La brevedad de unos veranos frescos e inseguros

The spectrophotometer measured reflectance at 20 nm intervals in the wavelength range 400- 700 nm. The equation for the estimation of melanin density was based on previous results:15

MD400= 100[0.035307 + 0.009974(R420–R400)]

where MD400is an estimate of the percentage of the epidermis of the skin at the upper inner

arm that contains melanin, and R400and R420denote respectively the averages of three

measurements of reflectance at 400 nm and 420 nm made at that site. Melanin estimated in this way was previously found to be closely correlated (r=0.68) with histopathological

measurements of the density of cutaneous melanin in 3 mm punch biopsies taken at the upper inner arm after the reflectance measurements were taken.15_{As evidence of the high}

reproducibility of measurements made by the single observer, the percentage of total variation in MD400at the upper inner arm in session one attributed to within-person variation in the three

measurements was 0.3 percent. The intraclass correlation was 0.99, calculated from a one-way random effects model using ICC(1,1) from Shrout and Fleiss:21

withBMSbeing the between-subjects mean square,WMSbeing the within-subjects mean square andkthe number of ratings, which is three in our situation.

7.3.4 Data analysis

For each subject, mean melanin density was calculated by averaging the measurements made at the end of spring, summer, autumn and winter. The average of the two end of winter

readings was used as the winter measurement. These means were then averaged to provide the group means presented in Table 1. For analyses where melanin density estimates at the buttock were involved, three male and four female subjects were excluded because they had a recent history of nude sunbathing or had used a solarium without wearing underwear. One person, with readings more than four standard deviations higher than the mean of the sample, was excluded from calculation of means and standard deviations.

Effect of body hair on the melanin density estimates.

A paired t-test was used to test whether removal of hair produced a significant effect on the melanin density estimates and a t-test was used to compare the means of men and women. An intraclass correlation coefficient was calculated between the unshaved and shaved

measurements from a two-way mixed effects model using formula ICC [3,1] from Shrout and Fleiss:21

withBMSbeing the between-subjects mean square,EMSbeing the residual sum of squares andkthe number of ratings, which is two in our situation. This model was applied because the unshaved and shaved measurements can be seen as two fixed judges.

The relationship between the effect of hair and the four hair characteristics was further investigated using analysis of variance. The amount of hair was dichotomised as little hair

(combining categoriesof‘no hair’and ‘little’)and more than a little (combining categoriesof ‘notthatmuch’,‘a fairbit’and ‘a lot’).

Seasonal variation in the melanin density estimates.

To depict the seasonal variation in melanin estimates at the buttock and upper inner arm, a sinusoidal model was fitted by linear regression with a period of 12 months:

MD400 i= β0+β1sin 12 2ti +β2cos 12 2ti

where tiis the month of measurement (0-12) of the ithMD400reading. The ANOVA F-test was

used to decide whether there was significant seasonal variation and the amplitude was

calculated using the formula 2

2 2 1    . ICC = EMS k BMS EMS BMS ) 1 (    ICC = WMS k BMS WMS BMS ) 1 (   

Effect of body hair on skin type classification.

The percentage of subjects misclassified when melanin at the buttock was measured in the presence of body hair was calculated. Measurements after shaving are the best estimates of thetrue values, and the measurements with hair are theobserved valuesthat would be seen during fieldwork if subjects were not shaved. The melanin estimates were dichotomised at the median. Subjects with melanin estimates lower than the median are referred to as havinglow melaninand subjects with melanin estimates higher than the median are referred to as having

high melanin.

We next assessed to what extent any non-differential measurement error due to body hair would influence the results of a hypothetical unmatched case-control study with 150 cases and 300 population-representative controls. With melanin dichotomised at the median, 150 would have lower-than-median melanin. A ratio of 2:1 comparing the odds of low melanin among cases with the odds of low melanin among controls is suggested by the results of our recent case-control study.12_{This would require 100 cases to have low melanin. This categorisation is}

referred to as thetrue classification. To calculate theobserved classificationbased on melanin estimated without shaving, we applied the misclassification percentages estimated as outlined in the paragraph above. The odds ratio was then re-calculated based on the categorisation with misclassification.

Measurement error is differential when the misclassification is different for cases compared to controls. This could occur when hair characteristics at the buttock such as amount, colour, type and length of hair are different for cases compared to controls, so that the effect of shaving of the hair at the buttock is different for cases and controls. As far as we are aware, no studies have investigated this possibility. There is evidence that both melanoma and non-melanoma cases have on average 15% (women) to 30% (men) less cutaneous melanin at the buttock than controls.12_{As a test of whether there could be differential measurement error, we}

calculated the Spearman correlation between the effect of shaving (measured by the difference between the melanin estimates at the unshaved and the shaved buttock) and the amount of melanin at the buttock. To assess the extent to which differential measurement error due body hair would influence the results of the hypothetical unmatched case-control study, we created a hypothetical group of cases (those of our subjects with the lowest melanin estimates) and a hypothetical group of controls (all of our subjects). Sufficient subjects were chosen as cases to make the average melanin at the shaved buttock 30% lower for the cases than for controls. The melanin estimates of both groups were dichotomised at the median of the controls. The misclassification due to body hair for the group of cases and controls was then calculated using the buttock melanin estimates with and without shaving.

To calculate the effect on the odds ratio, we calculated first theobserved classificationby applying the misclassification percentages in our hypothetical example. The odds ratio was then re-calculated based on the observed categorisation with differential misclassification. Effect of seasonal variation on skin type classification.

The percentage of subjects misclassified when measurements were made at different times of the year was calculated. Thetrue valuefor each person was taken to be the winter

measurement and theobserved valuewas one of those four seasonal measurements chosen at random. The percentage of subjects misclassified when melanin was measured randomly in any of the four seasons was then calculated. Because the misclassification that resulted depended upon which value happened to be chosen for each individual (one of the four

seasonal values), we repeated this 10,000 times, and used the mean of the 10,000 misclassification percentages as the estimated misclassification.

To assess to what extent any non-differential measurement error due to seasonal variation would influence the results of a hypothetical unmatched case-control study, we used the same hypothetical case-control data as outlined above. To calculate theobserved classification

based on melanin estimates randomised according to their time of measurement, we used the misclassification percentages estimated. The odds ratio was then re-calculated base on the categorisation with misclassification.

Measurement error could be differential when different proportions of cases and controls are measured in any period of the year. The extreme possibilities are that all cases were measured in summer with all controls measured in winter, and that all cases were measured in winter with all controls measured in summer. Thetrue values(the winter measurements) were

dichotomised at the median. Theobserved valueswere dichotomised at the median of values for the controls (measured in winter on one occasion, and in summer on the other). The misclassification percentages were then calculated.

To calculate theobserved classification,we applied the relevant misclassification percentages to the case and control groups separately. The odds ratio was re-calculated based on this classification.

7.4 R

The phenotypic characteristics of the study subjects who completed all five sessions are shown in Table 1. More women than men happened to have brown, hazel or green eyes (p<0.03) and women also had higher average melanin estimates at the upper inner arm (p<0.01).

Table 1. Demographic details of study subjects stratified by gender.

Study factor Men (n=49) Women (n=55)

Age distribution 20-29 years 24.5% (12) 23.6% (13) 30-39 years 26.5% (13) 27.3% (15) 40-49 years 30.6% (15) 29.1% (16) 50-59 years 18.4% (9) 20.0% (11) Eye colour Brown 14.3% (7) 25.5% (14) Hazel or green 28.6% (14) 38.2% (21) Blue or grey 57.1% (28) 36.4% (20) Hair colour

Black or dark brown 24.5% (12) 32.7% (18) Mid or light brown 46.9% (23) 40.0% (22) Mousy or light blond 22.4% (11) 25.5% (14)

Red 6.1% (3) 1.8% (1)

Mean melanin density % [SD]

Upper inner arm 1.66 [0.96] 2.17 [0.85]

Shaved buttock 0.61 [0.67] 0.65 [0.61]

Unshaved buttock 0.87 [0.62] 0.66 [0.59] Notes

2. For the mean melanin density, the average was taken of the spring value, summer value, autumn value and average two winter values.

3. For the melanin density results of the buttock, three men and four women were excluded due to nude sunbathing and/or solarium use.