake amounts after a power transformation followed by a spline transformation detected only negligible deviation from normality, AD = 0.54, p>0.2 (see Figure 6). Results for p99 are shown in Table 4. When no covariates are included, the results from both models are similar, and the additional spline transformation does not make a difference.

A run with ISUF applied on subsets of the data, in particular, males and females, aged 1 through 5 and 30 through 40, confirmed the age effect earlier found with BBN. However, for sex, opposite age-effects are estimated. Whereas BBN estimates higher percentiles for males, ISUF estimates higher percentiles for females. A closer look at the results for each subpopulation shows that the variation between males is smaller than between females. As a result, the usual intake distribution for males is narrow compared to the distribution for females. Further, the uncertainty intervals are wider for ISUF than for BBN (see Table 4)

Case 3: Patulin, bimodal distributions of intake

This example demonstrates a case where normality cannot be achieved using a simple log or power transformation. A relevant question is whether the more complex spline transformation of the ISUF model would be appropriate.

Patulin is a mycotoxin which is mainly found on apple products. Consumption data of 1279 Dutch children aged two through six years, recorded on two non-consecutive days, were used [START_REF] Ocké | Dutch National Food Consumption Survey-Young Children 2005/2006[END_REF]. The concentration data for patulin was derived from monitoring programmes performed in the Netherlands in 2002-2006 by VWA. Levels are reported in Boon et al. (2009. in press). Patulin was detected in two foods (apple juice and apple sauce canned) which were linked to 83 foods as recorded in the food consumption survey of young children. In total, 45 samples were available, 13 concentration measurements were detect, the number of non-detects was 32. The 83 apple products in the food consumption survey were consumed on 90% of the days. In more detail, among the 1279 children in this study, 1076 (84%) consumed at least one of these apple products on both study days, 160 (12%) on only one study day, and 43 (3%) on none of the study days.

The power transformation was close to zero and was replaced by a logarithmic transformation. The logarithmic transformation was not sufficient to approach normality (see Figure 7b, where the distribution of the log transformed intake amounts is shown). In this mixture distribution, two or three constituent intake distributions are visible. To convert the multimodal intake amount distribution into an approximately unimodal distribution, a spline function with 11 knots was needed (Figure 7c). After fitting the spline to the logarithmic transformed intake data (Figure 7d), normality was not rejected according to the AD statistic (AD = 0.49, p > 0.25).

Fitting the BBN model and comparing the results with likelihood ratio tests revealed a dependency of intake amount on age (see Figure 8a,b). However, modelling age did not explain the bimodal nature of the distribution. In Figure 9, a histogram (a) of the marginal residual distribution is shown together with the corresponding q-q plot (b). It is apparent that normality assumptions were violated (AD = 4.07, p<0.005).

This example demonstrates how nonnormality can arise as a result of aggregating foods.

Figure 10 shows a number of intake amount distributions of patulin after a logarithmic transformation. Figure 10(a-l), show the distributions for foods as recorded in the food consumption survey for cases where 100 or more positive intake data are available.

In Table 5, it is shown for a selected percentile (p99) that the ISUF and BBN results were different in this case. The BBN usual intake values, both age specific and without any covariate, were all higher than the overall ISUF estimate.

Discussion

Two models for estimating the long-term exposure distribution of dietary intake of substances on foods have been compared. The betabinomial-normal model (BBN) estimates the usual intake distribution whether or not as a function of covariates. The Iowa State University Foods model (ISUF) estimates the usual intake distribution, but cannot address covariates in the statistical model (although in the C-SIDE implementation of ISUF a priori data adjustments can be made for non-person-specific biases such as season or day of the week).

To meet the normality assumptions, data are transformed first by a log or power function, and, in case of ISUF, this can be followed by an additional spline transformation to achieve normality. Both methods separately estimate the individual intake amount distribution and the distribution of individual intake frequencies before calculating the unconditional usual intake distribution. For dietary exposure data, even after a log or power transformation, non-normality occurs frequently in our experience, and it is worthwhile to have a closer look at this phenomenon. Intake amounts are calculated by multiplying food consumption data with average concentration levels of substances present in various foods. Each intake amount may be the sum of contributions due to the consumption of various foods and, generally, the resulting distribution is a mixture of distributions related to individual foods. When these foods differ in consumptions rates and/or concentrations, multimodal distributions will arise.

But even if the intake of a substance appears to originate from only one food the intake distribution may be a mixture: the food may be consumed as an ingredient of a more complex dish or may be processed in a number of ways with each processing type having different processing factors. Even when single food distributions are unimodal, the aggregate distribution may be multimodal, and this effect is most pronounced when not all foods are consumed on all days.

One can easily imagine some people eating cooked potatoes on a fraction of the days, others fried, some as an ingredient like potato flour or people that do not consume potatoes at all. Also, people vary their choice of potato product between days. It is obvious that transforming data in order to have normal distributed intake values is a huge simplification of the rather complex intake patterns lying behind it. The patulin case illustrates this. Figure 10 shows that, after a logarithmic transformation, constituent distributions are all unimodal, but the total intake distribution of patulin is definitively multimodal (Figure 7b).

Given that non-normality is common for aggregated intake, what is the role of formal normality tests and more informal graphical procedures? With only slight deviations from normality and with large sample sizes (as we often have) formal normality tests easily give significant results. Testing normality, e.g. using the Anderson-Darling (AD) test, is in many dietary risk applications like asking a question one already knows the answer to. Therefore, our proposal is to have a closer look at the non-normal behaviour of the data. We advocate the use of graphical methods like the q-q plot and histograms of the estimated marginal error distribution to study the applicability of the normal model and not to rely on test results.

The acrylamide case illustrates our proposal. According to the AD statistic, a power transformation is insufficient to approximate normality, but an additional spline transformation shows no lack of fit. However, the q-q plots for BBN and ISUF are visually very similar (Figure 2). Non-normal behaviour is mainly found in the left tail of the distribution, whereas for substances with negative health effects as acrylamide the individuals at risk are at the right-tail of the distribution. The resulting percentiles are all in the same range and confirm our idea that it is acceptable to use BBN to estimate the usual intake distribution. The patulin case demonstrates an intake amount distribution where non-normality manifests itself as a multimodal distribution. The results in Table 5 show that the estimates of the p99 percentiles for BBN (without any covariates) and ISUF are highly different and lie far outside each other's uncertainty intervals. The BBN estimate is much higher because a unimodal normal distribution is fitted where a multimodal would have been appropriate leading to an overestimation of the upper tail. We conclude that BBN here is likely to be unreliable, and it should not be used. In ISUF, intrinsic to the method, normality is always achieved.

The glycoalkaloid case is an intermediate one. Based on the q-q plot, the applicability of BBN remains questionable. However, the estimates of the p99 percentiles for BBN (without covariates) and ISUF match remarkably well (see Table 4) and it is not clear that BBN is inappropriate for intake assessment.

We conclude that the choice of the appropriate model for modelling usual intake based on incidental consumption patterns should be made on a case-by-case basis. When a logarithmic or power transformation results in approximately normal data, the BBN model is preferred over the more complex ISUF model. Moreover, ISUF is not applicable when the intake distributions depend on covariates, whereas BBN is. BBN is fairly robust against departures of normality as shown in the acrylamide and glycoalkaloid cases, where estimated percentiles of BBN are in the same range as results obtained with ISUF. Even when the normality assumption is questionable both methods may provide similar results, as in the glycoalkaloids case. The patulin case presents an example of bimodal or perhaps multimodal distributed intakes. In Figure 7b, three constituent intake distributions appear to be visible, probably relating to different consumed foods (see Figure 10). Since the additional spline transformation made the distribution closer to normal (Figure 7d), the ISUF model seems to be a better choice in this case. However, theoretical considerations and preliminary results using a simulation model indicate that also the ISUF model may not give reliable results for distributions of intakes that result from consumption of various foods. Based on these results we conclude that more research is necessary to develop a method to perform intake calculations based on multimodal intake distributions.

While the spline transformation in ISUF will always give a normal distribution for the transformed intake amounts, this transformation itself may destroy the assumptions necessary for the variance components model used for estimating the variance of usual intake. In our three examples, the ISUF spline transformation needed 6, 11 and 11 knots in the spline, respectively, to achieve normality. Clearly, higher numbers increase the nonlinearity of the transformation and, eventually, may violate mixed model assumptions as uncorrelated errors and additivity on the transformed scale. In both models transformations may be chosen based on parameters that have to be estimated from the data. These are the power transformation in BBN and ISUF and the ISUF spline transformation. [START_REF] Gurka | Extending the Box-Cox transformation to the linear mixed model[END_REF] concluded that in the context of linear mixed models variance components may be estimated with bias when an estimated transformation of data is being used. In their case they considered the power transformation but the same reasoning seems valid for a spline transformation.

If intakes are dependent on covariates (e.g. age, or sex) then the ISUF model as implemented in MCRA 6 can only be applied on subsets of the data, which implies a stronger dilution of the information in the data as compared to the covariate analysis as employed in BBN. This is illustrated by the increased size of the uncertainty intervals of ISUF compared to BBN. [START_REF] Dodd | A technical guide to C-SIDE[END_REF]. Figure 2. The q-q plot of the acrylamide intake amounts after power transformation (a) as performed in BBN (AD = 1.76, p<0.005) and after power and spline transformation (b) as performed in ISUF (AD = 0.57, p>0.15). Figure 5. Histogram together with best fitting normal distribution (a) and q-q plot (b) for the marginal residuals for the glycoalkaloid intake after fitting the BBN model as a function of age and sex. A significant deviation from normality is observed according to the AD statistic (AD = 38.19, p<0.005).

Figure 6. Histogram together with best fitting normal distribution (a) and q-q plot (b) for the intake amounts of glycoalkaloids after power and spline transformation using the ISUF model. Normality is not rejected according to the AD statistic (AD = 0.54, p>0.2).

  a large number of times from both the betabinomial (intake frequency)

  stable and interpretable parameterization. It can be shown that the mean and variance of npos are equal to: nπ and n

9

  Detailed description of ISUF implementation in MCRA Modelling the intake frequency distributionThe individual intake frequency distribution is approximated via a number of classes (default 21, other values can be selected by the user) arranged by the proportion of days on which there is a positive intake (p m ). Using a binomial distribution for each class, the fraction of individuals in each class ( by optimising the fit of the predicted proportions of individuals with 0, 1, 2, ... intake days to the observed proportions.

  normality is rejected at the 85% confidence level, then the number of knots p is increased and the spline fit is repeated (until a maximum of 22 knots).

  component and a within-person component. The within-person variance component can be heterogeneous, that is, it can be different for different individuals. In the model the betweenperson variance 2 B σ and the mean and the variance of the within-person variance component distribution ( 2 0 σ and 2 W σ ) are estimated using standard statistical methods (ANOVA).

B

  power transformed positive intake amount data ij y of individual i (i=1, ..., n) on day j (j=1, ..., n i ), where ) (i c α represents the fixed effects for category c to which individual i belongs (e.g. age, sex), and where i β and ij ε are uncorrelated normally distributed random terms for between-person and within-person variation, with variance 2

  (b) as estimated with BBN are shown. The average frequency for acrylamide intake on any

Figure 1 .

 1 Figure 1. Distribution of intake amounts of acrylamide before (a) and after (b) 0.262 th power transformation. The best fitting normal distribution is shown for comparison.

Figure 3 .

 3 Figure 3. Estimated beta density for acrylamide intake probabilities (a) and backtransformed cumulative normal density function for positive usual intake amounts (b) obtained with BBN.

Figure 4 .

 4 Figure 4. Means of observed and modelled glycoalkaloid intake frequencies (a) and intake amounts (b). All curves are splines with 4 df. The outer curves in the intake frequency plot show large individual variation by 2.5% and 97.5% percentiles of the fitted betabinomial distribution. The intake amount plot shows separate curves for males (upper) and females (lower). Vertical bars in the intake amount plot are between-(left) and within-individual (right) standard deviations.

Figure 7 .

 7 Figure 7. Intake amounts of patulin: natural scale (a), after logarithmic transformation (b; ISUF), and after an additional spline transformation (d; ISUF). Graph c shows the spline fit of the logarithmic-transformed intake amounts as function of the theoretical residuals. The best fitting normal distribution is shown for comparison.

Figure 8 .

 8 Figure 8. Modelling of daily intake frequency (a) and intake amount (b) of patulin as a function of age. The outer curves in the intake frequency plot show large individual variation by 2.5% and 97.5% percentiles of fitted betabinomial distribution. Vertical bars in the intake amount plot are between-person (left) and within-person (right) standard deviations.

Figure 9 .

 9 Figure9. Histogram together with best fitting normal distribution (a) and q-q plot (b) for the marginal residuals for patulin after fitting the BBN model with age effect. Deviation from normality is significant according to the AD statistic (AD = 4.07, p<0.005).

Figure 10 .

 10 Figure 10. Intake amounts of patulin after a logarithmic transformation for foods as recorded in the food consumption survey (a) apple juice unsweetened; (b) apple sauce canned; (c) lemonade squash; (d) fruit drink concentrate; (e) syrup fruit all tastes; (f) lemonade three fruit drink; (g) lemonade fruit drink 15-20 mg vitamin C; (h) fruit drink Wicky; (i) syrup average dilution; (j) yogurt flavoured fruit drink Yoki; (k) ice based on fruit; (l) apple syrup. The best fitting normal distribution is shown for comparison. Despite the fact that all AD statistics are significant, the visual impression is that all distributions are approximate lognormal.

Table 1 .

 1 Differences between the BBN model as implemented in MCRA (see Detailed description of BBN implementation in MCRA) and as discussed in[START_REF] Slob | Probabilistic dietary exposure assessment taking into account variability in both amount and frequency of consumption[END_REF]

Table 2 .

 2 Differences between implementations of the ISUF model in MCRA (see Detailed description of ISUF implementation in MCRA) and C-SIDE

Table 3 .

 3 Estimated percentiles of usual intake (ng/kg bw/d) of acrylamide (with 95% uncertainty intervals).

Table 4 .

 4 Estimated percentile (p99) of usual intake (ng/kg bw/d) of glycoalkaloids according to four models (with 95% uncertainty intervals). For ISUF (age/sex), subpopulations of females and males aged 1 through 5 and 30 through 40 are analysed. The number of consumers (n) is 6187 unless otherwise indicated.

Table 5 .

 5 Estimated percentile (p99) of usual intake (ng/kg bw/d) of patulin (with 95% uncertainty intervals).

•

  Number of words total file: 9213 • Text without tables and figures: 8304 • The paper is not intended for a special issue.

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Table 1 .

 1 Differences between the BBN model as implemented in MCRA (see Detailed description of BBN implementation in MCRA) and as discussed in[START_REF] Slob | Probabilistic dietary exposure assessment taking into account variability in both amount and frequency of consumption[END_REF]

		MCRA	Slob (2006)
	parameterization of beta	expected frequency π ,	classical parameters
	distribution	overdispersion factor ϕ	( β α , )
	data transformation	logarithmic or power	logarithmic
	covariable (e.g. age) model	polynomial or cubic	Various models e.g.chosen
		smoothing spline (Hastie &	from a familiy of non-
		Tibshirani 1990)	monotone regression
			functions (Slob 2002).
	cofactor (e.g. sex) model	π as a function of cofactor;	selected regression
		interaction with covariable is	parameters and/or variance in
		optional	covariable model may be
			estimated separately for
			levels of cofactor
	bootstrap uncertainty limits	yes	no

Table 2 .

 2 Differences between implementations of the ISUF model in MCRA (see Detailed description of ISUF implementation in MCRA) and C-SIDE[START_REF] Dodd | A technical guide to C-SIDE[END_REF].

		MCRA	C-SIDE
	use of sampling weights	no	yes
	adjustment for nuisance	no	yes
	and/or period effects
	number of classes in	21 (default, can be changed)	51
	frequency model
	estimation of intake	5,000 iterations (default, can	50,000 iterations
	probability distribution	be changed)
	parameters
	modelling correlated within-	no	yes
	individual amounts
	percentiles calculated for	grid of 400 points + user-	grid of 400 points
		defined values
	bootstrap uncertainty limits	yes	no

Table 3 .

 3 Estimated percentiles of usual intake (ng/kg bw/d) of acrylamide (with 95% uncertainty intervals).

	BBN		ISUF without spline	ISUF with spline
	p50 642	(566, 724)	641	(568, 724)	621	(545, 690)
	p95 1093	(902, 1270)	1108	(960, 1267)	1079	(937, 1238)
	p99 1342	(1053, 1585)	1344	(1127, 1583)	1317	(1116, 1547)
	p99.9 1655	(1350, 2040)	1597	(1290, 1931)	1580	(1270, 1878)

Table 5 .

 5 Estimated percentile (p99) of usual intake (ng/kg bw/d) of patulin (with 95% uncertainty intervals).

	Page 31 of 41
	Model
		age 2	age 6
	BBN (age)	81 (17, 193)	47 (12, 100)
		total population
	BBN	70 (13, 143)
	ISUF	31 (10, 65 )

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Acknowledgement

The authors would like to thank Paul Goedhart for developing the betabinomial normal module and Jac Thissen for his support in writing the MCRA software. We also thank Wout Slob for his advice and many helpful comments on the paper. This research was sponsored by the Food and Consumer Product Safety Authority of the Netherlands (VWA) and the Ministry of Agriculture, Nature and Food Quality in the Netherlands.