Elena Demuru

Silvia Rossi

Leonardo Ventura

Luigino Dal Maso

Stefano Guzzinati

Alexander Katalinic

Sebastien Lamy

Valerie Jooste

Corrado Di Benedetto

Roberta De Angelis
email: roberta.deangelis@iss.it

Liesbet Van Eycken

Jean-Michel Billette

Angela Mariotto

Estimating complete cancer prevalence in Europe: validity of alternative vs standard completeness indexes

Keywords: cancer prevalence, cancer registries, cancer survivors, cancer survivorship, EUROCARE, Europe, SEER program Frontiers in Oncology frontiersin.org 01

Introduction: Comparable indicators on complete cancer prevalence are increasingly needed in Europe to support survivorship care planning. Direct measures can be biased by limited registration time and estimates are needed to recover long term survivors. The completeness index method, based on incidence and survival modelling, is the standard most validated approach.

Methods: Within this framework, we consider two alternative approaches that do not require any direct modelling activity: i) empirical indices derived from long established European registries; ii) pre-calculated indices derived from US-SEER cancer registries. Relying on the EUROCARE-6 study dataset we compare standard vs alternative complete prevalence estimates using data from 62 registries in 27 countries by sex, cancer type and registration time.

Results: For tumours mostly diagnosed in the elderly the empirical estimates differ little from standard estimates (on average less than 5% after 10-15 years of registration), especially for low prognosis cancers. For early-onset cancers (bone, brain, cervix uteri, testis, Hodgkin disease, soft tissues) the empirical method may produce substantial underestimations of complete prevalence (up to 20%) even when based on 35-year observations. SEER estimates are comparable to the standard ones for most cancers, including many early-onset tumours, even when derived from short time series (10-15 years). Longer observations are however needed when cancer-specific incidence and prognosis differ remarkably between US and European populations (endometrium, thyroid or stomach).

Discussion: These results may facilitate the dissemination of complete prevalence estimates across Europe and help bridge the current information gaps.

Introduction

Cancer prevalence statistics enumerate the number, or the proportion, of people in a population living after a cancer diagnosis at a specific date. Unlike other surveillance metrics based on cancer registries' observations, such as incidence or survival, direct measures of prevalence are intrinsically incomplete, as they cannot include the cancer survivors diagnosed before the start of registration. Complete prevalence must be necessarily estimated to recover long term survivors, especially when the period of registration is limited.

The completeness index method is one of the most accurate and used methods to estimate complete prevalence starting from limited-duration prevalence measured by cancer registries [START_REF] Capocaccia | Estimating the completeness of prevalence based on cancer registry data[END_REF]. Based on incidence and relative survival modelling and on their relationship with prevalence, this method provides a correction factor, the so-called completeness index, or R-index, to complete cancer-specific registries observations. The completeness index method has been systematically validated and applied since many years in the USA [START_REF] Merrill | Cancer prevalence estimates based on tumour registry data in the surveillance, epidemiology, and end results (SEER) program[END_REF], where complete prevalence statistics are published annually as an integral part of the SEER Cancer Statistics [START_REF] Howlader | SEER cancer statistics review, 1975-2017[END_REF]. A software to implement the method is distributed by the National Cancer Institute, along with completeness indexes derived from the SEER registries datasets [START_REF]national cancer institute COMPREV software[END_REF].

Conversely, in Europe complete prevalence estimates are not systematically available in all countries with active population-based cancer registries. European cancer prevalence estimates by country are made available by GLOBOCAN (5), however they are limited to 5years since diagnosis [START_REF] Bray | Global estimates of cancer prevalence for 27 sites in the adult population in 2008[END_REF]. Occasionally, on a project basis, the completeness index method has been applied to European CRs data to derive complete prevalence of rare cancers [START_REF] Mallone | Methodological aspects of estimating rare cancer prevalence in Europe: the experience of the RARECARE project[END_REF][START_REF] Gatta | Rare cancers are not so rare: the rare cancer burden in Europe[END_REF][START_REF]Rarecare-net project[END_REF] or frequent cancers by European country and area [START_REF] Micheli | Cancer prevalence European registry areas[END_REF][START_REF] Capocaccia | Mugno e on behalf of the EUROPREVAL working group. Measuring cancer prevalence in Europe: the EUROPREVAL project[END_REF]. Complete prevalence is periodically estimated through the completeness index approach only in Italy [START_REF] Guzzinati | Characteristics of people living in Italy after a cancer diagnosis in 2010 and projections to 2020[END_REF][START_REF]Italian Cancer figures, report 2014: Prevalence and cure of cancer in Italy[END_REF], where the method was first proposed. Experiences in other countries refer to limited-duration prevalence [START_REF] Haberland | German Cancer statistics[END_REF] or to different methods [START_REF] Colonna | Time trends and short term projections of cancer prevalence in France[END_REF][START_REF] Colonna | Grosclaude PFrench Network of Cancer Registries (FRANCIM). Total and partial cancer prevalence in the adult French population in 2008[END_REF][START_REF] Maddams | Projections of cancer prevalence in the united kingdom, 2010-2040[END_REF][START_REF] Rossi | Estimates of cancer burden in Italy[END_REF][START_REF] Herrmann | Cancer survivors in Switzerland: a rapidly growing population to care for[END_REF]. Only some European registries operating since the 50s, such as those in Nordic countries or Slovenia, are able to measure a virtually complete prevalence without any estimation [START_REF]NORDCAN online data tool, version 9.2[END_REF][START_REF]Slovenian cancer registry annual reports[END_REF].

Integrating traditional surveillance metrics with accurate complete prevalence estimates is of increasing importance, given the remarkable growth of cancer survivors in all ageing societies. They represent a heterogeneous population, in terms of healthcare needs and quality of life, that should be better quantified and qualified [START_REF] De Moor | Cancer survivors in the united states: prevalence across the survivorship trajectory and implications for care[END_REF][START_REF] Hao | The economic burden of prostate cancer -a Swedish prevalence-based register study[END_REF][START_REF] Sharp | The magnitude and characteristics of the population of cancer survivors: Using population-based estimates of cancer prevalence to inform service planning for survivorship care[END_REF][START_REF] Bluethmann | Anticipating the "Silver tsunami": Prevalence trajectories and comorbidity burden among older cancer survivors in the united states[END_REF][START_REF] Dal Maso | Cancer cure and consequences on survivorship care: Position paper from the Italian alliance against cancer (ACC) survivorship care working group[END_REF][START_REF] Colonna | Health status of prevalent cancer cases as measured by mortality dynamics (cancer vs. noncancer): Application to five major cancers sites[END_REF]. Given this background, closing the existing gaps in Europe is one of the priorities in cancer surveillance.

Promoting the use and dissemination of complete cancer prevalence indicators by country in Europe was one of the goals of the European Joint Action on Cancer iPAAC (Innovative Partnership for Action Against Cancer) [START_REF]iPAAC joint action, work package 7 on cancer information and registries[END_REF]. Exploring the feasibility of viable solutions to facilitate the use of completeness indexes was part of the project's activities.

With this purpose, in the present study we compared the standard method of deriving prevalence completeness index in Europe (by modelling incidence and survival data from European populations) with alternative approaches that do not require any statistical modelling, namely: i) empirical indexes derived from the longest prevalence data available from European registries; ii) publicly available model-based indexes estimated from SEER-US data [START_REF]national cancer institute COMPREV software[END_REF]. The study aims to assess under which conditions of application (registration time length and cancer type) these "nonstandard" approaches may adequately surrogate the reference method, which remains the "gold standard".

Nowadays, indeed, cancer prevalence observations are available for time series and populations to a much greater extent than when R-indexes were first proposed [START_REF] Capocaccia | Estimating the completeness of prevalence based on cancer registry data[END_REF]. Assessing application conditions of empirical R-indexes may facilitate the use and dissemination of complete prevalence estimates across Europe and contribute to bridge the present information gaps. For the same reasons it is worth exploring the application limits to European data of SEER-US indexes that are publicly available and ready to be used.

Materials and methods

The study relies on the dataset of the EUROCARE-6 project, a wide collaborative study on cancer survival and prevalence in Europe [START_REF]European Network of cancer registries (ENCR) call for data protocol 201[END_REF] based on cancer registries data. The dataset includes pseudonymised individual data on cancer patients' incidence and life status, as well as life tables and resident population in each registry.

For the purpose of the study we selected 62 general cancer registries from 27 European countries (21 with national population coverage) providing prevalence data up to 1/1/2013, the most recent common prevalence index date available in the dataset. At this date the maximum duration of registration ranged from 5 to 35 years, with median at 20 years.

The following four different types of analyses were conducted each using a specific dataset depending on the scope. Cancer registries included 5% to 50% coverage of the 27 countries' population (Table 1 To compare complete prevalence values estimated from the different completeness indexes we performed distinct analyses for a selection of 30 common index cancers. Cancer entities were defined according to the Third Revision of the International Classification of Diseases for Oncology (ICDO-3). Only malignant primary cancers were included, except for brain and urinary bladder (Supplementary Materials, Table A1). Non-malignant tumours proportion by registry ranges from 0 to 28% for brain cancer and from 0 to 54% for urinary bladder, thus reflecting varying registration criteria across Europe. The first primary tumour for each cancer entity was considered, meaning that each person was counted only once and that people with multiple primary cancers affecting different sites contribute to prevalence counts of different entities. Consequently, cancer-specific counts do not sum up to counts of all cancers combined.

Observed limited-duration prevalence

Limited-duration prevalence observed in each registry population was computed at the index date with the counting method, available in the SEER*Stat software [START_REF][END_REF] by enumerating the number of patients known to be alive at the index date. Life-table survival probabilities stratified by registry, sex, grouped age at diagnosis (0-59, 60-74, 75+), cancer site and 5-year period of diagnosis, were attributed to patients lost to follow-up to count those estimated alive at the prevalence index date. Age at the prevalence date was detailed in 5-year groups and 85+. The proportion of lost to follow-up is generally very low, below 2% in most countries.

Completeness index estimation (R-index)

R-index at duration d (R d ) is defined as the ratio of prevalence at duration d to estimated complete prevalence. It expresses an estimation of percent completeness of a given limited-duration prevalence. Complete prevalence is therefore estimated dividing the number of observed prevalent cases at a given duration d (N d ) by the corresponding R-index at the same duration [START_REF] Capocaccia | Estimating the completeness of prevalence based on cancer registry data[END_REF].

For each cancer we derived R-index by sex, age at prevalence date (i) in 5-year age groups and annual registration duration (d). Model-based and empirical approaches were both considered. i) European empirical R-index (EU emp) Empirical R-indexes were obtained from the pool of registries in dataset a) (Table 1) as the ratio of the observed prevalent cases at duration d to the observed prevalent cases at the maximum duration (35 years), namely R i,d = N i,d =N i,35 . Age at prevalence date was grouped in 5-year classes except for extreme ages (0-29 and 80+) for which wider groupings were used to avoid random fluctuations due to the scarce number of cases. Using these empirical indexes is to assume that observed 35-year limited duration prevalence equals (i.e. is sufficiently close to) complete prevalence.

ii) Standard European model-based R-index (EU mod)

For the pool of registries in dataset b) (Table 1) we computed incidence rates and relative survival (RS) with the SEER*Stat software [START_REF][END_REF]. RS, the ratio of observed survival in a group of cancer patients to the expected survival in a comparable group from the general population, was determined using the Ederer 2 cohort method. Incidence and survival data were stratified by cancer type, sex, 5-year period of diagnosis (1980-1984, 1985-1989, 1990-1994, 1995-1999, 2000-2004, 2005-2009, 2010-2014) and age at diagnosis (5-year and 85+ for incidence; cancer-specific strata for relative survival are given in Table A1 Supplementary Materials). We modelled pooled incidence and relative survival data following the standard methodology (2). We fitted a mixture "cure-model" of Weibull type to RS data. These models assume that only a fraction of patients will die of the disease, with time to death following a Weibull We fitted two alternative logistic age-cohort models to incidence rates stratified by age and period of diagnosis. Non-parametric cohort-effect was modelled through 10year groups and parametric dependency on age at diagnosis was assumed by using respectively an exponential or a sixdegree polynomial. Both models were estimated with the SAS LOGISTIC procedure.

Parameters of survival and incidence models were then imported in the software implementing the completeness index standard method (COMPREV) ( 4) to produce European model-based R-indexes.

iii) SEER model-based R-index (SEER mod)

Model-based R-indexes, estimated by the US National Cancer Institute (NCI) from the SEER-Program cancer registries data, were extracted from the COMPREV software (4).

Validation of the completeness indexes

The completeness index method allows to estimate any limitedduration prevalence beyond the longest observed period. Prevalence at any duration d 2 can be estimated dividing observed prevalence at maximum available duration d 1 by the ratio of the two corresponding R-indexes: R d1 /R d2 .

We used this property to validate R-indexes estimated by modelling European data, i.e. by using the gold standard method. For each eligible registry observed, 20-year prevalence was compared with estimated 20-year prevalence. To simulate a registration activity shorter than 20 years, observed prevalence was artificially truncated at durations d=5,10,15 years. The goodness of fit was measured separately for each cancer type as the weighted average percent relative difference in absolute value between estimated (N') and observed (N) 20-year number of prevalent cases (APRD):

APRD = o r ( N 0 20,r -N 20,r N 20,r )w r  100
Registry-specific proportions of cancer cases (w r ) were used as weights. The absolute value of the relative difference avoids compensations between under-and over-estimations and provides a maximum average discrepancy compared to observations. The registries used for this validation (dataset c in Table 1) did not coincide with those used for estimating European model-based R-indexes (dataset b in Table 1).

Comparison of complete prevalence estimates

Cancer-, sex-, age-and duration-specific prevalence completeness indexes were applied to observed prevalence at maximum available duration in each of the 62 registries in dataset d) to obtain estimates of complete prevalence at 1/1/2013. Standard model-based complete prevalence estimates were compared to those obtained with alternative R-indexes (EU emp or SEER mod).

Weighted average percent relative difference between alternative and standard estimates of complete prevalence (PRD) was analysed by cancer site, sex and grouped registration duration (10-14 years, 15-19 years, 20-24 years, 25-35 years). The resident population covered by each registry was used as weight in the average.

Results

Incidence and relative survival models

In general, mixture cure models fitted data well and observed relative survival generally lied within the confidence limits estimated for predicted survival (examples are reported in the Supplementary Materials, Figure A1). Moreover, in most cases the survival curves reached a plateau within 20 years of follow-up, meaning that the cure assumption is satisfied in this time interval.

Diagnostic plots and values of the Akaike Information Criterion (AIC) showed that polynomial models fitted incidence data much better than exponential models for all the considered cancer types (Supplementary Materials, Figure A2). This is particularly evident for cancers at early onset or with bimodal age at diagnosis. Age polynomials provide indeed higher flexibility in modelling age trends compared to the exponential model.

Trends of the completeness indexes

Some examples of cancer-specific completeness indexes trends by age at prevalence date and duration of registration are shown in Figures 123. The comparison of the three different methods (SEER mod, EU mod and EU Emp) is restricted to the age range 30-79 years for which R-index can be estimated for all methods by 5-year age classes. Wider groups (0-29 and 80+) are in fact needed to compute empirical indexes for extreme age ranges with few cases.

Completeness index increases with the length of registration period and is higher for cancers at low prognosis (Figure 1) than for those at high to medium prognosis (Figure 2). A reduced survival implies indeed a more complete observed prevalence. Generally, R-index is close to 100% at young age and decreases with advancing age at prevalence date. For early onset tumours (Figure 3), however, young survivors can be partly not observable depending on the length of registration activity. Prevalence completeness is highest for low prognosis cancers diagnosed mainly in the elderly (Figure 1). At 15 years of registration, R-index is above 80-90% with minimum values for the eldest survivors. The empirical index trend is less smooth compared to model-based Rindexes because, being based on observations, it is more subject to random fluctuations, as also proven by confidence intervals (not shown in the graphs). At 35-years of registration all methods provide R-index values around 100%, meaning that such duration is sufficiently long to detect practically all survivors. Prevalence completeness is intermediate for higher prognosis cancers diagnosed in middle to old age (Figure 2).

Validation of the completeness indexes

Tables 2A, B report observed 20-year prevalence proportion per 100,000 for the pool of registries in the validation dataset, for male and female populations, respectively. The weighted average percent relative differences, in absolute value, between registry-specific 20year observed and standard estimated prevalence (APRD) is also Average discrepancies between estimates and observations decrease as registration length increases. Particularly with registration times of 15 years the fit to observations is always good (APRD are well below 5%, maximum 6.3% for cervical cancer). At 10 years the validation is equally satisfying for all cancers examined (APRD values do not exceed 5%) except for young-onset cancers (cervix uteri, thyroid, brain and, to lesser extent, skin melanoma, bones, testis and Hodgkin lymphoma), suggesting that 15-year observed prevalence provides a more robust basis for this class of tumours.

Conversely prevalence observations limited to 5-years lead to less precise estimates in most of the cases (APRD exceed 5%) especially, but not only, for young-onset cancers (21% for cervical cancer, 12.5% for prostatic cancer).

Comparative assessment of complete prevalence estimates

Empirical (EU Emp) and SEER (SEER mod) complete prevalence estimates were compared to the standard model-based estimates (EU mod) for all 62 eligible cancer registries (dataset d). PRD between alternative and standard complete prevalence estimates of some index tumours is plotted in Figure 4 by registration time length (from 5 to 35 years).

Consistently with Figures 1,2, when considering cancers at late age at onset with low (pancreas, lung) or good prognosis (colonrectum and breast), the empirical estimates (Figure 4, blue crosses) approach model-based estimates as registration length increases. PRD values between -5% and 0 are indeed reached already after 10 years of registration. Conversely, for testicular and cervical cancers empirical indexes provide complete prevalence estimates that are systematically lower than model-based estimates (PRD at about -10% or -20% respectively) regardless of the registration time length, consistently with R-index patterns for early-onset tumours (Figure 3).

Differences between SEER and standard European complete prevalence estimates (Figure 4, purple circles) are almost null at all durations for pancreatic and breast cancers, and after 20 years of observation, for colorectal and lung cancers. Being model-based, SEER R-indexes reproduce standard estimates better than the empirical indexes for cervical and testicular cancers (PRD approaching zero with growing registration time).

A complete picture of percent relative differences between alternative and standard complete prevalence estimates is given in Tables 3A, B (EU Emp vs EU mod) and Tables 4A, B (SEER mod Vs EU mod), as a function of the duration of registration, starting from the group of 10 registries in operation for 10-14 years to the group of 17 registries active for 25-35 years. Mean standard complete prevalence proportion and PRD values in each pool of registries are reported by sex and cancer site. Negative values of PRD indicate an average underestimation of complete prevalence compared to the standard method.

The empirical R-index underestimates compared to the gold standard (Tables 3A, B) but the difference declines as registration time increases. The two methods lead to similar complete prevalence (PRD not exceeding 5% in absolute value) already after 10 or 15 years of registration for most cancers of the elderly, including those at highest prevalence (breast, prostate, colon and rectum, bladder) and those at poorest prognosis (e.g. oesophagus, larynx, gallbladder, pancreas, multiple myeloma) that show the lowest discrepancies. Most tumours at early onset represent an exception to this general pattern. PRD values reach 10-20% (testis, brain, bones, soft tissues and cervical cancers, Hodgkin lymphoma) and are scarcely sensitive to the duration of registration. On the contrary, more comparable estimates were observed for skin melanoma and thyroid cancers, both at early onset and with remarkably rising incidence across Europe. CLL/SLL, Chronic lymphocytic leukaemia/small lymphocytic lymphoma; AML, Acute myeloid leukaemia; CML, Chronic myeloid leukaemia. The validation is limited to cancer registries with at least 20 years of observations at 1/1/2013 that were not used to estimate R-index. Pooled observed 20-y prevalence proportion and weighted average percent relative differences in absolute value (APRD, %) between observed and estimated 20-years prevalence by cancer site are shown. Estimates are derived by applying completeness indexes to observed prevalence truncated at 5, 10 and 15 years and the average is weighted using the registry-specific number of prevalent cases.

SEER R-indexes may provide either under-or over-estimations of standard complete prevalence (Tables 4A, B) that diminish as registration time grows. They provide similar estimates to the standard method after 10 or 15 years of registration for most tumours and, being based on models as well, even for most of early onset tumours (Hodgkin lymphoma, soft tissues, bones, cervix uteri, skin melanoma). Wider discrepancies were instead found when incidence and survival patterns in US and European populations determine differences between standard and SEER R-index values (non-Hodgkin lymphomas, thyroid, corpus uteri, testis, brain, larynx and stomach cancers). Notably PRD values (within 5%) for male brain cancer do not properly reflect the actual differences between SEER and standard R-index by age (under-and over-estimations are compensated in the weighted average) regardless of the duration of registration.

This comparative assessment of the alternative methods to derive complete cancer prevalence is summarised in Table 5 to facilitate readability and use of the results. The validation is limited to cancer registries with at least 20 years of observations at 1/1/2013 that were not used to estimate R-index. Pooled observed 20-y prevalence proportion and weighted average percent relative differences in absolute value (APRD, %) between observed and estimated 20-years prevalence by cancer site are shown. Estimates are derived by applying completeness indexes to observed prevalence truncated at 5, 10 and 15 years and the average is weighted using the registry-specific number of prevalent cases.

Discussion

To our knowledge, this is the first study exploring the validity of alternative approaches to derive prevalence completeness indexes. The study relies on an exceptionally wide European population-based dataset covering 50% of the population of the 27 countries involved.

Model-based R-indexes were introduced more than 20 years ago [START_REF] Capocaccia | Estimating the completeness of prevalence based on cancer registry data[END_REF]. Nowadays observations of cancer prevalence are available for time series and populations of much greater extension, thus testing the validity of empirical indexes that have now become available is relevant for a wider application of the method. The completeness index method is indeed particularly suited for local registry-based applications that rely on the available observed limited-duration prevalence.

Other methods to estimate complete prevalence include those modelling prevalence as a function of cancer-specific incidence and survival, both derived from cancer registries' data. Unlike the completeness index method, these methods do not rely on observed limited-duration prevalence and are more suited to derive time projections of cancer prevalence or national estimates in countries with partial registration coverage [START_REF] Colonna | Time trends and short term projections of cancer prevalence in France[END_REF][START_REF] Colonna | Grosclaude PFrench Network of Cancer Registries (FRANCIM). Total and partial cancer prevalence in the adult French population in 2008[END_REF][START_REF] Maddams | Projections of cancer prevalence in the united kingdom, 2010-2040[END_REF][START_REF] Rossi | Estimates of cancer burden in Italy[END_REF][START_REF] Bluethmann | Anticipating the "Silver tsunami": Prevalence trajectories and comorbidity burden among older cancer survivors in the united states[END_REF].

From the validation study, a registration time period of at least 10 years turned out to be necessary to safely apply the prevalence completeness index method, confirming this cut-off as a general recommendation.

In many situations empirical R-index was found to provide complete prevalence estimates comparable to the "gold-standard". Registries' observation time window, cancer specific incidence age Percent relative difference (%) by registration length at 1/1/2013 of complete prevalence estimates obtained with SEER model-based or EU empirical R-index against EU model-based estimate as reference value. Each point corresponds to one of the 62 registries in dataset d of Table 1.

profile and prognosis act as modulating factors. For tumours mainly diagnosed in the elderly, EU empirical and EU model-based Rindexes led to similar results (within an average tolerance of 5%) when applied to prevalence data observed for at least 10 years.

By contrast, the empirical method underestimates very longterm survivorship for tumours with early age at onset, even when based on 35 years of observations. For this specific class of neoplasms, model-based methods are structurally more suited to capture unobserved survivors in the very long term. This limitation is also reflected in the estimation of all cancers that include a nonnegligible proportion of juvenile cancers. Using model-based completeness indexes derived from external rather than local patients' populations (SEER versus European) led to comparable prevalence estimates for the majority of cancers, even when applied to minimum registration periods (10 years). The list includes also most of the early onset tumours and, as a consequence, the complex of all cancer sites. Notable discrepancies were instead observed as a result of geographical differences in cancer incidence and survival patterns, regardless of the natural history of the disease (age at onset and prognosis). This, for instance, is the case of endometrial and thyroid cancers, or of brain tumours, as the inclusion criteria of non-malignant entities may vary between SEER and European registries, thus affecting the consistency of estimates. The results we obtained were coherent with the patterns of the relevant factors influencing cancer prevalence, e.g. age at prevalence date, low to high cancer prognosis, incidence age profile, length of the registration time period.

European model-based R-index values were slightly higher than those estimated from SEER data consistently with the prognostic differences between European and USA cancer patients, the latter generally reported to present more favourable survival levels [START_REF] Allemani | Global surveillance of trends in cancer survival 2000-14 (CONCORD-3): Analysis of individual records for 37 513 025 patients diagnosed with one of 18 cancers from 322 population-based registries in 71 countrie[END_REF]. Differences are also partly due to incidence modelling choices. SEER R-indexes were indeed often derived by adopting exponential rather than polynomial incidence models [START_REF]national cancer institute COMPREV software[END_REF]. Finally, differences between IARC and SEER rules for identifying multiple primary tumours could also have an impact.

  In the examples shown (breast, colorectal and corpus uteri cancers), at 15 years of registration, R-index varies from 95-100% to 50-70% as a function of age at prevalence date. SEER R-index values are slightly lower compared to those based on European data, reflecting a more favourable prognosis for US patients. At 35 years, model-based Rindexes tend to converge to 100% (95-98% for the eldest age group).Cancers at early onset show the lowest R-index values and the most marked variations (Figure3). At 15 years, observed prevalence is far from being complete for most age groups, particularly for bone cancers that are almost equally diagnosed at all ages. A registration period of 35 years appears insufficient to observe all long-term survivors, as shown by the residual gap (up to 50%) between empirical and model-based R-index estimates. By contrast, SEER and standard R-index, which are both model-based, show a quite similar age profile.

FIGURE 1

 1 FIGURE 1 Prevalence completeness index (R index) at 1st January 2013 estimated for some tumours at low prognosis (oesophagus, pancreas, gallbladder) according to alternative methods: SEER model-based, EU model-based, EU empirical by age at prevalence date and registration time length (15 and 35 years).

  reported and is obtained by artificially truncating observed prevalence at 5,10 and 15 years.

FIGURE 2

 2 FIGURE 2 Prevalence completeness index (R-index) at 1st January 2013 estimated for some frequent medium-high prognosis tumours (breast, colon-rectum, corpus uteri) according to alternative methods: SEER model-based, EU model-based, EU empirical by age at prevalence date and registration time length (15 and 35 years).

FIGURE 3

 3 FIGURE 3 Prevalence completeness index (R-index) at 1st January 2013 estimated for some tumours diagnosed at young age (testis, bones, cervix uteri) according to alternative methods (SEER model-based, EU model-based, EU empirical by age at prevalence date and registration time length (15 and 35 years).

FIGURE 4

 4 FIGURE 4

TABLE 1

 1 Description of the registries included in each analysis-specific dataset.Registries in dataset c) and b) plus: Belgium, Cyprus, Czech Republic, England, Ireland, Latvia, Poland, Herault, Lille, Poitou Charentes (France), Bremen, Federal States (BR,MW-PSA,THU), Hamburg (Germany), Bergamo, Puglia Barletta Andria-Trani, Catania-Messina-Enna, Latina, Monza-Brianza, Napoli, Nuoro, Palermo, Piacenza, Reggio Emilia, Siracusa, Sondrio, Taranto, Umbria (Italy), Southern Portugal (Portugal), Castellon, Girona (Spain), Friburg, Ticino (Switzerland)

	Dataset	Type of analysis	Registration length (years)	Number of registries	Registries	Population (% study coverage)
	a)	Empirical index	35	8	Denmark, Estonia, Finland, Iceland, Norway, Scotland, Geneva (Switzerland), Parma (Italy)	23,592,911 (5%)
	b)	Model-based index	>=30	11	Registries in dataset a) plus: Austria, Slovenia, Tarragona (Spain)*	34,806,065 (8%)
	c)	Validation of completeness indexes	>=20	20	Bulgaria, Lithuania, Malta, The Netherlands, Northern Ireland, Wales, Balearic (France), Modena, Ragusa, Romagna (Italy) Islands, Basque Country, Granada (Spain), Graubünden and Glarus, Eastern Switzerland (Switzerland), Bas Rhin, Doubs, Haut-Rhin, Isere, Somme, Tarn	44,230,482 (10%)
	d)	Complete prevalence estimation	>=5	62		231,214,391 (51%)

*The registry of Tarragona is included in dataset b) and not in d) because limited-duration prevalence is available at 1/1/2012. Population covered by the registries in each dataset and percent coverage of the 27 European countries that participated in EUROCARE-6 included in the study are shown. National registries are in bold. distribution, while the others are considered as cured. The non-linear regression procedure (NLIN) available in the SAS Software (SAS System for Windows, version 9.4; SAS Institute, Cary, NC) was used to estimate model parameters.

  TABLE 2A Validation of European model-based R-index, men.

			APDR, 20-y prevalence estimated by truncating registries observations at
	Cancer site	Observed 20-y Prevalence	15 years	10 years	5 years
		Proportion x 100,00	%	%	%
	All sites	2,999	2.0	5.0	6.4
	Prostate	1,082	1.1	3.3	12.5
	Colon Rectum	488	1.2	2.8	6.0
	Bladder	354	1.1	2.9	5.5
	Skin melanoma	161	2.1	5.9	13.8
	Lung	157	1.3	3.1	3.3
	Kidney	138	1.4	4.5	8.4
	Non-Hodgkin lymphoma	122	0.9	3.1	5.7
	Testis	103	2.1	5.0	10.9
	Larynx	79	1.6	2.9	6.2
	Head and neck	76	1.1	2.9	5.0
	Stomach	61	2.0	4.4	9.7
	CLL/SLL	49	1.6	4.2	7.5
	Hodgkin lymphoma	38	3.1	5.4	9.3
	Thyroid	33	4.2	8.3	14.3
	Brain	32	4.6	9.5	13.8
	Multiple myeloma	31	1.0	3.5	6.1
	Soft tissues	30	2.2	3.1	4.3
	Oesophagus	27	1.5	3.4	5.7
	Liver	19	0.9	1.7	4.2
	Pancreas	16	1.3	5.1	6.8
	Penis	15	1.8	2.6	5.4
	AML	12	2.3	3.0	4.8
	CML	10	2.4	4.1	5.8
	Gallbladder	9	1.3	4.7	9.6
	Bones	9	3.0	6.3	10.4

  TABLE 2B Validation of European model-based R-index, women.

			APDR, 20-y prevalence estimated by truncating registries observations at
	Cancer site	Observed 20-y Prevalence	15 years	10 years	5 years
		Proportion x 100,00	%	%	%
	All sites	3,471	1.8	3.9	5.9
	Breast	1,537	0.9	1.9	3.5
	Colon Rectum	414	1.4	3.0	4.8
	Corpus Uteri	274	2.3	4.7	7.0
	Skin melanoma	218	2.3	6.1	11.8
	Cervix uteri	144	6.3	14.3	21.0
	Thyroid	119	5.4	12.0	16.3
	Ovary	110	0.7	1.1	5.7
	Non-Hodgkin lymphoma	105	1.4	2.8	4.6
	Bladder	94	2.0	4.8	7.7
	Lung	88	1.3	3.5	4.8
	Kidney	84	1.5	3.7	6.9
	Stomach	41	2.1	5.5	9.3
	Head and Neck	37	1.2	2.7	4.9
	CLL/SLL	36	1.6	4.1	8.2
	Hodgkin lymphoma	31	1.9	5.1	8.7
	Brain	26	4.9	10.8	18.1
	Multiple myeloma	26	1.1	4.1	7.3
	Soft tissues	22	1.6	3.8	7.5
	Pancreas	15	1.1	4.1	6.6
	AML	12	2.3	4.0	8.1
	Larynx	11	1.6	3.6	4.8
	Oesophagus	10	2.1	4.0	5.6
	Gallbladder	10	2.5	6.4	9.7
	Bones	8	2.0	3.5	6.2
	CML	8	3.1	5.5	10.7
	Liver	7	1.5	3.8	5.2

CLL/SLL: Chronic lymphocytic leukaemia/small lymphocytic lymphoma; AML, Acute myeloid leukaemia; CML, Chronic myeloid leukaemia.

  TABLE 3A Comparison between empirical and standard model-based complete prevalence at 1/1/2013 by cancer site for the 62 European registries included in the study grouped by registration time length (from 10-14 years to 25-35 years), Men.

	Registration time
	interval in years (number of registries)	10-14 y (10)	15-19 y (12)	20-24 y (13)	25-35 y (17)	Registration time length with PRD
		Standard		Standard		Standard		Standard		≤ 5%
	Cancer site	complete prev	PRD	complete prev	PRD	complete prev	PRD	complete prev	PRD
		Prop *100,000	%	Prop *100,000	%	Prop *100,000	%	Prop *100,000	%	number of years
	All cancers	3,476	-7.1	3,757	-4.5	3,747	-3.3	3,692	-2.2	>15
	Prostate	959	-2.8	1,190	-1.5	1,450	-0.5	1,225	0.0	>10
	Colon Rectum	539	-3.0	565	-2.0	501	-1.3	550	-0.8	>10
	Bladder	453	-2.2	456	-2.1	281	-2.1	462	-1.9	>10
	Non-Hodgkin lymphoma	232	-5.4	251	-4.8	247	-4.5	245	-4.0	>15
	Lung	195	-7.3	197	-4.6	180	-2.3	171	-1.1	>15
	Kidney	182	-5.6	203	-3.1	173	-2.2	184	-1.4	>15
	Testis	154	-9.4	160	-10.5	166	-10.2	167	-8.4	none
	Skin melanoma	146	-4.3	171	-2.7	186	-2.4	213	-2.4	>10
	Larynx	103	-2.7	97	-3.6	79	-2.2	95	-1.5	>10
	Stomach	100	-5.2	106	-4.2	67	-3.5	96	-2.8	>10
	Head and Neck	93	-3.6	85	-2.4	108	-1.3	89	-0.6	>10
	Thyroid	89	0.7	79	-0.9	53	-0.8	73	-3.9	>10 *
	Hodgkin lymphoma	70	-10.6	66	-9.1	59	-8.1	59	-6.7	none
	CLL/SLL	55	-4.2	58	-2.0	64	-1.4	55	-0.9	>10
	Liver	47	-3.1	49	-1.1	28	-1.0	36	-0.7	>10
	Brain	45	-14.4	47	-10.6	42	-9.7	54	-8.5	none
	Multiple myeloma	37	-3.0	39	-1.3	36	-0.4	38	-0.2	>10
	Soft tissues	35	-15.7	37	-13.8	36	-13.2	37	-10.7	none
	Pancreas	22	-3.5	24	-0.4	23	0.2	21	-0.1	>10
	Oesophagus	18	-2.0	20	-0.8	28	-0.4	18	0.0	>10
	Penis	19	-4.5	18	-4.5	17	-3.6	19	-3.3	>10
	AML	16	-1.6	21	-3.0	16	-3.2	15	-1.9	>10
	Bones	15	-20.6	18	-20.7	16	-19.2	18	-18.3	none
	Gallbladder	13	-4.1	11	-2.3	10	-0.7	12	-0.3	>10
	CML	11	1.6	13	-0.7	14	-0.7	12	-0.2	>10
	CLL/SLL, Chronic lymphocytic leukaemia/small lymphocytic lymphoma; AML, Acute myeloid leukaemia; CML, Chronic myeloid leukaemia.
	* for thyroid cancer values of PRD grow as registration length increases and for female thyroid cancer PRD slightly exceeds 5% after 25 years of registration (consistently with Empirical vs EU
	model-based R-index patterns).
	Weighted average percent relative difference (PRD, %) between empirical and standard model-based complete prevalence estimates (the average is weighted using registries population).
	Registration time length with PRD values not exceeding 5%.

  TABLE 3B Comparison between empirical and standard model-based complete prevalence at 1/1/2013 by cancer site for the 62 European registries included in the study grouped by registration time length (from 10-14 years to 25-35 years), Women.

	Registration time
	interval in years (number of registries)	10-14 y (10)	15-19 y (12)	20-24 y (13)	25-35 y (17)	Registration time length with PRD
	Cancer Site	Standard complete prev	PRD	Standard prev complete	PRD	Standard prev complete	PRD	Standard prev complete	PRD	≤ 5%
		Prop *100,000	%	Prop *100,000	%	Prop *100,000	%	Prop *100,000	%	number of years
	All cancers	4,380	-8.4	4,388	-6.7	4,305	-5.4	4,369	-4.1	>20
	Breast	1,700	-4.8	1,831	-4.1	1,869	-3.0	1,777	-2.0	>10
	Colon Rectum	477	-4.0	485	-3.0	443	-2.4	497	-1.7	>10
	Thyroid	371	-0.4	278	-2.2	217	-3.1	257	-6.1	>10 *
	Corpus Uteri	341	-5.4	305	-4.0	328	-2.8	343	-2.6	>10
	Cervix Uteri	268	-21.1	225	-20.2	258	-20.5	230	-21.3	none
	Non-Hodgkin lymphoma	203	-6.2	209	-5.6	207	-5.4	212	-4.5	>20
	Skin melanoma	185	-8.2	232	-5.8	262	-5.4	289	-5.4	>20
	Ovary	157	-9.2	145	-9.8	153	-8.9	151	-8.4	none
	Bladder	114	-4.4	120	-4.2	77	-3.6	124	-3.2	>10
	Kidney	115	-7.1	111	-4.6	109	-4.0	110	-2.8	>15
	Lung	85	-4.7	90	-2.8	81	-1.1	100	-0.5	>10
	Stomach	79	-4.6	77	-5.0	46	-5.2	75	-5.1	>10
	Hodgkin lymphoma	61	-12.3	57	-13.2	49	-11.0	52	-9.1	none
	CLL/SLL	41	-2.4	40	-0.9	48	-0.4	42	-0.2	>10
	Brain	37	-14.4	38	-9.8	32	-9.5	47	-8.0	none
	Head and Neck	39	-5.8	39	-4.4	42	-2.9	44	-2.0	>15
	Multiple myeloma	32	-2.2	33	-1.1	31	-0.5	34	-0.1	>10
	Soft tissues	31	-18.4	31	-16.6	31	-16.5	33	-14.6	none
	Liver	20	-5.5	17	-2.5	9	-2.2	15	-2.3	>15
	Pancreas	20	-3.4	22	-0.3	20	0.2	20	-0.1	>10
	Gallbladder	17	-1.5	14	-0.6	11	-0.4	13	-0.7	>10
	AML	15	-6.7	19	-6.1	18	-4.9	15	-4.1	>20
	Bones	14	-15.0	15	-18.3	15	-18.2	14	-17.3	none
	Larynx	11	-2.6	12	-4.5	11	-2.9	11	-2.5	>10
	CML	9	-1.8	10	-1.2	10	-0.2	9	-0.5	>10
	Oesophagus	6	-1.9	7	-0.8	9	-0.3	7	-0.5	>10
	CLL/SLL, Chronic lymphocytic leukaemia/small lymphocytic lymphoma; AML, Acute myeloid leukaemia; CML, Chronic myeloid leukaemia.
	* for thyroid cancer values of PRD grow as registration length increases and for female thyroid cancer PRD slightly exceeds 5% after 25 years of registration (consistently with Empirical vs EU
	model-based R-index patterns).
	Weighted average percent relative difference (PRD, %) between empirical and standard model-based complete prevalence estimates (the average is weighted using registries population).
	Registration time length with PRD values not exceeding 5%.

  TABLE4AComparison between SEER and standard model-based complete prevalence at 1/1/2013 by cancer site for the 62 European registries included in the study grouped by registration time length (from 10-14 years to 25-35 years), Men. Chronic lymphocytic leukaemia/small lymphocytic lymphoma; AML, Acute myeloid leukaemia; CML, Chronic myeloid leukaemia. * PRD for male Brain cancer reflect compensations of under/over-estimates between SEER and Standard R-index. Weighted average percent relative difference (PRD, %) between SEER and standard model-based complete prevalence estimates (the average is weighted using registries population). Registration time length with PRD values not exceeding 5%.

	Registration time
	interval in years (number of registries)	10-14 y (10)	15-19 y (12)	20-24 y (13)	25-35 y (17)	Registration time length with PRD
		Standard		Standard		Standard		Standard		≤ 5%
	Cancer site	complete prev	PRD	complete prev	PRD	complete prev	PRD	complete prev	PRD
		Prop *100,000	%	Prop *100,000	%	Prop *100,000	%	Prop *100,000	%	number of years
	All cancers	3,476	-1.2	3,757	-1.1	3,747	-1.3	3,692	-0.7	>10
	Prostate	959	2.3	1,190	1.3	1,450	0.9	1,225	0.2	>10
	Colon Rectum	539	8.7	565	5.3	501	3.8	550	1.3	>15
	Bladder	453	7.1	456	4.1	281	2.6	462	0.6	>15
	Non-Hodgkin lymphoma	232	-9.8	251	-5.0	247	-4.5	245	-2.4	>15
	Lung	195	8.0	197	5.0	180	4.8	171	2.3	>15
	Kidney	182	6.3	203	4.7	173	3.6	184	2.0	>15
	Testis	154	7.8	160	5.7	166	3.8	167	1.4	>20
	Skin melanoma	146	6.9	171	4.4	186	2.6	213	1.1	>15
	Larynx	103	8.9	97	7.2	79	4.1	95	1.3	>20
	Stomach	100	-6.8	106	-4.7	67	-2.5	96	-0.8	>15
	Thyroid	89	20.2	79	14.4	53	10.6	73	5.3	>20
	Hodgkin lymphoma	70	2.3	66	3.8	59	4.3	59	3.3	>10
	CLL/SLL	55	-1.3	58	-0.5	64	-1.1	55	-0.8	>10
	Liver	47	-0.4	49	-0.3	28	-0.6	36	-0.3	>10
	Brain	45	3.2	47	4.4	42	4.6	54	3.1	none *
	Multiple myeloma	37	-4.2	39	-1.9	36	-0.8	38	-0.1	>10
	Soft tissue	35	2.6	37	2.4	36	0.8	37	-0.2	>10
	Pancreas	22	2.1	24	1.9	23	1.7	21	0.7	>10
	Oesophagus	18	4.9	20	2.1	28	1.6	18	0.4	>10
	AML	16	-0.1	21	4.1	16	4.9	15	4.6	>10
	Bones	15	1.0	18	-0.7	16	-1.6	18	-3.3	>10
	Gallbladder	13	4.6	11	2.7	10	2.0	12	0.8	>10
	CML	11	-8.5	13	-0.3	14	1.9	12	1.9	>15
	CLL/SLL,

  TABLE 4BComparison between SEER and standard model-based complete prevalence at 1/1/2013 by cancer site for the 62 European registries included in the study grouped by registration time length (from 10-14 years to 25-35 years), Women. Chronic lymphocytic leukaemia/small lymphocytic lymphoma; AML, Acute myeloid leukaemia; CML, Chronic myeloid leukaemia. Weighted average percent relative difference (PRD, %) between SEER and standard model-based complete prevalence estimates (the average is weighted using registries population). Registration time length with PRD values not exceeding 5%.

	Registration time
	interval in years (number of	10-14 y (10)	15-19 y (12)	20-24 y (13)	25-35 y (17)	Registration
	registries)									time length with
	Cancer site	Standard complete prev	PRD	Standard complete prev	PRD	Standard complete prev	PRD	Standard complete prev	PRD	PRD ≤ 5%
		Prop *100,000	%	Prop *100,000	%	Prop *100,000	%	Prop *100,000	%	number of years
	All cancers	4,380	2.8	4,388	2.8	4,305	2.5	4,369	1.6	>10
	Breast	1,700	0.1	1,831	0.5	1,869	0.6	1,777	0.3	>10
	Colon Rectum	477	6.2	485	4.3	443	3.5	497	1.6	>15
	Thyroid	371	7.1	278	6.2	217	5.3	257	3.0	>20
	Corpus Uteri	341	22.3	305	14.9	328	9.6	343	3.8	>25
	Cervix Uteri	268	-5.8	225	-2.1	258	-1.0	230	0.6	>15
	Non-Hodgkin lymphoma	203	-9.1	209	-5.5	207	-4.9	212	-2.9	>20
	Skin melanoma	185	6.6	232	4.9	262	3.7	289	1.9	>15
	Ovary	157	4.1	145	3.9	153	3.7	151	2.6	>10
	Kidney	115	0.9	111	1.4	109	1.4	110	0.7	>10
	Bladder	114	5.2	120	3.2	77	2.2	124	0.5	>10
	Lung	85	6.3	90	4.3	81	3.2	100	1.3	>15
	Stomach	79	-13.7	77	-10.2	46	-7.4	75	-3.6	>25
	Hodgkin lymphoma	61	2.0	57	2.9	49	3.0	52	2.2	>10
	CLL/SLL	41	0.0	40	0.9	48	0.6	42	0.3	>10
	Brain	37	13.3	38	14.8	32	13.1	47	7.7	none
	Multiple myeloma	32	-1.6	33	0.8	31	1.3	34	0.7	>10
	Soft tissues	31	-1.6	31	-2.2	31	-2.4	33	-1.9	>10
	Pancreas	20	2.6	22	2.8	20	2.3	20	1.0	>10
	Liver	20	7.1	17	4.5	9	3.7	15	1.2	>15
	Gallbladder	17	-1.5	14	0.3	11	0.7	13	0.5	>10
	AML	15	-2.5	19	1.9	18	3.3	15	2.8	>10
	Bones	14	7.2	15	2.8	15	0.9	14	-3.0	>15
	Larynx	11	1.4	12	2.0	11	0.8	11	0.1	>10
	CML	9	-13.7	10	-3.9	10	-0.7	9	1.3	>15
	Oesophagus	6	1.3	7	1.3	9	1.6	7	0.7	>10
	CLL/SLL,

Frontiers in Oncology frontiersin.org

Demuru et al. 10.3389/fonc.2023.1114701 Frontiers in Oncology frontiersin.org

10.3389/fonc.2023.1114701 Frontiers in Oncology frontiersin.org

Acknowledgments

The authors would like to thank Tonino Sofia for the Englishlanguage revision.

Funding

This study was funded by the European Commission (Grant Agreement no. 801520 HP-JA-2017, Innovative Partnership for Action Against Cancer, iPAAC Joint Action) and by the Italian Association for Cancer Research (AIRC) (Grant no. 21879). The funding agency played no role in designing the study, collecting, analyzing or interpreting the data, writing the report, or deciding whether or not to submit the article for publication.

Data availability statement

The datasets of empirical and standard model-based completeness indexes presented in this article are not readily available. Requests to access the datasets should be directed to RA, roberta.deangelis@iss.it.

Parametric mixed cure models of Weibull type were used for modelling survival [START_REF] Capocaccia | Estimating the completeness of prevalence based on cancer registry data[END_REF][START_REF] Merrill | Cancer prevalence estimates based on tumour registry data in the surveillance, epidemiology, and end results (SEER) program[END_REF]. More flexible cure fraction models could have been considered [START_REF] Andersson | Estimating and modelling cure in population-based cancer studies within the frame-work of flexible parametric survival models[END_REF][START_REF] Yu | Estimating the proportion cured of cancer: Some practical advice for users[END_REF] but the choice is limited to Weibull or exponential types in the COMPREV software.

The empirical indexes were derived by pooling data of 8 European registries with available 35-year observed prevalence at the index date. The limit at 35-years is arbitrary and just reflects the maximum available time span in the EUROCARE-6 dataset. However, it has been proven to provide a sufficient basis to estimate complete cancer prevalence for major cancers and for a variety of less frequent tumours with late age at onset. Lower values might be critical and extending this limit in applications to more recent prevalence index dates is advisable, considering the continuous progresses of cancer survival over time and the availability of longer registration time series.

Empirical indexes were subject to random fluctuations when based on sparse cases, for instance in correspondence of young age at prevalence date for tumours at late onset like pancreatic or prostatic cancer. However, such fluctuations are of scarce practical relevance because the index is applied to values of observed prevalence which are almost null in these circumstances. R-indexes were generally positively validated on a fully independent dataset of 20 registries, therefore showing that the estimation datasets used to derive model-based completeness indexes were sufficiently representative of the prevalence patterns in other European populations. However, we cannot exclude that for some neoplasms the geographical heterogeneity of incidence or prognosis may have required area-specific R-indexes.

Notably the empirical completeness R-indexes are easy to compute but inevitably refer to a specific point in time (the index date of the maximum observable cancer prevalence). Thus they must be computed on a date which is reasonably close to the index date of the limited-duration prevalence we want to complete.

Conversely model-based R-indexes require higher computational effort to model incidence and relative survival trends, but they dynamically evolve over time (the period of diagnosis is parameterised in the models) and R-index values for varying prevalence index dates can be derived through the Comprev software [START_REF]national cancer institute COMPREV software[END_REF].

In conclusion, the study tests the feasibility of using alternative formulations of the completeness index method to integrate limited-duration prevalence measured by population-based cancer registries. We focused on the European context where the lack of systematic data on the overall number of cancer survivors in many countries hinders the planning of health services and particularly survivorship care planning. This appears even more limiting in light of the future scenario in which the population of cancer survivors is indeed expected to increase significantly due to ongoing demographic changes and continued advances in therapies and diagnosis. Our results may facilitate the use and dissemination of complete cancer prevalence estimates across Europe and help to close the present information gaps.

Ethics statement

Ethical review and approval was not required for the study on human participants in accordance with the local legislation and institutional requirements. Written informed consent from the participants' legal guardian/next of kin was not required to participate in this study in accordance with the national legislation and the institutional requirements.

Author contributions

ED carried out the study and analysed the incidence and prevalence data. SR did quality checks, prepared the SEER*Stat study database and analysed the survival data. LV analysed the survival data. CB implemented the procedures to check the raw data and to generate the SEER*Stat study database. LM, SG, AK, SL, and VJ provided advice and revised the results. RA drafted the article, designed the study and the data quality checks. The EUROCARE-6 Working Group collected, prepared, and transmitted raw data for the study database, corrected data after quality controls, checked the results of the analyses and revised the final draft of the article. All authors interpreted results. All authors contributed to the article and approved the submitted version.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher's note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fonc.2023.1114701/ full#supplementary-material


Pierre Tittelein
email: pierre.tittelein@univ-artois.fr

Alain Cloutier
email: alain.cloutier@sbf.ulaval.ca

Benoît Bissonnette
email: benoit.bissonnette@gci.ulaval.ca

Keywords: Wood-cement, particleboard, low-density, gypsum panel, Welan Gum, wood residues

Gypsum boards form a very large part of the building walls and ceilings finishing market. However, they have poor screw-withdrawal resistance, low hardness and are highly sensitive to moisture. The objective of this study was to determine whether it is possible to make woodcement particleboards of the same density as gypsum boards while avoiding these drawbacks.

Wood-cement particleboards were made by pouring the wood-cement paste in a mould. This was made possible by adding a viscosity modifying mixture to the mixing water and a set accelerating mixture to improve wood/cement compatibility. The mechanical properties and surface quality of the wood-cement particleboards were improved by using, on the board surfaces, paper sheets that were the same as those used on gypsum boards.

The average specific gravity of the wood-cement particleboards was the same as gypsum boards, at 0.7. The average bending modulus of rupture obtained for the wood-cement particleboards was 10 MPa in the finishing paper principal direction and 5 MPa in the other direction compared to 5.5 MPa and 1.6 MPa respectively for gypsum boards. The average screwwithdrawal resistance of wood-cement particleboards was 570 N, that is, 1.7 times higher than for gypsum boards.

Main text 1 Introduction

Wood-cement particleboards have been on the market for a long time. At the beginning of the 20 th century, wood wool and magnesite were used to make low-density panels. Later, magnesite was replaced by cement. These panels were used for thermal and acoustic insulation and are still produced. In the late 1960s, "high-density" (specific gravity of about 1.3) woodcement panels, with smaller wood particles processed from industrial wood residues, were developed for structural applications [START_REF] Moslemi | The influence of cement/wood ratio and cement type on bending strength and dimentionnal stability of wood-cement composite panels[END_REF]. Nowadays, these panels are used as exterior walls, roof shingles and tiles for exterior applications. The most significant advantages of wood-cement boards are their high resistance to decay, fungi, insects and fire.

Gypsum boards are commonly used in North America for finishing interior walls and ceilings. They present several advantages: good fire resistance, lightness, low cost and easy installation. They also have drawbacks: low resistance to screw withdrawal, rather low hardness and high sensitivity to moisture. Also, gypsum is not available at low cost everywhere in the world.

The main problem in wood-cement panel design is the compatibility of these two materials. Wood can in fact inhibit cement setting. The effect of wood on cement setting depends on many factors, of which wood species and harvesting season have the greatest impact [START_REF] Govin | Modification of cement hydration at early ages by natural and heated wood[END_REF]. In fact, wood contains extractive compounds that dissolve in the mixing water. It is known that polysaccharides contained in wood extractives are responsible for the inhibition of cement setting [START_REF] Biblis | Sugar and other wood extractives -Effect of the setting of southern pine-cement mixture[END_REF][START_REF] Defo | Wood-cement compatibility of some Eastern Canadian woods by isothermal calorimetry[END_REF][START_REF] Herrera | Compatibility of four eastern Canadian woods with gypsum and gypsum-cement binders by isothermal calorimetry[END_REF][START_REF] Peschard | Effect of polysaccharides on the hydration of cement paste at early ages[END_REF][START_REF] Weatherwax | Effect of wood on setting of Portland cement[END_REF] because they prevent the forming of one of their main hydrates (C-S-H) [START_REF] Thomas | Retarding Action Of Sugars On Cement Hydration[END_REF].

Specific tests have been developed to quantify the compatibility of wood and cement.

Calorimetry allows the classification of wood species as a function of their compatibility with cement [START_REF] Defo | Wood-cement compatibility of some Eastern Canadian woods by isothermal calorimetry[END_REF][START_REF] Hachmi | A new technique to classify the compatibility of wood with cement[END_REF][START_REF] Hofstrand | Curing characteristics of wood particles from nine northern Rocky Mountain species mixed with Portland cement[END_REF][START_REF] Karade | Assessment of wood-cement compatibility: a new approach[END_REF][START_REF] Sandermann | Studies on mineral-bonded wood materials. IV. A short test of the aptitudes of woods for cement-bonded materials[END_REF][START_REF] Sauvat | A study of Ordinary Portland Cement hydration with wood by isothermal calorimetry[END_REF]]. It appears that most softwood species (e.g. pine, spruce and fir) are often more compatible than hardwood species (e.g. birch, maple and beech). A study of Canadian species [START_REF] Defo | Wood-cement compatibility of some Eastern Canadian woods by isothermal calorimetry[END_REF] showed that jack pine (Pinus banksiana Lamb.) presents the highest compatibility of the species studied. It was observed that putting a set accelerating admixture in the mixing water significantly improves compatibility [START_REF] Moslemi | Effect of various treatments and additives on wood-Portland cement-water systèms[END_REF][START_REF] Zhengtian | Influence of chemical additives on the hydration characteristics of western larch wood-cement-water mixture[END_REF], compensating for the inhibitory effect of wood extractive compounds.

The overall objective of this study is to design low-density wood-cement panels with higher resistance to screw withdrawal, higher hardness and less sensitivity to moisture than conventional gypsum boards. Experiments were carried by pouring a wood-cement paste in a mould. The mechanical properties and surface quality of the wood-cement particleboards were improved by using, on the board surfaces, paper sheets that were the same as those used on gypsum boards.

Materials and methods

Design approach

The most important characteristic required was a target specific gravity of about 0.7, similar to that of gypsum boards. To attain this, the wood-cement-water mixture used had a very high W/C ratio -about 1.2. Therefore, water not used for cement hydration occupies a volume during cement setting and then it evaporates, leaving space to air. The porosity created reduces final panel density and confers better insulating properties.

In order to make a low-density panel which is easy to fabricate, the wood-cement panels were not pressed. The wood-cement-water mixture was cast in a mould of the desired shape (560 x 460 x 14 mm 3 ) closed with a cover held in place by C-clamps. This fabrication process is closer to that of concrete than of wood particleboard.

As the wet mixture contained a lot of water (high W/C ratio), the segregation risk was high. The segregation observed here was different from that of conventional concrete because wood particles have a lower density than water. Therefore, wood particles tend to float in the mixture. The solution to this problem was to use an additive to increase the viscosity of the mixture, resulting in a more homogeneous consistency and easier moulding.

The bending modulus of rupture (MOR) of existing wood-cement particleboards with a specific gravity of 1.2 -1.4 is higher than 10 MPa [START_REF] Okino | Physico-mechanical properties and decay resistance of Cupressus spp. cement-bonded particleboards[END_REF]. Our target specific gravity was 0.7 with the aim of obtaining a MOR equal or higher to that of raw gypsum board (about 1.5 MPa) or gypsum board finished with paper (about 8 MPa). If the finishing paper has a good adherence on the panel, it increases its bending properties, including the MOR. The finishing paper provides a good surface for painting.

Materials used

Jack pine (Pinus banksiana) wood chips (obtained from a sawmill located near Shawinigan, Quebec, Canada) were refined in a Pallmann PSKM6 300 ring refiner. The particles were screened and those between 2 and 6 mm were retained.

Two cement types were tested:

o Type 10 cement o Type 30 cement with 5% of aluminous cement in order to obtain a fast setting time without the use of set accelerating admixture A set accelerating admixture ("Polarset" from "Grace" -only for Type 10 cement) and a viscosity modifying admixture ("Euco Nivo L" produced by "Euclide") containing Welan Gum and a superplasticizer were used.

Two types of paper are used in the manufacturing process of gypsum boards. On the top face, the paper is specially adapted for painting. On the back face, the paper has a lower quality.

The same products were used in our study (Commercialised by "Norampac" under trade names "Gypsum-Grey" and "Gypsum-Ivory").

Characterisation tests

In order to characterise and compare wood-cement and gypsum boards, their mechanical properties were tested. Determination of mechanical performance of wood particleboards is usually done following the ASTM D 1037-96 standard [17]. It allows determining the modulus of rupture (MOR) and the modulus of elasticity (MOE) that are the main bending properties of the board. This standard is normally reserved for wood particleboards but we also applied it to gypsum boards, for an easier comparison. It is important to note that the MOR and MOE calculated here have not a physical meaning of stress because the board is a composite and the formulas used are valid for a homogenous material. These properties have to be considered as global criteria that it allows comparison of the materials on a common basis. Screw-withdrawal resistance was also tested following the ASTM D 1037-96 standard.

The thermal properties of the wood-cement particleboards were measured by the fluxmeter method [START_REF] Lassue | Mesures fluxmétriques pour la caractérisation et la gestion optimale d'un mur solaire passif. 2ème colloque "Thermique des Systèmes à Température Modérée[END_REF]. The board was placed between two plates at a regulated temperature and a fluxmeter was glued on each side of it so that temperature and heat flux could be measured at the board surface which can be submitted to temperature variations. Heat capacity and thermal conductivity can be calculated from these four parameters (two temperatures, two heat fluxes).

Preliminary tests on gypsum boards

Preliminary tests were made on gypsum boards, in exactly the same conditions as those of the tests on our wood-cement boards, for comparison. Screw withdrawal-resistance was determined to be 330 N. The bending stiffness and the strength of the gypsum boards are mainly due to the finishing papers. The tensile stiffness and strength of these paper sheets is different along, and perpendicular to, the forming direction of the paper, so the bending tests were performed on samples oriented along these two directions. 1 shows that the finishing paper sheets multiply by 5 the gypsum board resistance in the direction of the fibres.

Preliminary tests on mixing formulation

Preliminary tests were also performed on the wood-cement mixing formulation to obtain a final specific gravity of 0.7. Many formulations were tested to reach the target final specific gravity, mechanical properties and the appropriate texture of the wet mixture. The parameters tested were water-to-cement weight ratio (W/C), wood-to-cement weight ratio (wd/C), quantity of Welan Gum, quantity of set accelerating admixture and board curing time.

Panel density greatly influenced the mechanical properties. This is why the results presented in this paper are not a comparison of mechanical properties obtained for various formulations, but the results obtained for a formulation that led to an appropriate texture and the required specific gravity.

These preliminary tests led to the use of the following characteristics for the formulations in order to obtain a good consistency and a specific gravity of 0.7:

• Water-to-Cement ratio: W/C = 1.15

• Wood-to-Cement ratio: wd/C = 0.5

• Volume percent of Welan Gum (reference: volume of water) = 2%

• Quantity of set accelerating admixture per kg of cement = 100 ml for Type 10 cement and 0 ml for Type 30 cement with 5% of aluminous cement.

Using this formulation the volume of fresh cement paste is about 50%. The mixing consistency was tested with a slump cone for Type 10 cement. The measured value is about 16 to 17 cm, corresponding to a fluid consistency, according to the NFP 18-451 standard.

Method of fabrication

A wooden mould was used to make each panel. It could be closed with a removable cover that allowed the mixture to be poured to a thickness of 15 mm. The surface was then levelled off with a wooden stick to reduce the panel thickness to 14 mm. The inside dimensions of the mould were 560 x 460 x 15 mm 3 when it was open and 560 x 460 x 14 mm 3 when closed.

Mixing was very important. If the mixing characteristics changed, the texture of the wet mixture changed significantly. The mixing sequence retained after preliminary tests is presented in Table 2. The wet mixture was poured into the mould, the surface was levelled off and the cover was fitted. The panel was drawn out of the mould 3 days later. The solid panel was then stored in a climate chamber at 23°C with 60% relative humidity for 9 to 23 days before mechanicals tests.

The procedure used for making wood-cement panels finished with paper is as follows: the backing paper was placed in the bottom of the mould, the wet mixture was poured in and the surface was levelled off; then the top paper was placed on top and the mould was closed.

Adhesion between the cover paper and cement was not investigated specifically at this stage, but based on experimental evidence, it develops satisfactorily with cement hydration, without any special means. Adhesion testing will be performed at a later stage using the gypsum board paper adhesion values as references.

Results and discussion

Change in density

The change in panel mass during curing (3 days in the mould) was measured to determine change in the panels' specific gravity (see Table 3). The specific gravity of the panel decreased by about 5% during the curing. The mould used was, thus, not perfectly impervious. Water was probably absorbed by the wooden mould itself. The panel mass reached a plateau about six days after removal from the mould, meaning that most of the free water of the cement paste had evaporated by then.

Bending properties of the raw wood-cement particleboard

Fourteen days after being made by the procedure described previously, the panels were tested in bending using the method described on section 2.3. The results obtained were about the same for accelerated Type 10 cement and Type 30 cement with 5% of aluminous cement. Tests made on each of the two principal directions of the particleboard did not reveal any differences in this result. Figure 1 shows the bending behaviour of the wood-cement panel compared to gypsum board, both without paper. This test was stopped before rupture but it is clear that, unlike gypsum board, wood-cement particleboard has a ductile behaviour. Table 4 shows the mean results obtained on three test specimens compared to those of gypsum board. It can be seen that the MOR of wood-cement particleboards is 40% higher than that of gypsum boards.

Bending properties of wood-cement particleboard with finishing paper

For Type 30 cement with 5% of aluminous cement, the paper does not stick at all, so use of this kind of cement mix was abandoned for the rest of the study. The results presented below are those obtained with Type 10 cement.

Mechanical tests were carried out on paper-covered boards 12 days after fabrication with a curing time of 3 days. Each test was made on 3 specimens and the mean value is presented here.

Two kinds of specimens were tested in the principal and in the perpendicular direction of the paper fibres. The strain-stress bending characteristics were completely different. In paper fibre direction, the panel had a fragile behaviour, while in the perpendicular direction it was very ductile (Figure 2). This is due to the tensile properties of the paper used that are much higher in the direction of the fibre. So, perpendicular to paper fibre direction, the paper failed at the beginning of the test and has not an important effect on bending test. That is why the panel have a ductile behaviour (as if there were no paper, see Figure 1). In paper fibre direction, the paper has an important contribution on mechanical properties. It plays a role of reinforcement (as steel in reinforced concrete). When the reinforcement failed, the whole board failed; that is why the behaviour is fragile. Table 5 presents the mean mechanical properties obtained for woodcement particleboards and gypsum boards. Twenty-six days after mixing and at the same specific gravity as gypsum boards, woodcement particleboards had a better MOR in the two directions and a 1.7 times higher screwwithdrawal resistance.

Regarding panel cutting, it can be done with a knife in the same way as for gypsum panels. Although the cut edge of the panel is not as neat as for gypsum (see Figure 3), this is not a major problem because panel joints are usually filled with plaster and covered by paper tape. Volume heat capacity 9.6 x 10 5 J m -3 K -1 (n=2, s=1.4 x 10 3 ) 6.8 x 10 5 J m -3 K -1

Table 6 shows the results obtained for the heat capacity and thermal conductivity of wood-cement particleboard and gypsum board using the test method described in section 2.3. It is interesting to note that wood-cement particleboard has quite low thermal conductivity, about three times lower than that of gypsum board. It can contribute to reducing the heating loss of building walls even if the contribution of the board is relatively low, given the insulation of the wall. This low thermal conductivity is mainly due to the high porosity of the wood-cement material compared to gypsum porosity (the conductivity of immobile air is very low, about 0.025 W m -1 K -1 ).

Conclusion

The aim of this project was to study the feasibility of replacing gypsum by wood-cement material in partition boards. These boards are fabricated by pouring the mixture directly on the covering sheet of paper that sticks with no glue, thanks to cement hydration. The mould used has a removable cover. The mixture is composed of jack pine particles obtained by refining wood residues, Type 10 cement, water, a set accelerating admixture to increase wood-cement compatibility and a viscosity modifying admixture to obtain a good wet paste texture.

It was shown that it is possible to make low-density (specific gravity of 0.7) wood-cement particleboard having better bending properties than gypsum board and having a screw withdrawal resistance that is 1.7 times higher. This point is very important because it means that no wall plug is needed to fix a screw if the load on this screw is not too high. These panels can be cut in the same way as for gypsum boards (with a knife), so that the set up process can be the same.

Moreover, the thermal conductivity measured is about three times lower than the one of gypsum board thanks to its high porosity. It is important because it allows increasing thermal resistance of the wall and then lowering building heating demand.

Future work should include a fire-resistance assessment which could be a critical point.

Other physical properties such as acoustic, dimensional stability and water resistance should also be determined. The formulation and the processing phases could be adapted for a better control on the final result and to develop a continuous manufacturing process. Finally, the economics and life cycle of the product should be assessed.

  of water in the mixture wd: Mass of wood in the mixture

Figure 1 :

 1 Figure 1: Characteristic stress-strain curve for a three-point bending test of wood-cement particleboard and gypsum board without paper.

Figure 2 :

 2 Figure 2: Characteristic stress-strain curve for a three-point bending test of wood-cement particleboard with finishing paper.

Figure 3 :

 3 Figure 3: Front of rupture of a wood-cement particleboard cut with a knife (on the right side of the photo; the other side was cut with a saw)

Table 1 :

 1 Bending properties of gypsum panels with and without finishing paper

	Orientation of the gypsum board	MOR (MPa)	MOE (GPa)
	Along principal direction of paper fibres	5.5 (n=5, s=0.05) 2.0 (n=5, s=0.08)
	Perpendicular to principal direction of paper fibres 1.6 (n=5, s=0.09) 1.4 (n=5, s=0.10)
	Without paper	1.1 (n=5,s=0.13) 1.2 (n=5, s=0.11)
	Table

Table 2 : Mixing sequence Added product Time (min) Mass of each component for about 1 L of mixture (g/L)

 2

	Dry materials (wood + cement)	0 min	180g (wd) + 359g (C)
	Water (about 3/4)	1 min	285g (3/4 W)
	Welan Gum (with the water remaining)	2 min	6.8g + 96g (1/4W)
	Set accelerating admixture (liquid)	5 min	48.5g
	Mixing stop	7 min

Table 3 :

 3 Evolution of panel specific gravity

	Stage	Specific gravity
	Manufacturing (wet mixture)	0.95 (+/-0.02)
	Mould removal (3 days after)	0.90 (+/-0.02)
	Long term (more than 9 days after)	0.70 (+/-0.02)

Table 4

 4

		: Bending strength and stiffness of wood-cement
	particleboard and gypsum boards without finishing paper
		Wood-cement particleboard	Gypsum board (without
		(without paper)	paper)
	MOR	2.2 MPa (n=2, s=0.1)	1.1 MPa (n=5, s=0.13)
	MOE	1.3 GPa (n=2; s=0)	1.2 GPa (n=5, s=0.11)

Table 5 :

 5 Mechanical properties of wood-cement particleboards and gypsum boards with finishing paper.

	Property		Gypsum board --	Wood-cement particleboard 12 days 26 days
	Specific gravity		0.7 (+/-0.02)	0.7 (+/-0.02)	0.7 (+/-0.02)
	In paper fibre	MOR	5.5 MPa (n=5, s=0.05)	7.1 MPa (n=4, s=0.9)	10.4 MPa (n=2, s=1.8)
	direction	MOE	2.0 GPa (n=5, s=0.08)	1.6 GPa (n=4, s=0.3)	2.9 GPa (n=2,s=0.4)
	Perpendicular to	MOR	1.6 MPa (n=5, s=0.09)	3.5 MPa (n=2, s=0.5)	5.8 MPa (n=2, s=0.4)
	paper fibre direction	MOE	1.4 GPa (n=5, s=0.10)	1.2 GPa (n=2, s=0.2)	2.2 GPa (n=2, s=0.1)
	Screw withdrawal resistance	330 N (n=3,s=13)	--	570 N (n=3, s=50)

Table 6 :

 6 Comparison of thermal properties of wood-cement and gypsum boards

		Wood-cement particleboard	Gypsum board 1
	Conductivity	0.11 W m -1 K -1 (n=3, s=0.04)	0.32 W m -1 K -1

Values given by "Placo" society for "Gyproc BA13" boards.

Acknowledgements

The authors gratefully thank François Paradis and Maxime Morency who, with their expertise in light concrete, have helped this project to progress. Thanks are also given to Thierry Chartier and Laurent Zalewski for the thermal characteristics measurement and to Aryl Joye for complementary tests on gypsum boards.

Title

Design of a low-density wood-cement particleboard for interior wall finish