Dominic Hames

Dr Yuzhi ; Cai
email: ycai@plymouth.ac.uk

Minimum sample size determination for generalized extreme value distribution

Keywords: Bootstraping, Generalized extreme value distribution, Return level, Sample size Bootstraping, Generalized extreme value distribution, Return level, Sample size

Minimum sample size determination for generalized extreme value distribution

Introduction

Sample size is very important in statistical analysis. However, the sample size required for a study usually depends on different factors such as the probability models used and the types of statistical tests applied. Various methods have been proposed in the literature on sample size determination. For example, [START_REF] Shieh | On power and sample size calculations for likelihood ratio tests in generalized linear models[END_REF] used the likelihood ratio test, [START_REF] Self | Power/sample size calculations for generalized linear models[END_REF] and [START_REF] Lubin | On power and sample size for studying features of the relative odds disease[END_REF] applied the score test, and [START_REF] Bickel | Mathematical Statistics (2nd edn)[END_REF] and [START_REF] Demidenko | Sample size determination for logistic regression revisited[END_REF] considered the Wald test. Ashour and Shalaby (1983) derived some Bayesian and non-Bayesian estimators for sample size when the underlying distribution is a Weibull idstribution, and [START_REF] Ashour | Estimation of sample size for the Burr failure model[END_REF] [START_REF] Marcus | Estimating population size with exponential failure[END_REF] approach to estimate the sample size in the case when the distribution is the Lomax distribution, i.e. the Pareto distribution of the second kind.

The generalized extreme value (GEV) distribution has been used widely in many areas because the extreme value theory guarantees that the maximum group values will follow a GEV distribution if the group size tends to infinity. For example, in coastal engineering, we could assume that the maximum annual sea-levels will approximately follow the GEV distribution, and hence a GEV model is often fitted to the maximum annual data. In this paper, we study the sample size determination in the case when the underlying distribution is the GEV distribution, and we assume that the group size is large enough for us to use the GEV model. However, in reality limited data sets are available , or it can be very expensive or even impossible to collect a large number of such data. Therefore, it is very important to develop a method for estimating the accuracy of any study or the minimum sample size required for such a study. Let x i (i = 1, . . . , n) be the maximum value of group i. It is well known that under certain regular conditions the maximum likelihood estimators (MLE) of the parameters are normally distributed as n approaches infinity. However, for any finite values of n, the distributions of the estimators are unknown, and hence the distributions of any functions of the estimators, such as return levels, are also unknown.

The main purpose of the paper is to develop a method for determining the minimum sample size based on the asymptotic distribution of MLEs. We will focus on the return level as it is a very important quantity in coastal engineering and environmental sciences and it provides crucial information in, for example, the design of flood defences. The developed methodology can be easily extended to other models and other quantities of interest. The arrangement of the paper is as follows. In Section 2, we develop the methodology for determining the sample size. Simulation studies are given in Section 3 and applications in Section 4. Some discussions and conclusions are given in Section 5.

The method

The GEV distribution function is defined by

F (x; µ, σ, ξ) = e -[ 1+ξ ( x-µ σ )] -1/ξ (1) for 1 + ξ x-µ σ > 0,
where µ ∈ R is the location parameter, σ > 0 the scale parameter and ξ ∈ R the shape parameter. Let β = (µ, σ, ξ) be the parameter vector. Suppose we are interested in estimating the τ th quantile of the GEV, which is given by

x = µ - σ ξ [1 -(-ln τ ) -ξ ], (2)
where 0 < τ < 1. So, if τ = 0.99, the 0.99th quantile may correspond (in an analysis of annual maxima) to the 100-year return level. We need to decide the minimum sample size so that the statistical inferences on the return level are proper. Note that in the following we illustrate our method by using the 100-year return level, any other quantities of interest can be dealt with similarly.

The basic idea of the proposed method is given below. If the sample size n is large enough, then the maximum likelihood estimator (MLE) of β should be normally distributed, hence any functions of the MLE, such as the return level. As we only have one observed data set, it would be difficult to check the normality of the MLE of the return level. Therefore, we propose to apply the bootstrap method with replacement to the observed data set. Suppose we generated M bootstrap samples each of size n. Then we should expect that the MLEs of the return level based on the bootstrap samples should also be normally distributed. Standard bootstrap methodology guarantees that the MLEs form a random sample of a normal distribution for the return level. In this paper, we use the Shapiro-Wilk test to check the normality of the MLEs of the return level. If we have to reject the null hypothesis, i.e. the MLEs are normally distributed, then we may conclude that the sample size n is not large enough at a given significant level. So we need to collect more samples and to apply the above procedure to the enlarged sample. This process should be continued until we failed to reject the null hypothesis. The details of the method are given below.

Let y 1 = (y 11 , . . . , y 1n ) be the observed data.

Step 1. Obtain M -1 bootstrap samples (with replacement) from y 1 , denoted by y m = (y m1 , . . . , y mn ), where m = 2, . . . , M .

Step 2. For m = 1, . . . , M , let x

(1) mj be the first j values of y m . That is x

(1) mj = (y m1 , . . . , y mj ), where j = n 0 , . . . , n and n 0 is large enough for parameter estimation.

Step 3. For fixed j, obtain K -1 bootstrap samples (with replacement) from x Step 5. Carry out the Shapiro-Wilk normality test on (k) mj (k = 1, . . . , K) and record the p-value, denoted by p mj , of the test statistic, where m = 1, . . . , M and j = n 0 , . . . , n.

Step 6. For j = n 0 , . . . , n calculate

pj = 1 M M m=1 p mj , s 2 j = 1 M -1 M m=1 (p mj -pj ) 2 .
and construct a 100(1 -α)% confidence interval pj ± t * s j , where t * is the critical value obtained from a t-distribution with M -1 degrees of freedom.

Step 7. Let N be the number such that for any j > N we have pj -t * s j > α. As pj -t * s j is the lower band of the confidence interval, we are 100(1 -α)% confident that the minimum number of samples required for obtaining a properly estimated return level is N . It is worth mentioning that the standard theory of maximum likelihood was developed for the case when the support of the distribution does not depend on unknown parameters, see, for example, Rao (1993). For GEV distribution, this is not the case because the support of the distribution must satisfy 1 + ξ(x -µ)/σ > 0. However, [START_REF] Smith | Maximum likelihood estimation in a class of non-regular cases[END_REF] studied this problem thoroughly and showed that (a) if ξ > -0.5, then the MLEs of the model parameters are asymptotically normally distributed; (b) if -1 < ξ < -0.5, then the MLEs can be obtained but are not asymptotically normally distributed; and (c) if ξ < -1, then it is usually not possible to obtain the MLEs. Note that when ξ ≤ -0.5, the GEV distribution has a very short bounded right tail which, as Cole (2001) pointed out, is rarely encountered in applications of extreme value analysis. Therefore the theoretical limitations of the maximum likelihood method have little effect in practice. So in this paper we focus on the case ξ > -0.5. Indeed, all the real data sets considered in this paper have a reasonable long right tail, and hence the developed method can be safely applied.

To investigate the performance of the proposed method, we carried out extensive simulation studies which are given in the next section.

Simulation studies

Simulation study 1

Consider the GEV model given by

F (x; µ, σ, ξ) = e -[1-0.11(x-100)/13] 1/0.11 (3)
for 1 -0.11 (x -100) /13 > 0. So, the true parameter values are: µ = 100, σ = 13 and ξ = -0.11. Furthermore, the 100-year return level is given by

x = 100 + 13[1 -(-ln 0.99) 0.11 ]/0.11 = 146.93, (4)
Note that the true parameter values were chosen arbitrarily.

The statistical software R was used to generate a random sample of size n = 200 from the above GEV model. In this simulation study, we take M = K = 50, n 0 = 25 and α = 0.05. By applying the developed method to this data set, we obtained the results shown in Figure 1, where the lighter curve shows the average p-values pj against the sample size j = 25, . . . , 200, the darker curves are the corresponding lower and upper limits of the 95% confidence interval, i.e. pj ± t * s j (j = 25, . . . , 200). The horizontal line is at α = 0.05, and the vertical line is at N = 40. It is seen that for j ≥ 40 all curves are above the horizontal line, indicating that the minimum sample size we could take is N = 40 in this case. So if the data represent the maximum annual values of sea levels at a particular site, then 40 years' data would give a for good estimate of the return levels in terms of the normality of the MLE. Now we compare the two fitted GEV models: one was fitted to the first 40 values of the simulated data, the other to all the data. The true and the estimated values are shown in Table 1 smaller than those based on the first 40 values. However, the estimated values are all very similar to the true parameter values. Note that the standard error of the estimated return level was obtained by using the delta method, and that a 95% confidence interval for each parameter can be constructed easily by using the estimated standard errors. The diagnostic plots in Figure 2 also shows that the two fitted models are very similar.

Simulation study 2.

In simulation study 1 we only dealt with one simulated data. In this simulation study, we repeat the above simulation study on 70 independently simulated data sets, each of size 200. So the average performance of the method can be assessed.

For each simulated data and for different sample sizes, we recorded the sample average p-values of the test statistic. Then the final average p-values are obtained by averaging over the 70 simulated data sets. Figure 3 shows the average p-values against the sample size and the corresponding 95% confidence interval. The lower limit of the confidence interval at a sample size N = 40 is 0.047, and for any sample size n > 40, all the curves are above the horizontal line. This suggests that on average, the performance of the method is very stable over different simulated data sets.

Applications

In the applications of the developed method, we consider four real data sets obtained from [START_REF] Reiss | Statistical analysis of extreme values[END_REF]. The first data set is the maximum annual sea-levels (in meters) in Venice from 1931 to 1981, containing 51 values. The mean sea level at Venice is 0.52m.

In this application we consider the sea levels relative to the mean sea level. The second data set is the Iceland maximum annual wind speed (in meters per second) data in the years 1912 to 1992 with measurements for two years missing. We ignore the missing data in this application, hence the data set contains 79 values. The third data set is the maximum annual discharges (in cubic meters per second) of the Harricana River at Amos (Quebec, Canada) from 1915 to 1983, containing 69 values. The fourth data set is the maximum annual De Bilt temperatures (in Celsius) from 1849 to 1981, containing 133 values. The scatter plots of the four data sets are given in Figure 4.

All the four data sets are not long. We would like to estimate the minimum sample size required for making reasonable statistical inferences on the 100-year return level, and hence to see what confidence we can place in these estimates and whether further data are required.

Because the data are annual maximums, it is reasonable to fit a GEV model to each data set, hence the developed method can be used. For each of them, the minimum sample size was taken to be 25, because for smaller sample sizes we often have difficulties in fitting a GEV model to them. The largest sample size was taken to be the total number of observations in each data set. Furthermore, the number of bootstrap samples obtained from each data set and from its subsets with different sample sizes is 50. That is, we let M = K = 50. For larger values we have very similar results. Figure 5 shows the average p-values of the Shapiro-Wilk test statistic together with a 95% confidence interval for each data set, where the horizontal lines are at α = 0.05, and the vertical lines are at 50, 72, 44 and 44 respectively, indicating the minimum sample size required in each case. Note that the total sample size of Venice sea-levels is only 51. Figure 5(a) shows it is difficult to make a sensible conclusion about the minimum sample size required in this case. So more data need to be collected. Figure 5(b) shows that all three curves are above the horizontal line for sample sizes greater than 71. This suggests that the minimum sample size can be taken as N = 72. Both Figure 5(c) and(d) suggest that the minimum sample size can be taken as N = 44. Therefore, except for the Venice sea-levels data set, all other data sets are large enough for making good statistical inferences on the return level.

To compare the model fitted to the data of minimum sample size with the model fitted to the whole data set, we produced Table 2 which shows that no significant differences at a 95% level between the two estimated return levels for each data set: one is based on the minimum sample sizes and the other is based on the whole data sets. This is because the corresponding 95% confidence intervals overlap. Note that the larger standard error value in the second row of Table 2 for the Iceland maximum annual wind speed data is caused by the approximation features of the delta method in calculating return levels for this data set.

Figure 6 shows the return level plots for the sea-level and wind-speed data sets, while Figure 7 is for the discharge and temperature data sets. In both figures, the left column corresponds to the minimum sample size, and the right column corresponds to the whole data set. These figures also show no significant differences in estimating return levels caused by using the minimum sample sizes.

A further statistical inferences about the sample size effects on the accuracy of the return levels can be carried out. We should expect that, generally, the standard errors of the MLEs of the return level decreases as the sample size increases. These standard errors tell us how much gain we will have if we increase the sample size. In other words, how much it would be worth paying to obtain a greater length of data. Figure 8 shows the average standard errors of the MLEs of the return level when the sample size increases from the minimum sample size up to another 300 data. Those 300 extra data were simulated from the fitted model by using the observed samples of minimum length. The average standard errors are based on 50 independently simulated samples each of size 300. From these plots, say, from Figure 8(b), we see that if we require the standard error of the MLE is less than 2.0, then we need at least 120 data instead of 72. That means that extra 48 data need to be collected in order to decrease the standard error of the MLE of the return level from 2.79

Return Level Plot

Figure 6: The return level plots of the GEV models fitted to the data of minimum sample sizes (left column), and the return level plots of the GEV models fitted to the whole data sets (right column). First row is for the Venice sea-level data, and the second row is for the Iceland wind-speed data.

11 to 2.0. This would provide useful information for a company to decide whether new data are worth collecting.

Return Level Plot

Comments and conclusion

In this paper, we proposed a simple method to determine the minimum sample size required for making statistical inferences on a statistical quantity of interest. The developed methodology is based on the standard theory of maximum likelihood and we illustrated the method through the estimation of the 100-year return level by using a GEV model. It is worth mentioning that for other probability models and other quantities of interest, the method proposed in this paper can also be used, provided that the MLE is normally distributed in large samples. However, we would expect that the minimum sample sizes required by making statistical inferences on different quantities may be different. Simulation studies and application results show that the method can be easily implemented and the fitted models based on the minimum sample size are very similar to the fitted models based on all the available data.

In this paper we have also demonstrated different applications of the developed method. In summary, this method can be used (a) to check whether an existing data set is long enough for making good statistical inference, (b) to decide how many more data need to be collected for making good statistical inference and (c) to make sure how much gain we will have in terms of confidence if we increase the sample size. Therefore, we expect that the developed method can be very useful in practice. We sincerely thank the referees for their very helpful comments and suggestions, according to which the paper has been modified. A separate paragraph has been added at the end of Section 2 to explain why the developed method can be used to GEV distributions. We also re-emphasized the asymptotic normality condition at the last section of the paper. An acknowledgement has also been added into the paper to thank the referees' comments which has improved the quality and the presentation of the paper significantly. The detailed responses are given below.

Referee's comments:

The standard theory of maximum likelihood is developed for the case when the distribution domain does not depend on unknown parameters, e.g. C.R. Rao (1993), "Linear Statistical Inference and Its Applications," New York: Wiley. Unfortunately, GEM, as defined in equation (1), does, namely, 1+ksi*(xmu)/sigma>0. The authors should provide theoretical justification why MLE is normally distributed in large sample.

Responses:

This is an excellent comment, many thanks! A separate paragraph has been added into the paper to discuss this problem. Generally speaking, Smith 2001) pointed out, is rarely encountered in applications of extreme value analysis. Therefore the theoretical limitations of the maximum likelihood method have little effect in practice. So in this paper we focus on the case kxi > -0.5. Indeed, all the real data sets considered in this paper have a reasonable long right tail, and hence the developed method can be safely applied.

The last section of the paper has also been modified to re-emphasize the importance of the asymptotic normality condition.

The reference C.R. Rao (1993) has also been added into the paper.

  also derived these estimators in the case of Burr type XII failure model. Abd-Elfattah and Bakoban (2003) obtained the estimators for sample size in case of a generalized gamma distribution, and et al. (2007) considered the

  mj , where k = 2, . . . , K. Step 4. Fit a GEV model to each data set x (k) mj , and calculate the return level (k) mj , m = 1, . . . , M , j = n 0 , . . . , n, k = 1, . . . , K.

3

 3

Figure 2 :

 2 Figure 2: The probability plot and the return level plot of the GEV models fitted to the first N = 40 simulated data (left column), and to the whole data set (right column) respectively in the Simulation Study 1. On the return level plots, the top and the bottom curves give a 95% confidence bands for the return levels.

6 Page 7 Figure 3 :

 673 Figure 3: Average p-values over 70 different simulated data sets together with a 95% confidence interval in the Simulation Study 2.

7

 7

Figure 4 :

 4 Figure 4: Scatter plots of (a) the maximum annual sea-levels in Venice, (b) the maximum annual wind speed in Iceland, (c) the maximum annual discharges of the Harricana River and (d) the maximum annual De Bilt temperature data.

Figure 5 :

 5 Figure 5: Average p-values and the corresponding 95% confidence interval for (a) the maximum annual sea-levels in Venice, (b) the maximum annual wind speed in Iceland, (c) the maximum annual discharges of the Harricana River and (d) the maximum annual De Bilt temperature data.

Figure 7 : 12 Page

 712 Figure7: The return level plots of the GEV models fitted to the data of minimum sample sizes (left column), and the return level plots of the GEV models fitted to the whole data sets (right column). First row is for the discharges of the Harricana River data, and the second row is for the De Bilt temperature data.

Figure 8 :

 8 Figure 8: The plots of the average standard errors of the MLEs of the return level against sample sizes for (a) the maximum annual sea-levels in Venice, (b) the maximum annual wind speed in Iceland, (c) the maximum annual discharges of the Harricana River and (d) the maximum annual De Bilt temperature data.

(

  1985) studied this problem thoroughly and showed that (a) kxi>-0.5, then the MLEs of the model parameters are asymptotically normally distributed; (b) if -1<kxi<-0.5, then the MLEs can be obtained but are not asymptotically normally distributed; and (c) if kxi<-1, then it is usually not possible to obtain the MLEs. Note that when kxi Page 17 of 17 URL: http://mc.manuscriptcentral.com/lssp E-mail: comstat@univmail.cis.mcmaster.5 , the GEV distribution has a very short bounded right tail which, as Cole (

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Table 1 :

 1 . As expected, the standard errors of the MLEs based on the whole data sets are True and estimated parameter values together with their standard errors (in brackets).

	4

Figure 1: Plot of the average p-values of the Shapiro-Wilk Normality test statistics together with a 95% confidence interval in the Simulation Study 1.

URL: http://mc.manuscriptcentral.com/lssp E-mail: comstat@univmail.cis.mcmaster.

ca Communications in Statistics -Simulation and Computation

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

Table 2 :

 2 Estimated return levels, where Return level 1 corresponds to the model fitted to data of minimum sample size, while the Return level 2 corresponds to the model fitted to all the data. Numbers in brackets are the corresponding standard errors.

	8

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								Page 12 of 17
				Return Level Plot		Return Level Plot
	Return Level	100 200 300	F r o	Return Level	100 200 300
			1e-01	1e+01 P e Return Period	1e+03	1e-01	1e+01 Return Period	1e+03
				e r Return Level Plot
	Return Level	28 30 32 34 36	1e-01	1e+01	R e v i e 1e+03 1e-01 w 28 36 32 Return Level	1e+01	1e+03
				Return Period		l n O Return Period
							y

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Communications in Statistics -Simulation and Computation

Acknowledgement

We would like to express our sincere thanks to the referees for their very constructive comments and suggestions which have greatly enhanced the quality and the presentation of the paper.


Silvia Caponi
email: caponi@science.unitn.it

Aldo Fontana

F Rossi

Marco Zanatta

Influence of

Keywords: glass, Raman spectroscopy, vitrification user supplied): quasi elastic scattering, vitreous germania glasses, vitreous germania, quasi elastic scattering, Raman light scattering glass, Raman spectroscopy, vitrification user supplied): quasi elastic scattering, vitreous germania glasses, vitreous germania, quasi elastic scattering, Raman light scattering

come

Introduction

During the past 10 years, many works have been devoted to study the structural and dynamical properties of complex materials [1][2][3][4][5]. One of the main problems is to understand the modification of the vibrational dynamics due to topological disorder of the system [6][7][8][9][10][11]. The fast dynamics in disordered systems includes two main contributions: the first is the low-frequency collective vibrations, the socalled boson peak (BP), and the second the relaxation dynamics that appears in light and neutron scattering spectra as quasielastic intensity (QES). Both these contributions are observed in spectra of all glass-forming systems as well as porous systems, polymers, and biological systems [13][14][15][16][17][18][19][20][21]. Hence, they are common features of dynamics in complex systems. Long times ago [22], the QES was assigned to the light coupling with relaxations of atoms or group of atoms between almost equivalent equilibrium positions described by a double well potential. This coupling can be direct or indirect; recently Sokolov et al. [19] have reported convincing results on v-SiO 2 and polystyrene in favor of the indirect mechanism. Substantially, according to this hypothesis, the contribution to the light scattering comes from the mechanical coupling of defects to the sound waves. Different studies were preformed to relate the QES temperature and frequency behaviors with the damping of acoustic modes [16][17][18][19]23]. In this paper, we report a detailed investigation of the low frequency Raman spectrum (< 200 cm -1 ) of vitreous and melted germania in a very large temperature range, from 10 K up to 1000 K, extending the temperature range investigated till now [21]. We compare our data with acoustic attenuation data in the framework of Jäckle model [22]. Our results suggest, indeed, that the acoustic attenuation involves the same physical mechanisms responsible for QES as discussed in this paper.

Experimental and Results

Our sample was prepared from GeO 2 powder (Aldrich, 99.99%) melted in platinum crucibles for about 1h at 1600 • C. The homogeneous and bubble free melt was subsequently quenched in air. The absence of crystallization was checked before the experiment by X-ray diffraction measurements. The samples were then polished in order to obtain good optical surfaces.

Raman scattering experiments, in a 90 • scattering geometry, were done using a standard experimental setup Jobin-Yvon U1000 in a wide frequency range, from -300 to 3000 cm -1 , in order to correctly subtract the underlying weak background of luminescence [25]. The light polarizations were perpendicular, VV and orthogonal, HV, to the scattering plane. Figure 1 shows the depolarized reduced intensity measured on v-GeO 2 , defined as:

I Red R (ω) = I Exp (ω) [n(ω, T ) + 1]ω ; ( 1
)
where I exp (ω) is the experimental datum and n(ω, T ) is the Bose-Einstein population factor. In order to compare spectra taken at different temperatures, they are normalized at the high frequency peaks, as shown in fig. 1c). The spectra show the BP, peaked at ∼ 50 cm -1 , and at lower frequency the QES. The lower panel, figure 1b) shows that, increasing temperature up to room temperature, there is no intensity variation of the BP. On the contrary, a strong increase of the scattering is observed at the 1a). Here, increasing temperature, the QES present an increasing less marked than before, while the BP shifts to lower frequency increasing its intensity. The boson peak temperature behaviour is not the object of the present work and we do not discuss it further, this study can be found in ref. [26].

We can model the Raman intensity in HV polarization as the sum of QES and BP contributes [17]:

I Red R = I QES (ω) + I BP (ω); (2)
where:

I BP (ω) = C v (ω)g(ω) [n(ω, T ) + 1] ω , (3)
and

I QES (ω) = C rel (ω)L(ω, T ), (4)
are the QES and BP contribution to the spectrum. Here v indicates the vibrational part, and rel the relaxation part; C(ω) is the coupling light-vibration function and g(ω) is the vibrational density of states. The QES contribution is described by the function L(ω, T ).

In the present investigation of the low frequency Raman scattering, we are able to measure the spectrum down to frequency shifts of 4 cm -1 . The increase below ∼ 4 cm -1 is caused by an elastic scattering due to a finite resolution of the spectrometer (∼ 2 cm -1 ). From the Raman spectra we have extracted the scattered intensity as function of temperature at 6 cm -1 integrating the signal in a frequency window of 1 cm -1 . The temperature dependence I QES (6cm -1 ) is shown in fig. 2 as dots: we can note a rapid increase up to T = 500 K, then a plateau which extend up to 800 K and, finally, a strong increase at higher temperatures. It's worth to notice that, at the chosen frequency, the evolution of the QES is not influenced by the shift and the intensity variation of the BP. This is evidenced in figure 2 where is also reported the evolution of the QES obtained from the squeezed spectra (triangles). In fact, dividing the x axis of the spectra by the frequency position of the Boson Peak maximum and scaling the Raman intensity imposing as well the conservation of the total number of vibrational states, a BP master curve has been obtained in a wide class of materials [13][14][15]17]. This procedure, called squeezing, is well described in the case of GeO 2 in ref. [26], where the squeezed spectra are presented at chosen temperatures from the liquid to the glassy phase. In that representation, the evolution of the QES is completely disentangled by the eventual intensity modification due to the BP variations. As reported in fig. 2, the comparison of the QE signals obtained in different ways presents slightly differences in the high temperature range, but the overview is not modified. In this work we try to understand the microscopic origin of QES analyzing its temperature evolution.

Discussion

As already suggested in literature [22] the QES can be due to the scattering from structural defects or damped sound waves which are characteristic of glassy state.

In fact the thermally activated relaxation process (TARP) can couple to light . Intensity of Quasi Elastic Scattering measured from the Raman spectra (dots) at 6 cm -1 as function of temperature; and intensity of Quasi Elastic Scattering at some chosen temperatures obtained from the squeezed spectra [26] in order to single out eventual contribution of the Boson Peak intensity variation (triangles).

directly, as was originally proposed by Jäckle [22] or indirectly, by coupling to phonons [19]. In order to compare our data with those obtained by the acoustic attenuation, we consider the internal friction, Q -1 , which is related to the QES scattering by Q -1 ∝ L(ω)ω [17]. In Eq. 4, the QES contribution, described by the function L(ω, T ), can be formulated as [22] L(ω, T )

∝ dV P (V ) τ (V ) 1 + ω 2 τ 2 (V ) (5)
where τ (V ) is the relaxation time for potential barriers of height V , and P (V ) is the distribution of barrier heights. Different choices of the distribution of barriers have been proposed in literature [22][23][24]27]. Concerning the model dependence of the analysis, it should be noticed that the frequency dependence it is found to be almost unaffected by the choice of the distribution function as already reported by Gilroy and Phillips [23] in the case of silica, while slight differences have been evidenced in the temperature evolution. We choose a Gaussian distribution, P (V ), of barriers V having a variance σ V . This distribution has been already used in the case of vitreous germania to optimize the acoustic attenuation data in a wide frequency and temperature range [24,29].

The results are shown in fig. 3. Here we report the acoustic attenuation measured in the ultrasonic region (20 MHz) [30], the one measured by Brillouin light scattering (25 GHz) [28] and the rescaled QES data at 180 GHz. The continuous curves are computed with parameters: σ V = 1750 K, τ 0 = 1.47 • 10 -14 s and A = 0.18. The parameter are the same reported in ref. [29] where the analysis of the acoustic To report the QES intensity in fig 3, we normalized the data on the extrapolation at 180 GHz. The good agreement between the QES and the acoustic attenuation extrapolated between 10 K e 800 K at the same frequency indicates the common origin of the two phenomena. At temperatures higher than 800 K the parallel ends and the QES increases while the extrapolation of acoustical attenuation at higher temperatures decreases. This difference could be due to the occurrence at these temperatures (higher than T g ) of the structural modifications from the glassy state to the liquid one, which contributes to QES with another relaxational process.

Conclusions

In conclusion, the similar spectral shape and temperature dependence of Raman data, in comparison with the temperature dependence of the acoustical attenuation, support the idea that QES and sound attenuation are due to the same mechanism. Following the interpretation of ultrasonic absorption this mechanism is described by a hopping model for structural defects with different atomic configurations of the structure.

F

Introduction

During the past 10 years, many works have been devoted to study the structural and dynamical properties of complex materials [1][2][3][4][5]. One of the main problems is to understand the modification of the vibrational dynamics due to topological disorder of the system [6][7][8][9][10][11]. The fast dynamics in disordered systems includes two main contributions: the first is the low-frequency collective vibrations, the socalled boson peak (BP), and the second the relaxation dynamics that appears in light and neutron scattering spectra as quasielastic intensity (QES). Both these contributions are observed in spectra of all glass-forming systems as well as porous systems, polymers, and biological systems [13][14][15][16][17][18][19][20][21]. Hence, they are common features of dynamics in complex systems. Long times ago [22], the QES was assigned to the light coupling with relaxations of atoms or group of atoms between almost equivalent equilibrium positions described by a double well potential. This coupling can be direct or indirect; recently Sokolov et al. [19] have reported convincing results on v-SiO 2 and polystyrene in favor of the indirect mechanism. Substantially, according to this hypothesis, the contribution to the light scattering comes from the mechanical coupling of defects to the sound waves. Different studies were preformed to relate the QES temperature and frequency behaviors with the damping of acoustic modes [16][17][18][19]23]. In this paper, we report a detailed investigation of the low frequency Raman spectrum (< 200 cm -1 ) of vitreous and melted germania in a very large temperature range, from 10 K up to 1000 K, extending the temperature range investigated till now [21]. We compare our data with acoustic attenuation data in the framework of Jäckle model [22]. Our results suggest, indeed, that the acoustic attenuation involves the same physical mechanisms responsible for QES as discussed in this paper.

Experimental and Results

Our sample was prepared from GeO 2 powder (Aldrich, 99.99%) melted in platinum crucibles for about 1h at 1600 • C. The homogeneous and bubble free melt was subsequently quenched in air. The absence of crystallization was checked before the experiment by X-ray diffraction measurements. The samples were then polished in order to obtain good optical surfaces.

Raman scattering experiments, in a 90 • scattering geometry, were done using a standard experimental setup Jobin-Yvon U1000 in a wide frequency range, from -300 to 3000 cm -1 , in order to correctly subtract the underlying weak background of luminescence [25]. The light polarizations were perpendicular, VV and orthogonal, HV, to the scattering plane. Figure 1 shows the depolarized reduced intensity measured on v-GeO 2 , defined as:

I Red R (ω) = I Exp (ω) [n(ω, T ) + 1]ω ; ( 1
)
where I exp (ω) is the experimental datum and n(ω, T ) is the Bose-Einstein population factor. In order to compare spectra taken at different temperatures, they are normalized at the high frequency peaks, as shown in fig. 1c). The spectra show the BP, peaked at ∼ 50 cm -1 , and at lower frequency the QES. The lower panel, figure 1b) shows that, increasing temperature up to room temperature, there is no intensity variation of the BP. On the contrary, a strong increase of the scattering is observed at the Philosophical Magazine PhMCaponi lower frequency. Above room temperature the scenario is different, fig. 1a). Here, increasing temperature, the QES present an increasing less marked than before, while the BP shifts to lower frequency increasing its intensity. The boson peak temperature behaviour is not the object of the present work and we do not discuss it further, this study can be found in ref. [26].

We can model the Raman intensity in HV polarization as the sum of QES and BP contributes [17]:

I Red R = I QES (ω) + I BP (ω); (2)
where:

I BP (ω) = C v (ω)g(ω) [n(ω, T ) + 1] ω , (3)
and

I QES (ω) = C rel (ω)L(ω, T ), (4)
are the QES and BP contribution to the spectrum. Here v indicates the vibrational part, and rel the relaxation part; C(ω) is the coupling light-vibration function and g(ω) is the vibrational density of states. The QES contribution is described by the function L(ω, T ).

In the present investigation of the low frequency Raman scattering, we are able to measure the spectrum down to frequency shifts of 4 cm -1 . The increase below ∼ 4 cm -1 is caused by an elastic scattering due to a finite resolution of the spectrometer (∼ 2 cm -1 ). From the Raman spectra we have extracted the scattered intensity as function of temperature at 6 cm -1 integrating the signal in a frequency window of 1 cm -1 . The temperature dependence I QES (6cm -1 ) is shown in fig. 2 as dots: we can note a rapid increase up to T = 500 K, then a plateau which extend up to 800 K and, finally, a strong increase at higher temperatures. It's worth to notice that, at the chosen frequency, the evolution of the QES is not influenced by the shift and the intensity variation of the BP. This is evidenced in figure 2 where is also reported the evolution of the QES obtained from the squeezed spectra (triangles). In fact, dividing the x axis of the spectra by the frequency position of the Boson Peak maximum and scaling the Raman intensity imposing as well the conservation of the total number of vibrational states, a BP master curve has been obtained in a wide class of materials [13][14][15]17]. This procedure, called squeezing, is well described in the case of GeO 2 in ref. [26], where the squeezed spectra are presented at chosen temperatures from the liquid to the glassy phase. In that representation, the evolution of the QES is completely disentangled by the eventual intensity modification due to the BP variations. As reported in fig. 2, the comparison of the QE signals obtained in different ways presents slightly differences in the high temperature range, but the overview is not modified. In this work we try to understand the microscopic origin of QES analyzing its temperature evolution.

Discussion

As already suggested in literature [22] the QES can be due to the scattering from structural defects or damped sound waves which are characteristic of glassy state.

In fact the thermally activated relaxation process (TARP) can couple to light . Intensity of Quasi Elastic Scattering measured from the Raman spectra (dots) at 6 cm -1 as function of temperature; and intensity of Quasi Elastic Scattering at some chosen temperatures obtained from the squeezed spectra [26] in order to single out eventual contribution of the Boson Peak intensity variation (triangles).

directly, as was originally proposed by Jäckle [22] or indirectly, by coupling to phonons [19]. In order to compare our data with those obtained by the acoustic attenuation, we consider the internal friction, Q -1 , which is related to the QES scattering by Q -1 ∝ L(ω)ω [17]. In Eq. 4, the QES contribution, described by the function L(ω, T ), can be formulated as [22] L(ω, T ) ∝ dV P (V )

τ (V ) 1 + ω 2 τ 2 (V ) (5)
where τ (V ) is the relaxation time for potential barriers of height V , and P (V ) is the distribution of barrier heights. Different choices of the distribution of barriers have been proposed in literature [22][23][24]27]. Concerning the model dependence of the analysis, it should be noticed that the frequency dependence it is found to be almost unaffected by the choice of the distribution function as already reported by Gilroy and Phillips [23] in the case of silica, while slight differences have been evidenced in the temperature evolution. We choose a Gaussian distribution, P (V ), of barriers V having a variance σ V . This distribution has been already used in the case of vitreous germania to optimize the acoustic attenuation data in a wide frequency and temperature range [24,29].

The results are shown in fig. 3. Here we report the acoustic attenuation measured in the ultrasonic region (20 MHz) [30], the one measured by Brillouin light scattering (25 GHz) [28] and the rescaled QES data at 180 GHz. The continuous curves are computed with parameters: σ V = 1750 K, τ 0 = 1.47 • 10 -14 s and A = 0.18. The parameter are the same reported in ref. [29] where the analysis of the acoustic To report the QES intensity in fig 3, we normalized the data on the extrapolation at 180 GHz. The good agreement between the QES and the acoustic attenuation extrapolated between 10 K e 800 K at the same frequency indicates the common origin of the two phenomena. At temperatures higher than 800 K the parallel ends and the QES increases while the extrapolation of acoustical attenuation at higher temperatures decreases. This difference could be due to the occurrence at these temperatures (higher than T g ) of the structural modifications from the glassy state to the liquid one, which contributes to QES with another relaxational process.

Conclusions

In conclusion, the similar spectral shape and temperature dependence of Raman data, in comparison with the temperature dependence of the acoustical attenuation, support the idea that QES and sound attenuation are due to the same mechanism. Following the interpretation of ultrasonic absorption this mechanism is described by a hopping model for structural defects with different atomic configurations of the structure.

Figure 1 .

 1 Figure 1. pannel a) and b) Raman spectra at chosen temperatures as shown in the label. c) high frequency part of spectra at some significant temperatures.

  Figure2. Intensity of Quasi Elastic Scattering measured from the Raman spectra (dots) at 6 cm -1 as function of temperature; and intensity of Quasi Elastic Scattering at some chosen temperatures obtained from the squeezed spectra[26] in order to single out eventual contribution of the Boson Peak intensity variation (triangles).

  analyzed over more than three decades in frequency.

Figure 3 .

 3 Figure 3. experimental data for Q -1 measured at 20 MHz (circles)[30], 25 GHz (stars). Lines are the evaluation of the TARP model at the same frequencies and the extrapolation at 6 cm -1 . Dots are the rescaled I QES .

Figure 1 .

 1 Figure 1. pannel a) and b) Raman spectra at chosen temperatures as shown in the label. c) high frequency part of spectra at some significant temperatures.

Figure 2

 2 Figure2. Intensity of Quasi Elastic Scattering measured from the Raman spectra (dots) at 6 cm -1 as function of temperature; and intensity of Quasi Elastic Scattering at some chosen temperatures obtained from the squeezed spectra[26] in order to single out eventual contribution of the Boson Peak intensity variation (triangles).

  analyzed over more than three decades in frequency.

Figure 3 .

 3 Figure 3. experimental data for Q -1 measured at 20 MHz (circles)[30], 25 GHz (stars). Lines are the evaluation of the TARP model at the same frequencies and the extrapolation at 6 cm -1 . Dots are the rescaled I QES .

http://mc.manuscriptcentral.com/pm-pml Philosophical Magazine & Philosophical Magazine Letters


Dorthe Grabau
email: dorthe.grabau@skane.se

Lisa Rydén

Marten Ferno

Christian Ingvar

Analysis of sentinel node biopsy -a single institution experience supporting the use of serial sectioning and immunohistochemistry for detection of micrometastases by comparing four different histopathologic laboratory protocols

Keywords: Sentinel node biopsy, breast cancer, immunohistochemistry, micrometastases, ITC Sentinel node biopsy, breast cancer, immunohistochemistry, micrometastases, ITC ALND, axillary lymph node dissection, FFPE, formalin fixed paraffin embedded, HE, haematoxylin and eosin, IHC, immunohistochemistry, ITC, isolated tumor cells, SLN, sentinel lymph node Sentinel node biopsy, breast cancer, immunohistochemistry, micrometastases, ITC ALND, axillary lymph node dissection, FFPE, formalin fixed paraffin embedded, HE, haematoxylin and eosin, IHC, immunohistochemistry, ITC, isolated tumor cells, SLN, sentinel lymph node

Analysis of sentinel node biopsy -a single institution experience supporting the use of serial sectioning and immunohistochemistry for detection of micrometastases by comparing four different histopathologic laboratory protocols

Introduction

During the last 10 years sentinel lymph node (SLN) biopsy has gained acceptance as the routine method for staging the ipsilateral axilla in women with early breast cancer. Preoperative procedures including the injection of radioactive colloidal substance and/or blue dye, scintigrames and gammaprobe handling and the intraoperative surgical technique is standardized and largely agreed upon. In the beginning of the 2000's Swedish guidelines for surgeons included SLN biopsy as standard procedure after a period of validation with respect to the false negative rate of axillary staging 1 .

On the other hand the work-up of sentinel nodes in the laboratory is still under debate. The 6 th edition of the pTNM classification introduced the concept of ITC in 2002 2,3 and stated that these should be considered as node negative for staging and treatment purposes. The 7 th edition 4,5 clarifies the concept and recommends finding all metastases >2 mm by macroscopically slicing the SLN in sections of 2 mm and to state the accuracy of the subsequent formalin fixed paraffin embedded (FFPE) protocol in finding micrometastases and ITC. In 2006 Swedish guidelines for SLN handling was largely adapted from the European guidelines 6 .

The risk of upstaging axillary status by a more thorough examination of SLNs has been considered an issue to be avoided because clinical data was based on only one histologic slice from each axillary lymph node 7 . Nevertheless, a recent paper on women with early stage breast cancer who underwent sentinel node biopsy reports that isolated tumor cells or micrometastases in regional lymph nodes were associated with a decreased disease free survival in women without adjuvant therapy and that disease free survival was improved in this patients group if they received adjuvant therapy 8 . Another review concludes that patients with metastases of 2 mm or smaller in axillary lymph nodes examined by a single HE section have a worse outcome compared to node negative patients 9 , but for patients treated by SLN the data is still inconclusive. A further review of SLN micrometastases concludes that SLN micrometastases are likely to represent an incremental detriment to prognosis and increased risk of non-SLN involvement 10 . In addition metastases uncovered in formerly negative axillary lymph node dissection (ALND) with a SLN protocol including IHC have prognostic significance in breast cancer patients 11 . The Swedish national figures show a worse outcome of patients with micrometastases in SLN compared to node negative patients 12 , but other reports have shown no difference in survival between SLN negative and those with micrometastases 13 .

These findings emphasize the need to optimize the accuracy of SLN pathology. At the same time, whatever method is chosen must not dramatically increase the cost and time spent for analysis.

In histopathological practice the technical quality of HE slides prepared from formerly frozen material occasionally can be inferior to material which was not frozen; freeze artifacts still show in the paraffin sections. This study address these problems by comparing the results of routine histopathologic work-up over four different time periods at the same institution using different protocols, all including frozen sections but with diverse methods for step sectioning and use of immunohistochemistry. In the last time period, laboratory organization was changed such that fewer laboratory technicians and pathologists were involved in frozen section diagnosis and in the subsequent work-up of the SLN.

Material and methods

The study was conducted on the consecutive series of the 1576 women with a first primary operable breast cancer treated at the University Hospital of Lund from January 1, 2001 to December 31, 2009 (Figure 1). Excluded were 25 women diagnosed in October 2008 because these women were analyzed by SLN using method 4 but before the laboratory was reorganized into work teams. Patients were selected by extraction from the data files of the pathologic department diagnosed with topography code for breast in the SNOMED system. By manual examination of the files patients with a previous history in the pathology files of invasive carcinoma in the breasts were excluded as were patients with previous malignancy elsewhere.

Men with breast cancer, benign cases and cases with in situ carcinoma were also excluded. A total of 27 women with synchronous bilateral breast cancer were included using the side showing the worse axillary status. The other side was excluded in these women.

The surgical procedure of SLN biopsy was preceded by subdermal injection with 99 Tc labeled nanocolloid followed by a scintigramme. Injection of 0.5 ml of Patent V Blue was performed intradermally after anesthesia in the operating room. Any node that was hot, blue, or palpable was considered a SLN and removed. The surgical procedure, instrument and surgical staff did not differ in the cohort period.

As a general rule frozen section examination was undertaken in up to four nodes with following examination of FFPE sections stained with HE and/or IHC with pan-anticytokeratins according to different protocols. Throughout the study period four different protocols of routine histopathological work-up of SLN were used (Figure 2). Generally SLNs of 4 mm or more were cut through the longitudinal axis and both halves examined. Smaller nodes were examined in toto. All specimens were examined by one or two HE stained frozen sections and no staining with IHC were performed intraoperatively. After formalin fixation and paraffin embedding the protocols differed. During the first period the sections were examined by one paraffin section and by immunohistochemical analysis with anticytokeratin in frozen negative cases (n=287) (Method 1). In the second period the SLNs were analyzed by step sectioning at three levels randomly chosen and by immunohistochemistry at the first level in frozen negative cases (n=148) (Method 2). The third period introduced step sectioning of SLNs at three fixed levels of 0.2 mm and use of immunohistochemistry only in suspicious cases (n=474) (Method 3). The last period included step sectioning of SLNs at three fixed levels of 0.2 mm with immunohistochemistry at every A review of the slides of all cases with positive SLN was undertaken and the 7 th edition of the AJCC and UICC classification was applied 4,14 . Women without detectable tumor cells in the nodes were designated node negative equal to cut off zero. Using a cut off of 0.2 mm women were staged as negative when they had no metastases or had ITC of 0.2 mm and smaller or with less than 200 tumor cells. Patients with micrometastases had metastases >0.2 mm or more than 200 tumor cells but not measuring more than 2.0 mm. A cut off of 2.0 mm separated women with metastases larger than 2.0 mm from all those with smaller ones.

The size of the metastatic deposits was determined on the slide where it was largest. In 2004 the 6 th edition of the AJCC was implemented and women with deposits of 0.2 mm or smaller or with ITC were hereafter not routinely offered axillary dissection. All other women with metastasis larger than 0.2 mm in at least one SLN were offered axillary dissection either in combination with the surgery for breast cancer due to a positive frozen section or in a second operative procedure as a result of a positive SLN on FFPE sections and thereby false negative frozen section of the SLN. One HE section from each block was examined and in difficult cases IHC was applied. Details of age of the patients, tumor size, histological grade, estrogen-and progesterone receptor status were recorded from the pathology reports. Histologic grade was assessed using the Nottingham modification 15 of the Scharff, Bloom and Richardson grading system 16 . Estrogen and progesterone receptor status was determined by IHC assay and carcinomas with >10% stained nuclei were considered positive. A mammography screening program was conducted in the local area since 1989 and women aged 45 to 74 were invited every 18-24 months.

Statistics

Differences between proportions were examined by chi-square test and p<0.05 was considered significant. Differences between continuous variables were analyzed by the Kruskal-Wallis test.

Results

Details of patients and tumor features are listed in Table 1. Tumor size did not differ between the four different study periods. About one fourth of the patients were 70 years or older and the median age of the patients was slightly increasing throughout the study. Histological grade was more often grade 3 in the last period and fewer patients had a diagnosis of lobular carcinoma in the later part of the study period. Receptor status did not differ among the study periods.

Of 1576 patients included in the study 70% had SLN biopsy, 20% were treated by primary ALND and 10% were allocated to other protocols without adequate determination of axillary status at the time of surgery (Figure 1). Frequency of patients treated by SLN biopsy was 63, 68, 69, and 86% in the four periods with different SLN examination. Using a cut off of zero for classifying SLNs with negative status, significantly more patients were node positive in the last 2a). When the cut off 0.2 mm/<200 cells was applied for negative status the difference was only borderline significant (p=0.07) (Table 2b). IHC was used in 72, 74, 21, and 92% of the cases treated by SLN biopsy. The median number of analyzed SLN per patient was 2 and did not differ between the periods.

Concentrating on the SLN totally negative and those with ITC of ≤0.2 mm/<200 cells or micrometastases of 2 mm or smaller some striking differences appeared. In the last period using method 4 with step sections at fixed intervals and IHC at every level, where frozen sections and step sections were performed by trained laboratory technicians, significant more patients were diagnosed with ITC or micrometastases in the SLNs (p<0.01). The number of patients with ITC and micrometastases was 9% higher when method 4 was used compared with method 1 and 2 using either just one HE section followed by IHC or one HE section and IHC followed by random step sections. Teamwork and intensive IHC in method 4 resulted in 13% more patients with ITC and micrometastases compared with the result of method 3 with step sections at fixed intervals. Frequency of women with ITC and micrometastases compared with those with macrometastases did not differ significantly between the study periods, which indicate that the ITC and micrometastases were found patients who previously were classified as node negative.

Frozen sections were reported positive to the surgeons if a metastasis of larger than 0.2 mm was encountered. The false negative rate of the frozen section technique was similar during the period for method 4 with intensive IHC of step sections in FFPE slides and team work and during the period for method 1 with IHC but without step sections. When method 2 and 3 without team work was used the false negative rate of frozen sections was higher. The present study shows overall more node positive patients in the period where method 4 was used including step sections at fixed intervals and intense use of IHC in hands of specially trained personal. At the same time more women were diagnosed with ITC and micrometastases in their SLNs without increasing the false negative rate of frozen sections. These results were accomplished by a relatively simple change in laboratory organization. Instead of all the laboratory workers handling all the material which came to the department, groups of workers was formed which handled only certain types of specimens, based on organ groups. Thus the number of assistants involved in the process of sentinel nodes was smaller which increased their expertise in this area of laboratory work.

Discussion

The introduction of team work also made possible a shift from the use of a metal stretch plate in the process of moving tissue sections to glass slides. A temperate water bath was used instead.

This improved the quality of the HE section to a degree that the frequency of patient with histologic grade 3 was for the first time within the limit of recommended value in Sweden. The shift to fewer women diagnosed with lobular carcinoma was caused by the introduction of Ecadherin IHC and possibly by a decreased use of hormone replacement therapy which has been seen in the population in resent years. The age of the patients is steadily increasing probably due to more active treatment of the elderly. By applying step sections and/or IHC to negative regional lymph nodes, the use of step sections increases the harvest of small metastases by about 7-13% and the addition of IHC will find about 15-30% more cases with small metastases 11,17 . Our results and the conclusion of results of another report 18 implies that smaller metastases will be missed if step sections and IHC of SLNs is left out. The varying false negative rate of metastasis obtained by frozen sections among the study periods indicates that small metastasis might be missed. The sensitivity of frozen section methodology is within the range found in other studies 19,20 . From the surgical point of view discussion is ongoing as to whether patients with micrometastases benefit from subsequent ALND because the frequency of local recurrence is extremely low 21,22 . However systemic therapy might improve survival even in patients with tumor deposits even as small as ITC 8 .

A consensus with regard to an optimal pathologic work-up of SLNs is hard to achieve because viewpoints differ about the objectives of the examination. A more modest work-up favors attempts to avoid stage migration and acknowledges the possibility of benign transportation of epithelial tissue to the SLNs. Up-staging of breast cancer patients implies that a more thorough method of SLN examination results in more positive cases 23 . The clinical implication of the additional metastases is not determined in the clinical trials where use of adjuvant systemic therapy is applied. Another caution against taking therapeutic action as a consequence of small metastatic deposits only detectable with IHC, is raised by the possibility of benign transportation of cells to the SLN 24 after needle diagnostic procedures or manipulation of the breast 25 .

Malignant cells might even be displaced to the SLNs without being metastasic in nature. Lately benign elements have been identified as elements of papillomas from the breast 26 .

Different models of handling of SLNs have been presented 27,28 and all models shows that using an acceptable number of steps and sections in routine work-up, results in missed deposits of small metastases. Furthermore, pathologists do not agree on what constitutes ITC [START_REF] Turner | Nodal stage classification for breast carcinoma: improving interobserver reproducibility through standardized histologic criteria and image-based training[END_REF] . Therefore the 7 th AJCC staging recommends slicing the SLN in 2 mm intervals and stating the sensitivity of the step section method used to detect small metastases afterwards. In addition clarifications of the concept of ITC and/or less than 200 cells have been reported 5 . The lymph node slices of 2 mm is obtained in practice by dividing the SLN by the longitudinal axis and this will always be an approximation since lymph nodes are of different size. One survey of routine practice in Europe revealed that 73% of participating institutions did IHC on SLNs [START_REF] Cserni | Pathological work-up of sentinel lymph nodes in breast cancer. Review of current data to be considered for the formulation of guidelines[END_REF] 28 but method 4 in this study seems to combine an acceptable level of work with an acceptable cost.

Both AJCC and European guidelines recommend step microscopic sections of SLN but both determine the size of the largest metastases on one section in two dimensions and do not take into account the third dimension that emerges from the step sectioning. Most important is ITC appearing in the deepest section. If another level is not examined this ITC might in fact be a macrometastasis. When the SLNs are step sectioned at fixed intervals the size of the metastases can be determined in three dimensions but no guidelines include size in the third dimension and this might underestimate the actual size of the metastasis.

Intraoperative procedures are considered optional and so far no guidelines deals with the fact that frozen section methodology also may introduce freeze artifacts in the FFPE sections. This makes routine examination of HE sections more difficult and the pathologist might miss metastases that easily would have been seen in sections from tissue which had not been frozen. In order to minimize these artifacts the training of the laboratory assistants is crucially important. The preparation of frozen sections is meticulous handwork and must be handled by specially trained laboratory assistants with have the opportunity to do the work often. The present work in the first three periods was carried out at a time when all the laboratory assistants prepared frozen sections as did most of the pathologists. In the last period team work was introduced and a larger fraction of SLN patients were diagnosed as positive with a larger fraction having smaller metastases.

There was still an acceptable level of false negative frozen section examinations, however.

This study has some draw backs. As it is a single institution study design, the different methods compared are based on examination of SLN in successive time intervals and comparison of the methods was not randomized during a fixed time interval. Also the frequency of patients treated by SLN was increasing during the study period, and thereby the frequency of positive nodes in the SLN population would be expected to increase. Therefore data from all breast cancer patients F o r P e e r R e v i e w 12 in the institution is considered and because the increase is general in the entire study population the increase in node positivity among patients with SLN is interpreted a being method related and not a result of selection bias. With the present study design reported here it will never be possible to prove that the increase in ITC and micrometastases found using method 4 is not simply a result of more patients having SLN performed. During the study period the indication for axillary clearance also changed so that only patients with a suspicion of, or preoperatively diagnosed regional metastases, would receive axillary clearance primarily. The protocol for the handling of nodes from axillary clearance was also altered before method 4 was used. The frequency of screening detected breast cancer in the population was not changed during the study. In patients undergoing SLN the increased number of ITC's and micrometastases were found in patients who had previously been classified as node negative and therefore the increase might be method related.

To our knowledge the results of work by a specialised team including laboratory technicians have not been studied earlier. Therefore we cannot state that the increase of 13% in ITC and micrometastases which we documented during the time period when method 4 was used is solely based on the result of the specialised team work or just the result of more intensive step sectioning and IHC.

If the handling of SLN is reserved to a small specialized group of laboratory technicians and pathologists it may be expected that the rate of false positive frozen sections be decreased. In fact one of the three false positive cases in the present series were due to the presence of benign nevus in the lymph node capsule, a condition of which not all pathologist are aware [START_REF] Pantanowitz | Benign axillary lymph node inclusions[END_REF] .

In conclusion future guidelines for pathologic work-up of sentinel nodes in women with breast cancer might include the recommendation of team work and IHC if frozen sections are to be used intraoperatively. This study shows that a method with team work and intensive step sections including IHC detected 13% more women with ITC or micrometastases.

F

Post operative tumor size was zero in a few patients included in a study using laser therapy [START_REF] Haraldsdottir | Interstitial laser thermotherapy (ILT) of breast cancer[END_REF] . In the first period a cohort study included women with early breast cancer with an expected risk of loco-regional recurrence of less than 1% in a protocol without axillary staging (N=9). On the other hand the work-up of sentinel nodes in the laboratory is still under debate. The 6 th edition of the pTNM classification introduced the concept of ITC in 2002 2,3 and stated that these should be considered as node negative for staging and treatment purposes. The 7 th edition 4,5 clarifies the concept and recommends finding all metastases >2 mm by macroscopically slicing SLN in 2 mm sections. It is also recommended that the accuracy of the subsequent formalin fixed paraffin embedded (FFPE) protocol in finding micrometastases and ITC be defined. In 2006 Swedish guidelines for SLN handling largely was adapted from the European guidelines 6 .

F

The risk of upstaging axillary status by a more thorough examination of SLNs has been considered an issue to be avoided because clinical data was based on only one histologic slice from each axillary lymph node 7 . Nevertheless, a recent paper on women with early stage breast cancer who underwent sentinel node biopsy reports that isolated tumor cells or micrometastases in regional lymph nodes were associated with a decreased disease free survival in women without adjuvant therapy and that disease free survival was improved in this patients group if they received adjuvant therapy 8 . Another review concludes that patients with metastases of 2 mm or smaller in axillary lymph nodes examined by a single HE section have a worse outcome compared to node negative patients 9 , but for patients treated by SLN the data is still inconclusive. A further review of SLN micrometastases concludes that SLN micrometastases are likely to represent an incremental detriment to prognosis and increased risk of non-SLN involvement 10 . In addition metastases uncovered in formerly negative axillary lymph node dissection (ALND) with a SLN protocol including IHC have prognostic significance in breast cancer patients 11 . The Swedish national figures show a worse outcome of patients with micrometastases in SLN compared to node negative patients 12 , but other reports have shown no difference in survival between SLN negative and those with micrometastases 13 .

These findings emphasize the need to optimize the accuracy of SLN pathology. At the same time, whatever method is chosen must not dramatically increase the cost and time spent for analysis.

In histopathological practice the technical quality of HE slides prepared from formerly frozen material occasionally can be inferior to material which was not frozen; freeze artifacts still show in the paraffin sections. This study address these problems by comparing the results of routine histopathologic work-up over four different time periods at the same institution using different protocols, all including frozen sections but with diverse methods for step sectioning and use of immunohistochemistry. In the last time period, laboratory organization was changed such that fewer laboratory technicians and pathologists were involved in frozen section diagnosis and in the subsequent work-up of the SLN.

Material and methods

The study was conducted on the consecutive series of the 1576 women with a first primary department diagnosed with topography code for breast in the SNOMED system. By manual examination of the files patients with a previous history in the pathology files of invasive carcinoma in the breasts were excluded as were patients with previous malignancy elsewhere.

Men with breast cancer, benign cases and cases with in situ carcinoma were also excluded. A total of 27 women with synchronous bilateral breast cancer were included using the side showing the worse axillary status. The other side was excluded in these women.

The surgical procedure of SLN biopsy was preceded by subdermal injection with 99 Tc labeled nanocolloid followed by a scintigramme. Injection of 0.5 ml of Patent V Blue was performed intradermally after anesthesia in the operating room. Any node that was hot, blue, or palpable was considered a SLN and removed. The surgical procedure, instrument and surgical staff did not differ in the cohort period.

As a general rule frozen section examination was undertaken in up to four nodes with following examination of FFPE sections stained with HE and/or IHC with pan-anticytokeratins according to different protocols. Throughout the study period four different protocols of routine histopathological work-up of SLN were used (Figure 2). Generally SLNs of 4 mm or more were cut through the longitudinal axis and both halves examined. Smaller nodes were examined in toto. All specimens were examined by one or two frozen sections. After formalin fixation and paraffin embedding the protocols differed. During the first period the sections were examined by one paraffin section and by immunohistochemical analysis with anticytokeratin in frozen negative cases (n=287) (Method 1). In the second period the SLNs were analyzed by step sectioning at three levels randomly chosen and by immunohistochemistry at the first level in frozen negative cases (n=148) (Method 2). The third period introduced step sectioning of SLNs at three fixed levels of 0.2 mm and use of immunohistochemistry only in suspicious cases (n=474) (Method 3). The last period included step sectioning of SLNs at three fixed levels of 0.2 mm with immunohistochemistry at every level in cases which were frozen negative or had a A review of the slides of all cases with positive SLN was undertaken and the 7 th of the AJCC and UICC classification was applied 4,14 . Women without detectable tumor cells in the nodes were designated node negative equal to cut off zero. Using a cut off of 0.2 mm women were staged as negative when they had no metastases or had ITC of 0.2 mm and smaller or with less than 200 tumor cells. Patients with micrometastases had metastases >0.2 mm or more than 200 tumor cells but not measuring more than 2.0 mm. A cut off of 2.0 mm separated women with metastases larger than 2.0 mm from all those with smaller ones.

The size of the metastatic deposits was determined on the slide where it was largest. In 2004 the 6 th edition of the AJCC was implemented and women with deposits of 0.2 mm or smaller or with ITC were hereafter not routinely offered axillary dissection. All other women with metastasis larger than 0.2 mm in at least one SLN were offered axillary dissection either in combination with the surgery for breast cancer due to a positive frozen section or in a second operative procedure as a result of a positive SLN on FFPE sections and thereby false negative frozen section of the SLN. Histologic grade was assessed using the Nottingham modification 15 of the Scharff, Bloom and

Richardson grading system 16 . Estrogen and progesterone receptor status was determined by IHC assay. A mammography screening program was conducted in the local area since 1989 and women aged 45 to 74 were invited every 18-24 months.

Statistics

Differences between proportions were examined by chi-square test and p<0.05 was considered significant. Differences between continuous variables were analyzed by the Kruskal-Wallis test.

Results

Details of patients and tumor features are listed in Table 1. Tumor size did not differ between the four different study periods. About one fourth of the patients were 70 years or older and the median age of the patients was slightly increasing throughout the study. Histological grade was more often grade 3 in the last period and fewer patients had a diagnosis of lobular carcinoma in the later part of the study period. Receptor status did not differ among the study periods.

Of 1576 patients included in the study 70% had SLN biopsy, 20% were treated by primary ALND and 10% were allocated to other protocols without adequate determination of axillary status at the time of surgery (Figure 1). Frequency of patients treated by SLN biopsy was 63, 68, 69, and 86% in the four periods with different SLN examination. Using a cut off of zero for classifying SLNs with negative status, significantly more patients were node positive in the last period both among women treated by SLN and among all women (p=0.01) (Table 2a). When the cut off 0.2 mm/<200 cells was applied for negative status the difference was only borderline significant (p=0.07) (Table 2b). IHC was used in 72, 74, 21, and 92% of the cases treated by SLN Concentrating on the SLN totally negative and those with ITC of ≤0.2 mm/<200 cells or micrometastases of 2 mm or smaller some striking differences appeared. In the last period using method 4 with step sections at fixed intervals and IHC at every level, where frozen sections and step sections were performed by trained laboratory technicians, significant more patients were diagnosed with ITC or micrometastases in the SLNs (p<0.01). The number of patients with ITC and micrometastases was 9% higher when method 4 was used compared with method 1 and 2 using either just one HE section followed by IHC or one HE section and IHC followed by random step sections. Teamwork and intensive IHC in method 4 resulted in 13% more patients with ITC and micrometastases compared with the result of method 3 with step sections at fixed intervals. Frequency of women with ITC and micrometastases compared with those with macrometastases did not differ between the study periods.

Frozen sections were reported positive to the surgeons if a metastasis of larger than 0.2 mm was encountered. The false negative rate of the frozen section technique was similar during the period for method 4 with intensive IHC of step sections in FFPE slides and team work and during the period for method 1 with IHC but without step sections. When method 2 and 3 without team work was used the false negative rate of frozen sections was higher.

Discussion

The present study shows overall more node positive patients in the period where method 4 was used including step sections at fixed intervals and intense use of IHC in hands of specially trained personal. At the same time more women were diagnosed with ITC and micrometastases in their SLNs without increasing the false negative rate of frozen sections. These results were The introduction of team work also made possible a shift from the use of a metal stretch plate in the process of moving tissue sections to glass slides. A temperate water bath was used instead.

This improved the quality of the HE section to a degree that the frequency of patient with histologic grade 3 was for the first time within the limit of recommended value in Sweden. The shift to fewer women diagnosed with lobular carcinoma was caused by the introduction of Ecadherin IHC and possibly by a decreased use of hormone replacement therapy which has been seen in the population in resent years. The age of the patients is steadily increasing probably due to more active treatment of the elderly.

By applying step sections and/or IHC to negative regional lymph nodes, the use of step sections increases the harvest of small metastases by about 7-13% and the addition of IHC will find about 15-30% more cases with small metastases 11,17 . Our results and the conclusion of results of another report 18 implies that smaller metastases will be missed if step sections and IHC of SLNs is left out. The varying false negative rate of metastasis obtained by frozen sections among the study periods indicates that small metastasis might be missed. The sensitivity of frozen section methodology is within the range found in other studies 19,20 .

From the surgical point of view discussion is ongoing as to whether patients with micrometastases benefit from subsequent ALND because the frequency of local recurrence is extremely low 21,22 . However systemic therapy might improve survival even in patients with tumor deposits even as small as ITC 8 . epithelial tissue to the SLNs. Up-staging of breast cancer patients implies that a more thorough method of SLN examination results in more positive cases 23 . The clinical implication of the additional metastases is not determined in the clinical trials where use of adjuvant systemic therapy is applied. Another caution against therapeutic action as a consequence of small metastatic deposits only detectable with IHC raise the possibility of benign transportation to the SLN 24 after needle diagnostic procedures or manipulation of the breast 25 and even malignant cells might be displaced to the SLNs without being metastasic in nature. Lately benign elements have been identified as elements of papillomas from the breast 26 .

Different models of handling of SLNs have been presented 27,28 and all models shows that using an acceptable number of steps and sections in routine work-up, results in missed deposits of small metastases. Furthermore, pathologists do not agree on what constitutes ITC [START_REF] Turner | Nodal stage classification for breast carcinoma: improving interobserver reproducibility through standardized histologic criteria and image-based training[END_REF] . Therefore the 7 th AJCC staging recommends slicing the SLN in 2 mm intervals and stating the sensitivity of the step section method used to detect small metastases afterwards. In addition clarifications of the concept of ITC and/or less than 200 cells have been reported 5 . The lymph node slices of 2 mm is obtained in practice by dividing the SLN by the longitudinal axis and this will always be an approximation since lymph nodes are of different size. One survey of routine practice in Europe revealed that 73% of participating institutions did IHC on SLNs [START_REF] Cserni | Pathological work-up of sentinel lymph nodes in breast cancer. Review of current data to be considered for the formulation of guidelines[END_REF] . More intensive protocols using IHC reveal more metastasis 28 Intraoperative procedures are considered optional and so far no guidelines deals with the fact that frozen section methodology also may introduce freeze artifacts in the FFPE sections. This makes routine examination of HE sections more difficult and the pathologist might miss metastases that easily would have been seen in sections from tissue which had not been frozen. In order to minimize these artifacts the training of the laboratory assistants is crucially important. The preparation of frozen sections is meticulous handwork and must be handled by specially trained laboratory assistants with have the opportunity to do the work often. The present work in the first three periods was carried out at a time when all the laboratory assistants prepared frozen sections as did most of the pathologists. In the last period team work was introduced and a larger fraction of SLN patients were diagnosed as positive with a larger fraction having smaller metastases.

There was still an acceptable level of false negative frozen section examinations, however.

This study has some draw backs. As it is a single institution study design, the different methods compared are based on examination of SLN in successive time intervals and comparison of the methods was not randomized during a fixed time interval. Also the frequency of patients treated by SLN was increasing during the study period, and thereby the frequency of positive nodes in the SLN population would be expected to increase. Therefore data from all breast cancer patients in the institution is considered and because the increase is general in the entire study population the increase in node positivity among patients with SLN is interpreted a being method related and not a result of selection bias.

If the handling of SLN is reserved to a small specialized group of laboratory technicians and pathologists it may be expected that the rate of false positive frozen sections be decreased. In fact In the first period a cohort study included women with early breast cancer with an expected risk of loco-regional recurrence of less than 1% in a protocol without axillary staging (N=9).

  which were frozen negative or had a metastasis of less than 2 mm on the frozen sections (n=186). During the last period the laboratory work was done by fewer, specially trained technicians and fewer pathologists. The number of laboratory technicians was concentrated from 12 to 5 and pathologists were decreased from about 14 to about 3. The laboratory technicians were specially trained in doing frozen sections on SLNs with fatty tissue around and inside the lymph nodes. The frozen sections were examined in the microscope by a pathologist looking for metastases together with a laboratory technician who participated in the analysis of the quality of the frozen section. This method is what we refer to as team work.

From 2001 to

 2001 Oct 2008 axillary lymph nodes from the axillary clearance were handled by isolation of the lymph nodes in formalin fixed surgical specimens and embedding one slice from each node often including several nodes in each block. From Oct 2008 and thereafter axillary the axillary clearance were bisected and macroscopically negative nodes were entirely embedded in separate blocks. One slice sufficed for macroscopically metastasic nodes.

  women treated by SLN and among all women (p=0.01) (Table

22 Figure 2 .Figure 3 .

 2223 Figure 2. Method of sentinel node work up in the four different periods

  operable breast cancer treated at the University Hospital of Lund from January 1, 2001 to December 31, 2009 (Figure1). Excluded were 25 women diagnosed in October 2008 because these women were analyzed by SLN using method 4 but before the laboratory was reorganized into work teams. Patients were selected by extraction from the data files of the pathologic

  than 2 mm on the frozen sections (n=186). During the last period the laboratory work was done by fewer, specially trained technicians and fewer pathologists. The number of laboratory technicians was concentrated from 12 to 5 and pathologists were decreased from about 14 to about 3. The laboratory technicians were specially trained in doing frozen sections on SLNs with fatty tissue around and inside the lymph nodes.

From 2001 to

 2001 Oct 2008 axillary lymph nodes were handled by isolation of the lymph nodes in formalin fixed surgical specimens and embedding one slice from each node often including several nodes in each block. From Oct 2008 and thereafter axillary lymph nodes were bisected and macroscopically negative nodes were entirely embedded in separate blocks. One slice sufficed for macroscopically metastasic nodes. One HE section from each block was examined and in difficult cases IHC was applied. Details of age of the patients, tumor size, histological -and progesterone receptor status were recorded from the pathology reports.

  median number of analyzed SLN per patient was 2 and did not differ between the periods.

  relatively simple change in laboratory organization. Instead of all the laboratory workers handling all the material which came to the department, groups of workers were formed which handled only certain types of specimens, based on organ groups. Thus the number of assistants involved in the process of sentinel nodes was smaller which increased their expertise in this area of laboratory work.

10 A

 10 consensus with regard to an optimal pathologic work-up of SLNs is hard to achieve because viewpoints differ about the objectives of the examination. A more modest work-up favors attempts to avoid stage migration and acknowledges the possibility of benign transportation of

  three false positive cases in the present series were due to the presence of benign nevus in the lymph node capsule, a condition of which not all pathologist are aware[START_REF] Pantanowitz | Benign axillary lymph node inclusions[END_REF] .In conclusion future guidelines for pathologic work-up of sentinel nodes in women with breast cancer might include the recommendation of team work and IHC if frozen sections are to be used intraoperatively. This study shows that a method with team work and intensive step sections including IHC detected 13% more women with ITC or micrometastases.

  used January 2001 to September 2003 Method 2 was used October 2003 to December 2004 Method 3 was used January 2005 to September 2008 Method 4 was used November 2008 to December 2009

22 Figure 2 . 23 Figure 3 .

 222233 Figure 2. Method of sentinel node work up in the four different periods

  . More intensive

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	protocols using IHC reveal more metastasis
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Table 1 .

 1 Turner RR, Weaver DL, Cserni G, et al. Nodal stage classification for breast carcinoma: improving interobserver reproducibility through standardized histologic criteria and image-based training. J. Clin. Oncol. 2008 Jan 10;26(2):258-263. 30. Cserni G, Amendoeira I, Apostolikas N, et al. Pathological work-up of sentinel lymph nodes in breast cancer. Review of current data to be considered for the formulation of guidelines. Eur. J. Cancer 2003 Aug;39(12):1654-1667. Patients and tumor characteristics of all women.

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Table 2 .

 2 a. Frequency of positive nodes in women primarily treated by SLN, ALND and other during the different methodologies of SLN handling, with a cut off for metastases at zero.

		Method 1	Method 2	Method 3	Method 4
			n Npos		n Npos		n Npos		n Npos
	Primary surgery	n	(%)	n	(%)	N	(%)	n	(%)
	SLN cut off 0	287	123 (43)	148	52 (35) 474 168 (35) 186	92 (49) p<0.01
	ALND	117	68 (58)	51	28 (55) 138	84 (61)	16	14 (88) p=0.12
	Other	53	46 (87)	20	16 (80)	71	57 (80)	15	15 (100) p=0.53
	Total cut off 0	457	237 (52)	219	96 (44) 683 309 (45) 217	121 (56) p=0.01
	* Other se figure 1.
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Table 2 .

 2 b. Frequency of positive nodes in women primarily treated by SLN, ALND and other during the different methodologies of SLN handling, with a cut off for metastases at 0.2 mm/200 cells.

		Method 1		Method 2		Method 3		Method 4
			n Npos		n Npos		n Npos		n Npos
	Primary surgery	n	(%)	n	(%)	n	(%)	n	(%)
	SLN cut off 0.2 mm/
	<200 cells	287	112 (39)	148	45 (30) 474 154 (32) 186	76 (41) p=0.06
	Total cut off 0.2 mm/
	200 cells	457	226 (49)	219	89 (41) 683 295 (43) 217	105 (48) p=0.07

Table 3 .

 3 Frequency of isolated tumor cells, micro-, and macrometastases in the intervals with different methodology of SLN handling.

		Method 1	Method 2	Method 3	Method 4
		n (%)	n (%)	n (%)	n (%)
	SLN Negative	165 (57)	97 (66)	311 (66)	94 (51)	p=0.01
	SLN ITC ≤ 0.2 mm/<200 cells	11 (4)	7 (5)	14 (3)	16 (9)
	SLN positive > 0.2 and ≤ 2.0 mm	25 (9)	14 (9)	36 (8)	18 (10)
	SLN positive > 2.0 mm	86 (30)	30 (20)	113 (24)	58 (31)
	Total	287	148	478	186

Table 4 .

 4 False negative results of frozen sections of SLN compared with FFPE sections using cut off 0.2 mm.

		Method 1	Method 2	Method 3	Method 4
		n (%)	n (%)	n (%)	n (%)
	SLN total negative	164 (57)	94 (64)	308 (65)	91 (49)
	ITC ≤ 0.2 mm/200 cells	11 (4)	7 (5)	14 (3)	15 (8)
	positive > 0.2 mm/200 cells
	positive > 0.2 and ≤ 2 mm	12 (4)	4 (3)	10 (2)	4 (2)
	positive >2 mm	73 (25)	25 (17)	96 (20)	49 (26)
	Frozen false negative met > 0.2 mm
	positive > 0.2 and ≤ 2 mm	13 (5)	9 (6)	25 (5)	13 (7)
	positive >2 mm	13 (5)	5 (3)	15 (3)	3 (2)
	Frozen false positive	1 (0)	2 (1)	0	0
	No frozen section	0	2 (1)	6 (1)	11 (6)
		287	148	474	186
	False negative rate	0,23	0,33	0,27	0,23
	Accuracy	0,91	0,89	0,92	0,91

  but method 4 in this study seems to combine an acceptable level of work with an acceptable cost.Both AJCC and European guidelines recommend step microscopic sections of SLN but both determine the size of the largest metastases on one section in two dimensions and do not take into account the third dimension that emerges from the step sectioning. Most important is ITC If another level is not examined this ITC might in fact be a macrometastasis. When the SLNs are step sectioned at fixed intervals the size of the metastases can be determined in three dimensions but no guidelines include size in the third dimension and this might underestimate the actual size of the metastasis.

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	appearing in the deepest section.
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Table 2 .

 2 a. Frequency of positive nodes in women primarily treated by SLN, ALND and other during the different methodologies of SLN handling, with a cut off for metastases at zero.

		Method 1		Method 2		Method 3		Method 4
			n Npos		n Npos		n Npos		n Npos
	Primary surgery	n	(%)	n	(%)	N	(%)	n	(%)
	SLN cut off 0	287	123 (43)	148	52 (35) 474 168 (35) 186	92 (49) p<0.01
	ALND	117	68 (58)	51	28 (55) 138	84 (61)	16	14 (88) p=0.12
	Other	53	46 (87)	20	16 (80)	71	57 (80)	15	15 (100) p=0.53
	Total cut off 0	457	237 (52)	219	96 (44) 683 309 (45) 217	121 (56) p=0.01
	* Other se figure 1.

Table 2 .

 2 b. Frequency of positive nodes in women primarily treated by SLN, ALND and other during the different methodologies of SLN handling, with a cut off for metastases at 0.2 mm/200 cells.

		Method 1		Method 2		Method 3		Method 4
			n Npos		n Npos		n Npos		n Npos
	Primary surgery	n	(%)	n	(%)	n	(%)	n	(%)
	SLN cut off 0.2 mm/
	<200 cells	287	112 (39)	148	45 (30) 474 154 (32) 186	76 (41) p=0.06
	Total cut off 0.2 mm/
	200 cells	457	226 (49)	219	89 (41) 683 295 (43) 217	105 (48) p=0.07

Table 3 .

 3 Frequency of isolated tumor cells, micro-, and macrometastases in the intervals with different methodology of SLN handling.

		Method 1	Method 2	Method 3	Method 4
		n (%)	n (%)	n (%)	n (%)
	SLN Negative	165 (57)	97 (66)	311 (66)	94 (51)	p=0.01
	SLN ITC ≤ 0.2 mm/<200 cells	11 (4)	7 (5)	14 (3)	16 (9)
	SLN positive > 0.2 and ≤ 2.0 mm	25 (9)	14 (9)	36 (8)	18 (10)
	SLN positive > 2.0 mm	86 (30)	30 (20)	113 (24)	58 (31)
	Total	287	148	478	186

Published on behalf of the British Division of the International Academy of Pathology Histopathology

Acknowledgements

The admirable work of the laboratory technicians in the breast team in 2008-2009 Iren Atakhan, Liv Gröntoft, Magdalena Nagy, Nadine Nyawakira, Anna Nilsson and Helen Svensson and the immunohistochemical laboratory is much appreciated. Also the residents Jacob Elebro and David Nord Gisselsson did a meticulous and highly professional work. This work was founded by Skaane County Council's Research and Development Foundation, and Governmental Funding of Clinical Research within the National Health Service. The authors whish to thanks to Robert Cameron for linguistic support of the manuscript. Acknowledgements The admirable work of the laboratory technicians in the breast team in 2008-2009 Iren Atakhan, Liv Gröntoft, Magdalena Nagy, Nadine Nyawakira, Anna Nilsson and Helen Svensson and the immunohistochemical laboratory is much appreciated. Also the residents Jacob Elebro and David Nord Gisselsson did a meticulous and highly professional work. This work was founded by Skaane County Council's Research and Development Foundation, and Governmental Funding of Clinical Research within the National Health Service.

The authors whish to thanks to Robert Cameron for linguistic support of the manuscript.

Post operative tumor size was zero in a few patients included in a study using laser therapy [START_REF] Haraldsdottir | Interstitial laser thermotherapy (ILT) of breast cancer[END_REF] .