Childhood Growth and Breast Cancer

B. L. De Stavola1 , I. dos Santos Silva1, V. McCormack1, R. J. Hardy2, D. J. Kuh2 and M. E. J. Wadsworth2

1 Department of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, London, United Kingdom.
2 Department of Epidemiology, University College London Medical School, London, United Kingdom.

Received for publication June 23, 2003; accepted for publication November 6, 2003.


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Adult height is known to be positively associated with breast cancer risk. The mechanism underlying this association is complex, since adult height is positively correlated with age at menarche, which in turn is negatively associated with breast cancer risk. The authors used prospective data from a British cohort of 2,547 girls followed from birth in 1946 to the end of 1999 to examine breast cancer risk in relation to childhood growth. As expected, adult height was positively associated with age at menarche and breast cancer. In childhood, cases were taller and leaner, on average, than noncases. Significant predictors of breast cancer risk in models containing all components of growth were height velocity at age 4–7 years (for a one-standard-deviation increase, odds ratio (OR) = 1.54, 95% confidence interval (CI): 1.13, 2.09) and age 11–15 years (OR = 1.29, 95% CI: 0.97, 1.71) and body mass index velocity (weight (kg)/height (m)2/year) at age 2–4 years (OR = 0.63, 95% CI: 0.48, 0.83). The effects of these variables were particularly marked in women with early menarche (age <12.5 years). These findings suggest that women who grow faster in childhood and reach an adult height above the average for their menarche category are at particularly increased risk of breast cancer.

body height; body weight; breast neoplasms; child; growth; menarche

Abbreviations: Abbreviations: BMI, body mass index; CI, confidence interval; OR, odds ratio; SD, standard deviation.


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Adult height is known to be positively associated with breast cancer risk at both a population level (13) and an individual level (47). Current views identify growth in childhood, a marker of nutrition and levels of hormones—such as growth factors and estrogens—as the underlying dimension linking height and breast cancer (711). However, the relation may be more complex, because age at menarche, which is a milestone in a girl’s growth trajectory, is negatively associated with breast cancer risk (12) but positively correlated with adult height (13). Few researchers have investigated how growth in childhood influences breast cancer risk (1421), mainly because recorded childhood growth data for women at risk of developing breast cancer are difficult to obtain, while recall of childhood anthropometric variables is likely to be poor.

We had the opportunity to investigate the role of childhood growth trajectories and age at menarche in breast cancer etiology using a British national cohort of approximately 2,500 women who have been followed since their birth in 1946 and for whom data on childhood growth, age at menarche, and adult-life risk factors for breast cancer have been recorded prospectively. Follow-up information collected through the end of 1999, when the cohort was 53 years old, was used in these analyses.


    MATERIALS AND METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Subjects
We analyzed data from the Medical Research Council National Survey of Health and Development. This is a study of a socially stratified birth cohort of 2,547 women and 2,815 men born during the week of March 3–9, 1946, in England, Scotland, and Wales (22, 23). The cohort comprised legitimate singleton births to the wives of all nonmanual and agricultural workers and to one in four wives of manual workers. Study participants have been actively followed from birth through childhood and adult life, up to the age of 53 years. Most of the contacts made in the study were home interviews or examinations carried out at school, where trained personnel collected demographic, anthropometric (height and weight), and reproductive data (for more details, see De Stavola et al. (24)). From 1993 to 1999, when the cohort members were aged 47–53 years, a postal health questionnaire was sent to all women in the study with whom there was still direct contact (25). Details on menopausal status and self-reported breast cancer diagnosis were thus collected, together with information on several other health indicators. In addition, all cohort members were "flagged" in the National Health Service Central Register at its inception in 1971, and this provided us with information on cancer registration, death, and emigration for all members of the cohort, including those still resident in the United Kingdom with whom there is no longer direct contact.

The present analyses were restricted to women who were alive and residing in the United Kingdom in 1971. A total of 114 women who died (none from breast cancer) and 176 who had emigrated before January 1, 1971 (and were lost to the study) were excluded. A further 70 women did not have any childhood height measurements and thus could not contribute to the analyses. This left 2,187 women available for study.

Childhood measurements of height and body mass index (BMI), defined as weight (kg)/height (m)2, were available for the ages of 2, 4, 6, 7, 11, and 14/15 years. Adult height (as a marker of total height achieved by the end of the adolescent growth spurt) was self-reported at age 26 years and was measured at ages 36 and 43 years; leg length was calculated at age 43 years from measures of sitting and standing height. Yearly rates of change ("velocities") between consecutive anthropometric measurements were calculated using in the denominators the exact differences in age at measurement. All anthropometric variables and velocities were standardized to have a zero mean value and a unit variance in order to facilitate comparisons of effects. Age at menarche was reported by the participants’ mothers when the girls were 15 years old or, when this information was not available, by the participants when they were 48 years old (n = 210); for 198 women (9 percent of those included in the present analyses), age at menarche was unknown. Information on other prenatal, birth, childhood, and adulthood variables was also used. This included birth weight, extracted from the birth records near the time of birth of the cohort members, birth order, and mothers’ reports of their own and fathers’ heights and of fathers’ occupations, all recorded at a home visit when the participants were 4 years old. Data on age at first birth and parity were recorded and were updated at successive follow-up visits. Of the available data on social class, we used the social class recorded at age 36 years, that is, before any breast cancer diagnosis.

Statistical methods
Follow-up time was defined from January 1, 1971 (when the women were aged 24 years) to the first among the following: breast cancer diagnosis, emigration, death, or December 31, 1999 (the final date for which National Health Service Central Register cancer registration data could be considered complete). Cox regression models defined on the age time scale were used to estimate rate ratios for a one-standard-deviation (1-SD) increase in height and BMI achieved at different ages and for a 1-SD increase in their interval-specific velocities. In each analysis, the proportional hazards assumption was checked using Schoenfeld’s residuals (26). We fitted both univariable and multivariable regression models when studying the effects of growth velocities. Thus, in multivariable models, the estimated effect of each velocity was controlled for the influence of the other included anthropometric variables.

Because of missing data, these analyses were based on the subsets of women for whom data on the relevant anthropometric measurements were available. To overcome the limitations of these complete-records analyses, we used a multiple imputation procedure (27, 28) to allow the inclusion of all 2,187 eligible subjects in every analysis. This multiple imputation procedure replaces missing values with several versions of imputed ones and relies on the assumption that missing data are missing at random, that is, that missingness does not depend upon unobserved or unobservable variables (29). The implementation of this procedure, described in the Appendix, required the fitting of logistic regression models (30) for breast cancer diagnosed by December 31, 1999 (i.e., when the women were aged 53 years), instead of Cox regression models. This was because of the complexities that arise when imputing survival data (31). For comparison, logistic regression models were also fitted to the complete records.

Cox and logistic regression analyses, as well as the multiple imputation procedure, were carried out in Stata 8 (32); the growth models fitted for the imputations were constructed using the latent variable structural equation modeling program Mplus 2.13 (33). All reported p values are two-sided.


    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Fifty-nine women out of 2,187 were diagnosed with breast cancer, at ages ranging from 36.4 years to 53.8 years (median, 49.2 years; 25th and 75th percentiles, 45.0 and 51.8). Of these women, 21 were known to have been premenopausal (age at diagnosis: 36–51 years) and nine were known to have been naturally postmenopausal (age at diagnosis: 46–53 years) at the time of diagnosis. A further 12 women had undergone hysterectomy before diagnosis or declared themselves to be postmenopausal at diagnosis but did not specify whether the menopause was natural. For the remaining 17, no information on age at menopause was available. Over 95 percent of the 2,128 women with no diagnosis of breast cancer were followed up to age 53.8 years, that is, to the end of 1999.

Data on childhood anthropometric measures were missing for 11–24 percent of the women, and data on height measurements in adulthood were missing for approximately 25 percent (table 1). Overall, the probability of a childhood measure’s not having been collected was found not to be related to height or BMI at later ages (when data were available) or to eventual breast cancer diagnosis. However, the availability of measures at age 15 years or older was weakly related to paternal social class (the odds of an adult measure’s being available were lower if the father was employed in a manual occupation; p = 0.02–0.08).


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TABLE 1. Mean values for prospective anthropometric measurements, Medical Research Council 1946 birth cohort,* United Kingdom, 1946–1999
 
A comparison of mean heights at different ages (up to adulthood) for breast cancer cases and noncases showed heights for cases to be consistently higher. The reverse was seen for mean BMI in childhood; the age at which BMI was at its lowest, a measure used to define the adiposity rebound (34, 35), was lower for cases than for noncases, on average (figure 1).



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FIGURE 1. Mean age-specific height and body mass index (BMI) (weight (kg)/height (m)2) values according to breast cancer status, Medical Research Council 1946 birth cohort, United Kingdom, 1946–1999. —, breast cancer cases; – – –, noncases.

 
Univariable models
The rate ratios (data not shown) and odds ratios estimated using the observed data (table 2) were very similar. There was a positive association between greater adult stature and breast cancer risk; the observed odds ratio for a 1-SD increase in adult height ranged from 1.28 for self-reported height at age 26 years to 1.37 for measured height at age 36 years, and the odds ratio for height measured or imputed at age 36 years was 1.28 (all borderline significant). Similar effects were found for a 1-SD increase in height at ages 7 and 15 years; at other ages, the direction of the effect was the same but much weaker. By contrast, a 1-SD increase in BMI at different ages appeared to be mildly protective (but none of the odds ratios were significant). The opposite effects of BMI and height at ages 2 and 4 years are in accord with their respective negative correlations, although at later ages BMI and height were positively correlated, particularly at age 11 years (table 3).


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TABLE 2. Estimated univariate odds ratios for breast cancer according to a one-standard-deviation increase in anthropometric measures at different ages, Medical Research Council 1946 birth cohort, United Kingdom, 1946–1999*
 

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TABLE 3. Correlation coefficients for height and BMI{dagger},{ddagger} values and velocities measured at different ages among 2,187 women followed to the age of 53 years, Medical Research Council 1946 birth cohort, United Kingdom, 1946–1999
 
The odds ratios for the height velocities (table 2), as opposed to their absolute values, identified the period between ages 4 and 7 years as the one in which height gains have the greatest association with breast cancer risk (observed odds ratio (OR) = 1.33, p = 0.04; multiple imputation OR = 1.31, p = 0.04). The estimated odds ratio for a 1-SD increase in height velocity between the ages of 11 and 15 years also indicated raised odds (observed OR = 1.16; multiple imputation OR = 1.12), while that for an increase between age 15 and adulthood (which is negatively correlated with most height velocities (table 3)) seemed to be protective (observed OR = 0.89; multiple imputation OR = 0.88), though neither was significant. None of the odds ratios for the BMI velocities were far from the null value of 1 or close to being significant.

These findings partly reflect the known association between early menarche and breast cancer risk. Women in the bottom third of the distribution of age at menarche (<12.5 years), on average, were taller in childhood (figure 2) and had greater height velocities at ages 4–7 years and 7–11 years (table 4). In our data, girls with an earlier age at menarche (<12.5 years) had 43 percent greater odds of contracting breast cancer (OR = 1.43, 95 percent confidence interval (CI): 0.73, 2.80) than girls in the top third of age at menarche (>=13.5 years). Despite this, girls with early menarche appeared to have two protective features: 1) they were shorter adults, mainly because they had slower height velocities after age 11 (table 4), and 2) they had greater BMI at all ages (figure 2). As expected, they also had a lower average leg length in adulthood (table 4). Thus, not all of the associations found between the separate growth velocities and breast cancer risk are consistent with the effect of age at menarche.



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FIGURE 2. Mean age-specific height and body mass index (BMI) (weight (kg)/height (m)2) values according to age at menarche, Medical Research Council 1946 birth cohort, United Kingdom, 1946–1999. —, age <12.5 years; – – –, age 12.5–13.4 years; - - - -, age >=13.5 years; – · –, missing data.

 

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TABLE 4. Selected mean values for observed height, height velocity, BMI,*,{dagger} and BMI velocity according to age at menarche among 2,187 women followed to the age of 53 years, Medical Research Council 1946 birth cohort, United Kingdom, 1946–1999
 
To clarify these results, we fitted a series of models that included either all of the height growth components or all of the BMI growth components, or both, and then conducted analyses stratified by age at menarche.

Multivariable models
Overall, similar estimates were found when the complete-records approach (i.e., using only the available data) and the multiple imputation procedure were used. The first set of results depends on the assumption that missing values were missing completely at random, that is, that they were unrelated to observed or unobserved data. Multiple imputation results instead rely on the assumption that the missing values were only missing at random, that is, that they may have been related to the observed data. Thus, if a correct multiple imputation procedure is implemented, the multiple imputation results are to be preferred, since they rely on less restrictive assumptions. These results are reported in table 5.


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TABLE 5. Joint estimates of odds ratios for breast cancer according to a one-standard-deviation increase in components of height and BMI*,{dagger} at different ages, Medical Research Council 1946 birth cohort, United Kingdom, 1946–1999{ddagger}
 
In the model with the height intercept at age 2 years plus all of the consecutive height velocities (a decomposition of the model with just adult height), the four height velocities from age 2 years to age 15 years showed positive effects (table 5). Among them, the height velocity from age 4 years to age 7 years had the greatest and most significant estimated effect (OR = 1.41, 95 percent CI: 1.08, 1.85; p = 0.01).

In the model containing all of the BMI components up to age 15 years (table 5), only BMI velocity at age 2–4 years seemed to be significantly protective (OR = 0.74, 95 percent CI: 0.57, 0.97; p = 0.02). Since average velocity at these ages was negative (figure 1), girls whose BMI decreased more slowly appeared to be at reduced risk for a given size at age 2 years and a given trajectory after age 4 years. One way in which this could happen is through slower height velocities at the same ages. Since height and BMI velocities at age 2–4 years are negatively correlated (table 3), this protective effect may simply reflect the opposite effect of concurrent height changes. However, when all of the height and BMI components were included in the same model, the effect of BMI velocity at age 2–4 years was strengthened in size and significance, while that for the corresponding height velocity was reduced, with all of the other effects left substantially unchanged (table 5). Controlling for known breast cancer risk factors such as age at first birth, the interval between menarche and first birth, parity, social class, and adult BMI did not substantially alter these results.

Stratification by category of age at menarche showed that among women with early menarche (age <12.5 years), the participants with breast cancer had gained height more quickly both between the ages of 4 and 7 years and between the ages of 11 and 15 years, making them, on average, 5 cm taller as adults (166.4 cm vs. 161.5 cm), with legs approximately 3 cm longer (77.8 cm vs. 74.9 cm). Cases in this group also had faster decreases in BMI at age 2–4 years, a later adiposity rebound, and slightly slower increases thereon, making them 1.5–2.0 kg/m2 lighter from age 4 years (figure 3). There were not such clear differences between cases and noncases in the other two age-at-menarche groups. When all noncases were compared, as expected, those with early menarche were, on average, shorter and heavier adults (figure 4); the opposite was observed among the cases (figure 5). Some of these observations were confirmed when interaction terms between growth velocities and age at menarche were included in the model with all of the height and BMI components. There was evidence that the effects of greater height velocities at ages 4–7 and 11–15 years were stronger for women with earlier ages at menarche (table 6). Similarly, the protective effect of slower decreases in BMI velocity at age 2–4 years seemed to be relevant only for women who had an early menarche (table 6). When we fitted a model containing only adult height, categories of age at menarche, and their interactions, we found the effect of tall adult stature to be significantly stronger for participants with early menarche; this is in line with the findings for the height velocities at ages 4–7 and 11–15 years (test for interaction: p = 0.04; test for linear trend across the three categories of age at menarche: p = 0.02). Repetition of these analyses with five categories of age at menarche instead of three (<11.75, 11.75–<12.5, 12.5–<13.5, 13.5–<14.25, and >=14.25 years, containing 10, 9, 18, 11, and 5 cases, respectively) led to very similar trends, with effects being strongest in the group with very early menarche. However, the numbers involved were too small for us to draw any inferences.



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FIGURE 3. Mean age-specific height and body mass index (BMI) (weight (kg)/height (m)2) values according to breast cancer status among women aged less than 12.5 years at menarche, Medical Research Council 1946 birth cohort, United Kingdom, 1946–1999. —, breast cancer cases; – – –, noncases.

 


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FIGURE 4. Mean age-specific height and body mass index (BMI) (weight (kg)/height (m)2) values in participants without breast cancer according to age at menarche, Medical Research Council 1946 birth cohort, United Kingdom, 1946–1999. —, age <12.5 years; – – –, age 12.5–13.4 years; - - - -, age >=13.5 years.

 


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FIGURE 5. Mean age-specific height and body mass index (BMI) (weight (kg)/height (m)2) values in participants with breast cancer according to age at menarche, Medical Research Council 1946 birth cohort, United Kingdom, 1946–1999. —, age <12.5 years; – – –, age 12.5–13.4 years; - - - -, age >=13.5 years.

 

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TABLE 6. Estimates* of odds ratios for breast cancer according to a one-standard-deviation increase in anthropometric measures at certain ages, by age at menarche, Medical Research Council 1946 birth cohort, United Kingdom, 1946–1999{dagger}
 
Note that although these stratified analyses were restricted to women with known ages at menarche and thus may have been affected by selection bias, the growth trajectories and adult heights of women with missing data on age at menarche were similar to the averages for women whose age at menarche was known (figure 2).


    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
In this study, we aimed to identify the components of growth that may drive the positive association between adult height and breast cancer risk while examining their relation with age at menarche.

Main findings
We found that, overall, breast cancer cases were taller and had been slimmer throughout childhood. Multivariable logistic regression models identified fast height gains between ages 4 and 7 years and 11 and 15 years and steep decreases in BMI between ages 2 and 4 years as the strongest positive predictors of breast cancer risk. When the analyses were stratified by category of age at menarche, the adverse effects of fast height velocities at ages 4–7 and 11–15 years appeared to weaken for women with later ages at menarche, and fast decreases in BMI between ages 2 and 4 years appeared to be harmful only for women with early menarche (age <12.5 years).

Strengths and weaknesses
Our results were based on prospectively recorded data and therefore were not affected by recall bias. Measurements of height and weight at several ages were available, allowing the modeling of individual growth trajectories. However, no anthropometric data were collected between the ages of 11 and 14 years, and thus we could not estimate the age of peak height velocity (i.e., the maximum yearly rate of height gain) or obtain smoother fits of the growth trajectories around these ages. However, age at peak height velocity is closely correlated with age at menarche (36). In addition, we did not have any measurements for the period between birth and age 2 years or measurements of birth length, so we could not examine the effect of growth in infancy. However, the inclusion of birth weight in either the univariable models or the multivariable models did not change any of the results.

As in all long-term cohort studies, the results were affected by missing data. This was of particular concern because the complete-records analyses of all growth components involved less than 40 percent of all subjects (803/2,187). We dealt with the potential biases of such analyses by adopting a multiple imputation procedure. Such an approach has been used in several recent epidemiologic publications (37, 38) and relies on the assumption that data are missing at random (29). The most crucial step of the multiple imputation procedure is the one that generates the imputed data (28). In our analyses, imputations were based on predictions generated from all of the available information relevant to the growth patterns and to the missingness mechanism. This included all of the nonmissing data on growth and age at menarche, as well as parental and family characteristics, birth weight, and breast cancer incidence in adult life. It was not possible to formally investigate whether data were truly missing at random or were affected by informative missingness (28). However, we had no a priori expectations that anthropometric data would be missing for some unmeasured reason(s), and we found only weak evidence that adult height measures were more likely to be missing if the girls’ fathers were in manual occupations. We accounted for this in the imputation step. Overall, the results obtained from the complete-records approach and the multiple imputation approach were very similar.

Stratifying the analyses by age at menarche facilitated the examination of different growth features, confirming well-known (36) and recent findings relating higher childhood BMI to earlier menarche and the latter to reduced height gains in adolescence (13, 39, 40). We did not use multiple imputation to deal with missing age at menarche, because this would have required simultaneous modeling of growth and timing of menarche via stronger assumptions than those used to deal with the missing anthropometric data. However, although we excluded 198 women for whom information on age at menarche was not available, their growth profiles were very close to the average profile of women for whom age at menarche was known (except when the data were too sparse—for example, for BMI at age 15 (figure 2)); this suggests that data on age at menarche were possibly missing completely at random. Thus, results obtained after exclusion of these women should not have been substantially affected by selection bias.

Interpretation
Tallness in adulthood is a recognized risk factor for female breast cancer (6). Its effect probably incorporates influences of some of the correlates of height, such as infant and childhood growth and nutrition (711). Early age at menarche is another established risk factor for breast cancer (12, 41). Its effect is associated with greater exposure to estrogens, which are likely to be promoters of this cancer (42). Before puberty, adrenal androgens are converted into estrogens in adipose tissues, and thus heavier girls have higher estrogen levels (43, 44). These, in turn, are linked to higher levels of growth hormone and thus to faster skeletal maturation and earlier onset of the pubertal growth spurt. Girls who undergo puberty earlier tend to be taller and heavier than their peers in childhood (45, 46).

Skeletal growth normally reaches completion approximately 2 years after menarche (36). Thus, girls with earlier puberty, on average, end their growth spurt at younger ages than other girls and as a result are shorter adults. This crossover in average height profiles for the different age-at-menarche groups was seen clearly in our data. At an individual level, however, variations in duration and intensity of the pubertal growth spurt may lead to greater adult height than would be predicted by age at menarche. Several interacting sex and growth hormones regulate the growth spurt (43, 47). Estradiol and insulin-like growth factor I, in particular, are thought to be involved in suppressing cell division after puberty and thus in switching off the process of linear growth (45). Our finding of significant interactions between timing of menarche and height velocity seems to indicate that elevated levels of some of these hormones during and after puberty may be important in the etiology of breast cancer. Unfortunately, no biologic samples were collected during childhood for this birth cohort, so no specific analyses are possible.

Our results agree with findings from several other studies. When childhood anthropometric data have been available, investigators have found that women who were tall and thin in childhood (18) or were lean at age 10–14 years (14) are at higher risk of breast cancer (at all ages or at premenopausal ages, respectively). When childhood anthropometric data were based on recall, results were similar. In a multinational case-control study of breast cancer among twins, cancer patients diagnosed at young ages recalled having been taller and lighter at age 10 years than their unaffected co-twins (20). In another two case-control studies carried out in the United States, premenopausal cases recalled having been significantly heavier, but not taller, at ages 12–13 years than their contemporaries (16), while postmenopausal cases recalled having reached their maximum height at younger ages than population-based controls (15). Similarly, analyses from the Nurses’ Health Study (17) found recalled greater body size at age 10 years to be associated with decreased risk of premenopausal breast cancer but not postmenopausal breast cancer. In that same study (17), higher peak height velocity was instead associated with both pre- and postmenopausal breast cancer risk, which is in agreement with results reported by Li et al. (15).

No associations between childhood height and breast cancer risk were found in two other studies (19, 21). The first study (19) was a case-control study of members of Kaiser Permanente, a health maintenance organization that had prospective medical records containing height measurements of their clients from childhood. Unfortunately, these data were collected irregularly, and each measure was available for only a small number of women, which limited the analyses to comparisons of averages in broad age groups. The second study (21), a case-control study conducted in a low-risk Chinese population, relied on self- and maternal recalls of how women compared with their peers in terms of height and weight at ages 10, 15, and 20 years. Therefore, only analyses of relative and not absolute differences in size were possible. Since the women in that study had a very late average age at menarche (>14 years), they corresponded to the late menarche group in our cohort. Thus, the failure to find an association between childhood growth and breast cancer risk in this Chinese population is consistent with our findings for the late menarche group.

Our results are based on cancer detected at relatively young ages (up to 53 years) and thus may apply only to risk of breast cancer at young, mainly premenopausal, ages. Studies involving a broader range of ages at diagnosis will be required to confirm the associations reported here and to investigate whether they are also relevant to postmenopausal breast cancer. Opportunities to undertake that work will arise as this cohort is followed further and as the other British national birth cohorts—those born in 1958 and 1970, which are known to have prepubertal growth patterns considerably different from those observed in the 1946 birth cohort (48)—reach the relevant ages for breast cancer risk.


    ACKNOWLEDGMENTS
 
The MRC Survey of Health and Development was funded by the United Kingdom Medical Research Council. This work was conducted within the MRC Co-operative Group on Life Course and Trans-generational Influences on Disease Risk (grant G9819083).


    APPENDIX
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
The Multiple Imputation Procedure

The multiple imputation procedure consisted of three steps: imputation, analysis, and summary. Briefly, in the imputation step, we jointly modeled the repeated measurements of height and body mass index (BMI) using a bivariate random-effects growth model. We then used the model’s estimated parameters and expected distributions to draw five sets of imputed replacements for the missing anthropometric values. In the analysis step, we fitted logistic regression models to the data generated in each imputation run. In the summary step, we summarized the results obtained from each imputed data set.

The procedure is outlined in detail below.

Imputation
Five sets of imputed values for the missing data on height and BMI were drawn from their distributions, conditional on the observed values, and merged with the available data to make five "imputed data sets." For every imputation, the mean of the conditional distribution of the missing values was a random draw from predicted values derived from a growth model fitted to the observed data. The variance of the conditional distribution used in each imputation was a random draw from the conditional variance implied by the growth model. Thus, when creating the five imputed data sets, we followed these imputation steps:

Step A
A random bivariate polynomial random coefficients model (49, 50) was fitted by maximum likelihood (using the expectation maximization algorithm to deal with missing-at-random values (33)) to repeated measures of height at ages 2, 4, 6, 7, 11, 15, 26, 36, and 43 years and repeated measures of BMI at ages 2, 4, 6, 7, 11, and 15 years, all assumed to be normally distributed. The mean values of the random coefficients were modeled as functions of birth weight, maternal height, birth order, father’s occupation during childhood, age at menarche, and breast cancer incidence. The individual predicted values of the missing height and BMI values and the estimated components of the conditional variance matrix were saved.

Step B
For every imputation step l, with l = 1, ..., 5:

i. the components of the conditional variance matrix were drawn from inverse Wishart distributions with parameters defined by the conditional variance estimated in step A;

ii. the imputed values for the missing height and BMI data were drawn from normal distributions with means given by the predicted values estimated in step A and the conditional variance matrix drawn in step Bi; and

iii. the missing values were replaced by imputed values and the data were saved as imputed data set l.

Analysis
Logistic regression analyses were carried out on each imputed data set, and the resulting estimated parameters (on the logarithmic scale) and variance matrix (for the log-transformed parameters) were saved.

Summary
The resulting estimates from all imputed data sets were summarized as estimated log odds ratios (and respective standard errors), following the method of Shafer (51).


    NOTES
 
Correspondence to Dr. Bianca De Stavola, Department of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, United Kingdom (e-mail: bianca.destavola{at}lshtm.ac.uk). Back


    REFERENCES
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 

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