THREE AUTHORS REPLY

THREE AUTHORS REPLY Goldberg and Terry raise several points of interest in their letter (1). These arise from the complexities of modeling—and then interpreting—the relationship between early-life longitudinal information and later-life outcomes. Because such analyses were at the core of our paper (2), we welcome the opportunity to clarify our results. The first point Goldberg and Terry raise concerns our report of no association between successive increments in standardized height and weight in infancy/early childhood (later referred to as z scores) and either total breast volume or percent water. Goldberg and Terry point out that the estimates that refer to these successive increments are mutually adjusted and hence, in their view, can only capture “direct effects” of each of these increments (1). We disagree with this interpretation, as explained below. This criticism would be correct if we had used absolute z scores when fitting the models. However, by using consecutive increments of z scores, we estimated the cumulative effect of increasing each age-specific z score by 1 unit. As De Stavola et al. (3) previously demonstrated in their equation 5, a model that is specified in terms of absolute values of an exposure measured longitudinally can be reparameterized as a model that includes the first of these measures and its consecutive increments, with the coefficients of the 2 model specifications having different interpretations. Letting Y denote percent water and Zj the z score measured at time j, for j = 1 . . . J, with Z1 indicating birth weight (or birth length), the 2 model specifications are E(Y|Z1,Z2,…,ZJ)=β0+β1Z1+β2Z2+…+βJZJ. (1) E(Y|Z1,Z2,…,ZJ)=β0+(∑j=1Jβj)Z1+(∑j=2Jβj)(Z2−Z1)+(∑j=3Jβj)(Z3−Z2)+…+βJZJ. (2) These equations show that the coefficient of each explanatory variable in the second specification (equation 2) is the sum of the coefficients for the corresponding and later z score terms in the first specification (equation 1). Hence, each regression coefficient in equation 2 is to be interpreted as the expected cumulative change in Y per 1-unit change in each of the relevant z scores and therefore in a sense represents a “total effect.” This is in contrast to the individual βj coefficients in equation 1 that could instead be interpreted as “direct effects.” However, we refrain from labeling these coefficients using this terminology, because of the additional assumptions (especially those of no unmeasured confounding) invoked in mediation analysis (4). The results presented in our paper (2) are for models specified as in equation 2 and covering the full range of measurements, that is, from birth to young adulthood. In response to Goldberg and Terry’s comments (1), therefore, we report here results from alternative versions of the second specification of the model (equation 2), where we vary the timing of the final increment when estimating the association between growth trajectories and MRI percent water (Table 1). The size and significance of these new sets of estimates show how it is still the later (postpubertal) measurements that exert the strongest impact, confirming our original interpretation. Table 1. Relative Change (Cumulative Linear Regression Models) in Magnetic Resonance Imaging Breast Percent Water at Age 21 Years With Birth Length, Birth Weight, and Height and Weight Velocities Between Birth and Age 21 Years (n = 480), Avon Longitudinal Study of Parents and Children, 1991–2014 Growth Variable Model of RC in MRI Percent Breast Watera P for Interactionb Model 1 Model 2 Model 3 Model 4 Model 5 RCc 95% CId RC 95% CI RC 95% CI RC 95% CI RC 95% CI Height, cm  Birth length 1.02 0.98, 1.07 0.99 0.93, 1.05 0.99 0.93, 1.06 0.98 0.93, 1.04 0.98 0.93, 1.03  Height increments between  specified agese   Birth to 3 months 1.02 0.96, 1.08 1.09 0.98, 1.20 1.08 0.98, 1.20 1.07 0.98, 1.16 1.06 0.98, 1.15 0.325   3–12 months 1.01 0.96, 1.07 0.93 0.82, 1.05 0.93 0.83, 1.05 0.94 0.85, 1.04 0.95 0.86, 1.04 0.843   1–3 years 1.02 0.97, 1.07 1.12 0.99, 1.25 1.12 1.00, 1.25 1.10 1.00, 1.21 1.10 1.00, 1.20 0.737   3–7 years 1.00 0.96, 1.05 0.92 0.82, 1.03 0.92 0.82, 1.02 0.94 0.86, 1.03 0.95 0.87, 1.03 0.224   7–10 years 1.06 1.00, 1.12 1.07 1.01, 1.13 1.06 1.01, 1.12 1.06 1.01, 1.11 0.052   10–12 years 0.97 0.95, 1.00 1.01 0.98, 1.03 1.01 0.99, 1.03 0.101   12–15 yearsf 1.07 1.04, 1.10 1.05 1.02, 1.08 0.475 Weight, kg  Birth weight 1.03 0.99, 1.06 1.03 0.99, 1.06 1.03 1.00, 1.07 1.04 1.01, 1.07 1.07 1.04, 1.10  Weight increments between specified agese   Birth to 3 months 0.99 0.97, 1.02 0.99 0.96, 1.01 0.99 0.97, 1.01 1.00 0.98, 1.02 1.01 0.99, 1.03 0.038   3–12 months 0.97 0.95, 1.00 0.97 0.95, 1.00 0.97 0.95, 0.99 0.98 0.96, 1.00 1.00 0.98, 1.03 0.104   1–3 years 1.00 0.97, 1.03 0.98 0.95, 1.01 0.97 0.94, 1.00 0.99 0.96, 1.01 1.02 1.00, 1.05 0.300   3–7 years 0.88 0.85, 0.91 0.97 0.92, 1.02 0.95 0.91, 1.00 0.94 0.90, 0.98 1.03 0.98, 1.09 0.347   7–10 years 0.91 0.87, 0.94 0.89 0.86, 0.93 0.94 0.91, 0.97 1.03 0.99, 1.08 0.153   10–12 years 0.93 0.91, 0.96 0.95 0.93, 0.97 0.94 0.92, 0.96 0.992   12–15 years 0.89 0.87, 0.90 0.89 0.88, 0.91 0.761   15–21 years 0.79 0.73, 0.85 0.118 Growth Variable Model of RC in MRI Percent Breast Watera P for Interactionb Model 1 Model 2 Model 3 Model 4 Model 5 RCc 95% CId RC 95% CI RC 95% CI RC 95% CI RC 95% CI Height, cm  Birth length 1.02 0.98, 1.07 0.99 0.93, 1.05 0.99 0.93, 1.06 0.98 0.93, 1.04 0.98 0.93, 1.03  Height increments between  specified agese   Birth to 3 months 1.02 0.96, 1.08 1.09 0.98, 1.20 1.08 0.98, 1.20 1.07 0.98, 1.16 1.06 0.98, 1.15 0.325   3–12 months 1.01 0.96, 1.07 0.93 0.82, 1.05 0.93 0.83, 1.05 0.94 0.85, 1.04 0.95 0.86, 1.04 0.843   1–3 years 1.02 0.97, 1.07 1.12 0.99, 1.25 1.12 1.00, 1.25 1.10 1.00, 1.21 1.10 1.00, 1.20 0.737   3–7 years 1.00 0.96, 1.05 0.92 0.82, 1.03 0.92 0.82, 1.02 0.94 0.86, 1.03 0.95 0.87, 1.03 0.224   7–10 years 1.06 1.00, 1.12 1.07 1.01, 1.13 1.06 1.01, 1.12 1.06 1.01, 1.11 0.052   10–12 years 0.97 0.95, 1.00 1.01 0.98, 1.03 1.01 0.99, 1.03 0.101   12–15 yearsf 1.07 1.04, 1.10 1.05 1.02, 1.08 0.475 Weight, kg  Birth weight 1.03 0.99, 1.06 1.03 0.99, 1.06 1.03 1.00, 1.07 1.04 1.01, 1.07 1.07 1.04, 1.10  Weight increments between specified agese   Birth to 3 months 0.99 0.97, 1.02 0.99 0.96, 1.01 0.99 0.97, 1.01 1.00 0.98, 1.02 1.01 0.99, 1.03 0.038   3–12 months 0.97 0.95, 1.00 0.97 0.95, 1.00 0.97 0.95, 0.99 0.98 0.96, 1.00 1.00 0.98, 1.03 0.104   1–3 years 1.00 0.97, 1.03 0.98 0.95, 1.01 0.97 0.94, 1.00 0.99 0.96, 1.01 1.02 1.00, 1.05 0.300   3–7 years 0.88 0.85, 0.91 0.97 0.92, 1.02 0.95 0.91, 1.00 0.94 0.90, 0.98 1.03 0.98, 1.09 0.347   7–10 years 0.91 0.87, 0.94 0.89 0.86, 0.93 0.94 0.91, 0.97 1.03 0.99, 1.08 0.153   10–12 years 0.93 0.91, 0.96 0.95 0.93, 0.97 0.94 0.92, 0.96 0.992   12–15 years 0.89 0.87, 0.90 0.89 0.88, 0.91 0.761   15–21 years 0.79 0.73, 0.85 0.118 Abbreviations: CI, confidence interval; MRI, magnetic resonance imaging; RC, relative change. a RC in breast percent water per 1–standard-deviation increment in the exposure of interest. bP value for the interaction of each height increment with birth length and of each weight increment with birth weight explored in model 5. c RC estimates were adjusted for all of the earlier height and weight measurements, and additionally for age and menstrual phase at MRI examination. Data on MRI breast percent water were log-transformed. Exponentiated estimated regression parameters are presented. d 95% CIs were calculated by exponentiating the original 95% CIs (as detailed in our paper (2)). e Height and weight growth measures from birth to age 10 years were derived using linear spline multilevel modeling of height and weight (as detailed by Howe et al. (5)). From age 10 years onward, growth measures were calculated from a piecewise mixed-effect model with knots at ages 10, 12, and 15 years (as detailed in our paper (2)). All growth measures and all growth differences were standardized, with regression coefficients representing expected changes per 1 standard deviation. f Adult height is attained by age 15 years, and therefore height increments between ages 15 and 21 years were not included in the model. Table 1. Relative Change (Cumulative Linear Regression Models) in Magnetic Resonance Imaging Breast Percent Water at Age 21 Years With Birth Length, Birth Weight, and Height and Weight Velocities Between Birth and Age 21 Years (n = 480), Avon Longitudinal Study of Parents and Children, 1991–2014 Growth Variable Model of RC in MRI Percent Breast Watera P for Interactionb Model 1 Model 2 Model 3 Model 4 Model 5 RCc 95% CId RC 95% CI RC 95% CI RC 95% CI RC 95% CI Height, cm  Birth length 1.02 0.98, 1.07 0.99 0.93, 1.05 0.99 0.93, 1.06 0.98 0.93, 1.04 0.98 0.93, 1.03  Height increments between  specified agese   Birth to 3 months 1.02 0.96, 1.08 1.09 0.98, 1.20 1.08 0.98, 1.20 1.07 0.98, 1.16 1.06 0.98, 1.15 0.325   3–12 months 1.01 0.96, 1.07 0.93 0.82, 1.05 0.93 0.83, 1.05 0.94 0.85, 1.04 0.95 0.86, 1.04 0.843   1–3 years 1.02 0.97, 1.07 1.12 0.99, 1.25 1.12 1.00, 1.25 1.10 1.00, 1.21 1.10 1.00, 1.20 0.737   3–7 years 1.00 0.96, 1.05 0.92 0.82, 1.03 0.92 0.82, 1.02 0.94 0.86, 1.03 0.95 0.87, 1.03 0.224   7–10 years 1.06 1.00, 1.12 1.07 1.01, 1.13 1.06 1.01, 1.12 1.06 1.01, 1.11 0.052   10–12 years 0.97 0.95, 1.00 1.01 0.98, 1.03 1.01 0.99, 1.03 0.101   12–15 yearsf 1.07 1.04, 1.10 1.05 1.02, 1.08 0.475 Weight, kg  Birth weight 1.03 0.99, 1.06 1.03 0.99, 1.06 1.03 1.00, 1.07 1.04 1.01, 1.07 1.07 1.04, 1.10  Weight increments between specified agese   Birth to 3 months 0.99 0.97, 1.02 0.99 0.96, 1.01 0.99 0.97, 1.01 1.00 0.98, 1.02 1.01 0.99, 1.03 0.038   3–12 months 0.97 0.95, 1.00 0.97 0.95, 1.00 0.97 0.95, 0.99 0.98 0.96, 1.00 1.00 0.98, 1.03 0.104   1–3 years 1.00 0.97, 1.03 0.98 0.95, 1.01 0.97 0.94, 1.00 0.99 0.96, 1.01 1.02 1.00, 1.05 0.300   3–7 years 0.88 0.85, 0.91 0.97 0.92, 1.02 0.95 0.91, 1.00 0.94 0.90, 0.98 1.03 0.98, 1.09 0.347   7–10 years 0.91 0.87, 0.94 0.89 0.86, 0.93 0.94 0.91, 0.97 1.03 0.99, 1.08 0.153   10–12 years 0.93 0.91, 0.96 0.95 0.93, 0.97 0.94 0.92, 0.96 0.992   12–15 years 0.89 0.87, 0.90 0.89 0.88, 0.91 0.761   15–21 years 0.79 0.73, 0.85 0.118 Growth Variable Model of RC in MRI Percent Breast Watera P for Interactionb Model 1 Model 2 Model 3 Model 4 Model 5 RCc 95% CId RC 95% CI RC 95% CI RC 95% CI RC 95% CI Height, cm  Birth length 1.02 0.98, 1.07 0.99 0.93, 1.05 0.99 0.93, 1.06 0.98 0.93, 1.04 0.98 0.93, 1.03  Height increments between  specified agese   Birth to 3 months 1.02 0.96, 1.08 1.09 0.98, 1.20 1.08 0.98, 1.20 1.07 0.98, 1.16 1.06 0.98, 1.15 0.325   3–12 months 1.01 0.96, 1.07 0.93 0.82, 1.05 0.93 0.83, 1.05 0.94 0.85, 1.04 0.95 0.86, 1.04 0.843   1–3 years 1.02 0.97, 1.07 1.12 0.99, 1.25 1.12 1.00, 1.25 1.10 1.00, 1.21 1.10 1.00, 1.20 0.737   3–7 years 1.00 0.96, 1.05 0.92 0.82, 1.03 0.92 0.82, 1.02 0.94 0.86, 1.03 0.95 0.87, 1.03 0.224   7–10 years 1.06 1.00, 1.12 1.07 1.01, 1.13 1.06 1.01, 1.12 1.06 1.01, 1.11 0.052   10–12 years 0.97 0.95, 1.00 1.01 0.98, 1.03 1.01 0.99, 1.03 0.101   12–15 yearsf 1.07 1.04, 1.10 1.05 1.02, 1.08 0.475 Weight, kg  Birth weight 1.03 0.99, 1.06 1.03 0.99, 1.06 1.03 1.00, 1.07 1.04 1.01, 1.07 1.07 1.04, 1.10  Weight increments between specified agese   Birth to 3 months 0.99 0.97, 1.02 0.99 0.96, 1.01 0.99 0.97, 1.01 1.00 0.98, 1.02 1.01 0.99, 1.03 0.038   3–12 months 0.97 0.95, 1.00 0.97 0.95, 1.00 0.97 0.95, 0.99 0.98 0.96, 1.00 1.00 0.98, 1.03 0.104   1–3 years 1.00 0.97, 1.03 0.98 0.95, 1.01 0.97 0.94, 1.00 0.99 0.96, 1.01 1.02 1.00, 1.05 0.300   3–7 years 0.88 0.85, 0.91 0.97 0.92, 1.02 0.95 0.91, 1.00 0.94 0.90, 0.98 1.03 0.98, 1.09 0.347   7–10 years 0.91 0.87, 0.94 0.89 0.86, 0.93 0.94 0.91, 0.97 1.03 0.99, 1.08 0.153   10–12 years 0.93 0.91, 0.96 0.95 0.93, 0.97 0.94 0.92, 0.96 0.992   12–15 years 0.89 0.87, 0.90 0.89 0.88, 0.91 0.761   15–21 years 0.79 0.73, 0.85 0.118 Abbreviations: CI, confidence interval; MRI, magnetic resonance imaging; RC, relative change. a RC in breast percent water per 1–standard-deviation increment in the exposure of interest. bP value for the interaction of each height increment with birth length and of each weight increment with birth weight explored in model 5. c RC estimates were adjusted for all of the earlier height and weight measurements, and additionally for age and menstrual phase at MRI examination. Data on MRI breast percent water were log-transformed. Exponentiated estimated regression parameters are presented. d 95% CIs were calculated by exponentiating the original 95% CIs (as detailed in our paper (2)). e Height and weight growth measures from birth to age 10 years were derived using linear spline multilevel modeling of height and weight (as detailed by Howe et al. (5)). From age 10 years onward, growth measures were calculated from a piecewise mixed-effect model with knots at ages 10, 12, and 15 years (as detailed in our paper (2)). All growth measures and all growth differences were standardized, with regression coefficients representing expected changes per 1 standard deviation. f Adult height is attained by age 15 years, and therefore height increments between ages 15 and 21 years were not included in the model. The second point Goldberg and Terry raise concerns whether our data provided any evidence of modification by birth size of the effect of weight and length increments at different ages (1). The last column of Table 1 shows the results of the corresponding interaction tests. Only the term for the interaction of birth weight with weight gain between birth and age 3 months indicates a weak synergism between them. In conclusion, we hope that these additional considerations will help to clarify some of the complexities of studying the relationship between early-life growth and MRI breast-tissue composition. Acknowledgments This work was funded by a Cancer Research UK project grant (grant C405/A12730 to I.d.-S.-S.). The Medical Research Council, the Wellcome Trust (grant 102215/2/13/2), and the University of Bristol provide core support for the Avon Longitudinal Study of Parents and Children. Conflict of interest: none declared. References 1 Goldberg M , Terry MB . Re: “Growth trajectories, breast size, and breast-tissue composition in a British prebirth cohort of young women” [letter] . Am J Epidemiol . 2018 ; 187 ( 9 ): 2069 . Google Scholar Crossref Search ADS 2 Denholm R , De Stavola B , Hipwell JH , et al. . Growth trajectories, breast size, and breast-tissue composition in a British prebirth cohort of young women . Am J Epidemiol . 2018 ; 187 ( 6 ): 1259 – 1268 . Google Scholar Crossref Search ADS PubMed 3 De Stavola BL , Nitsch D , dos Santos Silva I , et al. . Statistical issues in life course epidemiology . Am J Epidemiol . 2006 ; 163 ( 1 ): 84 – 96 . Google Scholar Crossref Search ADS PubMed 4 VanderWeele TJ . Mediation analysis: a practitioner’s guide . Annu Rev Public Health . 2016 ; 37 : 17 – 32 . Google Scholar Crossref Search ADS PubMed 5 Howe LD , Tilling K , Matijasevich A , et al. . Linear spline multilevel models for summarising childhood growth trajectories: a guide to their application using examples from five birth cohorts . Stat Methods Med Res . 2016 ; 25 ( 5 ): 1854 – 1874 . Google Scholar Crossref Search ADS PubMed © The Author(s) 2018. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png American Journal of Epidemiology Oxford University Press

THREE AUTHORS REPLY

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Abstract

Goldberg and Terry raise several points of interest in their letter (1). These arise from the complexities of modeling—and then interpreting—the relationship between early-life longitudinal information and later-life outcomes. Because such analyses were at the core of our paper (2), we welcome the opportunity to clarify our results. The first point Goldberg and Terry raise concerns our report of no association between successive increments in standardized height and weight in infancy/early childhood (later referred to as z scores) and either total breast volume or percent water. Goldberg and Terry point out that the estimates that refer to these successive increments are mutually adjusted and hence, in their view, can only capture “direct effects” of each of these increments (1). We disagree with this interpretation, as explained below. This criticism would be correct if we had used absolute z scores when fitting the models. However, by using consecutive increments of z scores, we estimated the cumulative effect of increasing each age-specific z score by 1 unit. As De Stavola et al. (3) previously demonstrated in their equation 5, a model that is specified in terms of absolute values of an exposure measured longitudinally can be reparameterized as a model that includes the first of these measures and its consecutive increments, with the coefficients of the 2 model specifications having different interpretations. Letting Y denote percent water and Zj the z score measured at time j, for j = 1 . . . J, with Z1 indicating birth weight (or birth length), the 2 model specifications are E(Y|Z1,Z2,…,ZJ)=β0+β1Z1+β2Z2+…+βJZJ. (1) E(Y|Z1,Z2,…,ZJ)=β0+(∑j=1Jβj)Z1+(∑j=2Jβj)(Z2−Z1)+(∑j=3Jβj)(Z3−Z2)+…+βJZJ. (2) These equations show that the coefficient of each explanatory variable in the second specification (equation 2) is the sum of the coefficients for the corresponding and later z score terms in the first specification (equation 1). Hence, each regression coefficient in equation 2 is to be interpreted as the expected cumulative change in Y per 1-unit change in each of the relevant z scores and therefore in a sense represents a “total effect.” This is in contrast to the individual βj coefficients in equation 1 that could instead be interpreted as “direct effects.” However, we refrain from labeling these coefficients using this terminology, because of the additional assumptions (especially those of no unmeasured confounding) invoked in mediation analysis (4). The results presented in our paper (2) are for models specified as in equation 2 and covering the full range of measurements, that is, from birth to young adulthood. In response to Goldberg and Terry’s comments (1), therefore, we report here results from alternative versions of the second specification of the model (equation 2), where we vary the timing of the final increment when estimating the association between growth trajectories and MRI percent water (Table 1). The size and significance of these new sets of estimates show how it is still the later (postpubertal) measurements that exert the strongest impact, confirming our original interpretation. Table 1. Relative Change (Cumulative Linear Regression Models) in Magnetic Resonance Imaging Breast Percent Water at Age 21 Years With Birth Length, Birth Weight, and Height and Weight Velocities Between Birth and Age 21 Years (n = 480), Avon Longitudinal Study of Parents and Children, 1991–2014 Growth Variable Model of RC in MRI Percent Breast Watera P for Interactionb Model 1 Model 2 Model 3 Model 4 Model 5 RCc 95% CId RC 95% CI RC 95% CI RC 95% CI RC 95% CI Height, cm  Birth length 1.02 0.98, 1.07 0.99 0.93, 1.05 0.99 0.93, 1.06 0.98 0.93, 1.04 0.98 0.93, 1.03  Height increments between  specified agese   Birth to 3 months 1.02 0.96, 1.08 1.09 0.98, 1.20 1.08 0.98, 1.20 1.07 0.98, 1.16 1.06 0.98, 1.15 0.325   3–12 months 1.01 0.96, 1.07 0.93 0.82, 1.05 0.93 0.83, 1.05 0.94 0.85, 1.04 0.95 0.86, 1.04 0.843   1–3 years 1.02 0.97, 1.07 1.12 0.99, 1.25 1.12 1.00, 1.25 1.10 1.00, 1.21 1.10 1.00, 1.20 0.737   3–7 years 1.00 0.96, 1.05 0.92 0.82, 1.03 0.92 0.82, 1.02 0.94 0.86, 1.03 0.95 0.87, 1.03 0.224   7–10 years 1.06 1.00, 1.12 1.07 1.01, 1.13 1.06 1.01, 1.12 1.06 1.01, 1.11 0.052   10–12 years 0.97 0.95, 1.00 1.01 0.98, 1.03 1.01 0.99, 1.03 0.101   12–15 yearsf 1.07 1.04, 1.10 1.05 1.02, 1.08 0.475 Weight, kg  Birth weight 1.03 0.99, 1.06 1.03 0.99, 1.06 1.03 1.00, 1.07 1.04 1.01, 1.07 1.07 1.04, 1.10  Weight increments between specified agese   Birth to 3 months 0.99 0.97, 1.02 0.99 0.96, 1.01 0.99 0.97, 1.01 1.00 0.98, 1.02 1.01 0.99, 1.03 0.038   3–12 months 0.97 0.95, 1.00 0.97 0.95, 1.00 0.97 0.95, 0.99 0.98 0.96, 1.00 1.00 0.98, 1.03 0.104   1–3 years 1.00 0.97, 1.03 0.98 0.95, 1.01 0.97 0.94, 1.00 0.99 0.96, 1.01 1.02 1.00, 1.05 0.300   3–7 years 0.88 0.85, 0.91 0.97 0.92, 1.02 0.95 0.91, 1.00 0.94 0.90, 0.98 1.03 0.98, 1.09 0.347   7–10 years 0.91 0.87, 0.94 0.89 0.86, 0.93 0.94 0.91, 0.97 1.03 0.99, 1.08 0.153   10–12 years 0.93 0.91, 0.96 0.95 0.93, 0.97 0.94 0.92, 0.96 0.992   12–15 years 0.89 0.87, 0.90 0.89 0.88, 0.91 0.761   15–21 years 0.79 0.73, 0.85 0.118 Growth Variable Model of RC in MRI Percent Breast Watera P for Interactionb Model 1 Model 2 Model 3 Model 4 Model 5 RCc 95% CId RC 95% CI RC 95% CI RC 95% CI RC 95% CI Height, cm  Birth length 1.02 0.98, 1.07 0.99 0.93, 1.05 0.99 0.93, 1.06 0.98 0.93, 1.04 0.98 0.93, 1.03  Height increments between  specified agese   Birth to 3 months 1.02 0.96, 1.08 1.09 0.98, 1.20 1.08 0.98, 1.20 1.07 0.98, 1.16 1.06 0.98, 1.15 0.325   3–12 months 1.01 0.96, 1.07 0.93 0.82, 1.05 0.93 0.83, 1.05 0.94 0.85, 1.04 0.95 0.86, 1.04 0.843   1–3 years 1.02 0.97, 1.07 1.12 0.99, 1.25 1.12 1.00, 1.25 1.10 1.00, 1.21 1.10 1.00, 1.20 0.737   3–7 years 1.00 0.96, 1.05 0.92 0.82, 1.03 0.92 0.82, 1.02 0.94 0.86, 1.03 0.95 0.87, 1.03 0.224   7–10 years 1.06 1.00, 1.12 1.07 1.01, 1.13 1.06 1.01, 1.12 1.06 1.01, 1.11 0.052   10–12 years 0.97 0.95, 1.00 1.01 0.98, 1.03 1.01 0.99, 1.03 0.101   12–15 yearsf 1.07 1.04, 1.10 1.05 1.02, 1.08 0.475 Weight, kg  Birth weight 1.03 0.99, 1.06 1.03 0.99, 1.06 1.03 1.00, 1.07 1.04 1.01, 1.07 1.07 1.04, 1.10  Weight increments between specified agese   Birth to 3 months 0.99 0.97, 1.02 0.99 0.96, 1.01 0.99 0.97, 1.01 1.00 0.98, 1.02 1.01 0.99, 1.03 0.038   3–12 months 0.97 0.95, 1.00 0.97 0.95, 1.00 0.97 0.95, 0.99 0.98 0.96, 1.00 1.00 0.98, 1.03 0.104   1–3 years 1.00 0.97, 1.03 0.98 0.95, 1.01 0.97 0.94, 1.00 0.99 0.96, 1.01 1.02 1.00, 1.05 0.300   3–7 years 0.88 0.85, 0.91 0.97 0.92, 1.02 0.95 0.91, 1.00 0.94 0.90, 0.98 1.03 0.98, 1.09 0.347   7–10 years 0.91 0.87, 0.94 0.89 0.86, 0.93 0.94 0.91, 0.97 1.03 0.99, 1.08 0.153   10–12 years 0.93 0.91, 0.96 0.95 0.93, 0.97 0.94 0.92, 0.96 0.992   12–15 years 0.89 0.87, 0.90 0.89 0.88, 0.91 0.761   15–21 years 0.79 0.73, 0.85 0.118 Abbreviations: CI, confidence interval; MRI, magnetic resonance imaging; RC, relative change. a RC in breast percent water per 1–standard-deviation increment in the exposure of interest. bP value for the interaction of each height increment with birth length and of each weight increment with birth weight explored in model 5. c RC estimates were adjusted for all of the earlier height and weight measurements, and additionally for age and menstrual phase at MRI examination. Data on MRI breast percent water were log-transformed. Exponentiated estimated regression parameters are presented. d 95% CIs were calculated by exponentiating the original 95% CIs (as detailed in our paper (2)). e Height and weight growth measures from birth to age 10 years were derived using linear spline multilevel modeling of height and weight (as detailed by Howe et al. (5)). From age 10 years onward, growth measures were calculated from a piecewise mixed-effect model with knots at ages 10, 12, and 15 years (as detailed in our paper (2)). All growth measures and all growth differences were standardized, with regression coefficients representing expected changes per 1 standard deviation. f Adult height is attained by age 15 years, and therefore height increments between ages 15 and 21 years were not included in the model. Table 1. Relative Change (Cumulative Linear Regression Models) in Magnetic Resonance Imaging Breast Percent Water at Age 21 Years With Birth Length, Birth Weight, and Height and Weight Velocities Between Birth and Age 21 Years (n = 480), Avon Longitudinal Study of Parents and Children, 1991–2014 Growth Variable Model of RC in MRI Percent Breast Watera P for Interactionb Model 1 Model 2 Model 3 Model 4 Model 5 RCc 95% CId RC 95% CI RC 95% CI RC 95% CI RC 95% CI Height, cm  Birth length 1.02 0.98, 1.07 0.99 0.93, 1.05 0.99 0.93, 1.06 0.98 0.93, 1.04 0.98 0.93, 1.03  Height increments between  specified agese   Birth to 3 months 1.02 0.96, 1.08 1.09 0.98, 1.20 1.08 0.98, 1.20 1.07 0.98, 1.16 1.06 0.98, 1.15 0.325   3–12 months 1.01 0.96, 1.07 0.93 0.82, 1.05 0.93 0.83, 1.05 0.94 0.85, 1.04 0.95 0.86, 1.04 0.843   1–3 years 1.02 0.97, 1.07 1.12 0.99, 1.25 1.12 1.00, 1.25 1.10 1.00, 1.21 1.10 1.00, 1.20 0.737   3–7 years 1.00 0.96, 1.05 0.92 0.82, 1.03 0.92 0.82, 1.02 0.94 0.86, 1.03 0.95 0.87, 1.03 0.224   7–10 years 1.06 1.00, 1.12 1.07 1.01, 1.13 1.06 1.01, 1.12 1.06 1.01, 1.11 0.052   10–12 years 0.97 0.95, 1.00 1.01 0.98, 1.03 1.01 0.99, 1.03 0.101   12–15 yearsf 1.07 1.04, 1.10 1.05 1.02, 1.08 0.475 Weight, kg  Birth weight 1.03 0.99, 1.06 1.03 0.99, 1.06 1.03 1.00, 1.07 1.04 1.01, 1.07 1.07 1.04, 1.10  Weight increments between specified agese   Birth to 3 months 0.99 0.97, 1.02 0.99 0.96, 1.01 0.99 0.97, 1.01 1.00 0.98, 1.02 1.01 0.99, 1.03 0.038   3–12 months 0.97 0.95, 1.00 0.97 0.95, 1.00 0.97 0.95, 0.99 0.98 0.96, 1.00 1.00 0.98, 1.03 0.104   1–3 years 1.00 0.97, 1.03 0.98 0.95, 1.01 0.97 0.94, 1.00 0.99 0.96, 1.01 1.02 1.00, 1.05 0.300   3–7 years 0.88 0.85, 0.91 0.97 0.92, 1.02 0.95 0.91, 1.00 0.94 0.90, 0.98 1.03 0.98, 1.09 0.347   7–10 years 0.91 0.87, 0.94 0.89 0.86, 0.93 0.94 0.91, 0.97 1.03 0.99, 1.08 0.153   10–12 years 0.93 0.91, 0.96 0.95 0.93, 0.97 0.94 0.92, 0.96 0.992   12–15 years 0.89 0.87, 0.90 0.89 0.88, 0.91 0.761   15–21 years 0.79 0.73, 0.85 0.118 Growth Variable Model of RC in MRI Percent Breast Watera P for Interactionb Model 1 Model 2 Model 3 Model 4 Model 5 RCc 95% CId RC 95% CI RC 95% CI RC 95% CI RC 95% CI Height, cm  Birth length 1.02 0.98, 1.07 0.99 0.93, 1.05 0.99 0.93, 1.06 0.98 0.93, 1.04 0.98 0.93, 1.03  Height increments between  specified agese   Birth to 3 months 1.02 0.96, 1.08 1.09 0.98, 1.20 1.08 0.98, 1.20 1.07 0.98, 1.16 1.06 0.98, 1.15 0.325   3–12 months 1.01 0.96, 1.07 0.93 0.82, 1.05 0.93 0.83, 1.05 0.94 0.85, 1.04 0.95 0.86, 1.04 0.843   1–3 years 1.02 0.97, 1.07 1.12 0.99, 1.25 1.12 1.00, 1.25 1.10 1.00, 1.21 1.10 1.00, 1.20 0.737   3–7 years 1.00 0.96, 1.05 0.92 0.82, 1.03 0.92 0.82, 1.02 0.94 0.86, 1.03 0.95 0.87, 1.03 0.224   7–10 years 1.06 1.00, 1.12 1.07 1.01, 1.13 1.06 1.01, 1.12 1.06 1.01, 1.11 0.052   10–12 years 0.97 0.95, 1.00 1.01 0.98, 1.03 1.01 0.99, 1.03 0.101   12–15 yearsf 1.07 1.04, 1.10 1.05 1.02, 1.08 0.475 Weight, kg  Birth weight 1.03 0.99, 1.06 1.03 0.99, 1.06 1.03 1.00, 1.07 1.04 1.01, 1.07 1.07 1.04, 1.10  Weight increments between specified agese   Birth to 3 months 0.99 0.97, 1.02 0.99 0.96, 1.01 0.99 0.97, 1.01 1.00 0.98, 1.02 1.01 0.99, 1.03 0.038   3–12 months 0.97 0.95, 1.00 0.97 0.95, 1.00 0.97 0.95, 0.99 0.98 0.96, 1.00 1.00 0.98, 1.03 0.104   1–3 years 1.00 0.97, 1.03 0.98 0.95, 1.01 0.97 0.94, 1.00 0.99 0.96, 1.01 1.02 1.00, 1.05 0.300   3–7 years 0.88 0.85, 0.91 0.97 0.92, 1.02 0.95 0.91, 1.00 0.94 0.90, 0.98 1.03 0.98, 1.09 0.347   7–10 years 0.91 0.87, 0.94 0.89 0.86, 0.93 0.94 0.91, 0.97 1.03 0.99, 1.08 0.153   10–12 years 0.93 0.91, 0.96 0.95 0.93, 0.97 0.94 0.92, 0.96 0.992   12–15 years 0.89 0.87, 0.90 0.89 0.88, 0.91 0.761   15–21 years 0.79 0.73, 0.85 0.118 Abbreviations: CI, confidence interval; MRI, magnetic resonance imaging; RC, relative change. a RC in breast percent water per 1–standard-deviation increment in the exposure of interest. bP value for the interaction of each height increment with birth length and of each weight increment with birth weight explored in model 5. c RC estimates were adjusted for all of the earlier height and weight measurements, and additionally for age and menstrual phase at MRI examination. Data on MRI breast percent water were log-transformed. Exponentiated estimated regression parameters are presented. d 95% CIs were calculated by exponentiating the original 95% CIs (as detailed in our paper (2)). e Height and weight growth measures from birth to age 10 years were derived using linear spline multilevel modeling of height and weight (as detailed by Howe et al. (5)). From age 10 years onward, growth measures were calculated from a piecewise mixed-effect model with knots at ages 10, 12, and 15 years (as detailed in our paper (2)). All growth measures and all growth differences were standardized, with regression coefficients representing expected changes per 1 standard deviation. f Adult height is attained by age 15 years, and therefore height increments between ages 15 and 21 years were not included in the model. The second point Goldberg and Terry raise concerns whether our data provided any evidence of modification by birth size of the effect of weight and length increments at different ages (1). The last column of Table 1 shows the results of the corresponding interaction tests. Only the term for the interaction of birth weight with weight gain between birth and age 3 months indicates a weak synergism between them. In conclusion, we hope that these additional considerations will help to clarify some of the complexities of studying the relationship between early-life growth and MRI breast-tissue composition. Acknowledgments This work was funded by a Cancer Research UK project grant (grant C405/A12730 to I.d.-S.-S.). The Medical Research Council, the Wellcome Trust (grant 102215/2/13/2), and the University of Bristol provide core support for the Avon Longitudinal Study of Parents and Children. Conflict of interest: none declared. References 1 Goldberg M , Terry MB . Re: “Growth trajectories, breast size, and breast-tissue composition in a British prebirth cohort of young women” [letter] . Am J Epidemiol . 2018 ; 187 ( 9 ): 2069 . Google Scholar Crossref Search ADS 2 Denholm R , De Stavola B , Hipwell JH , et al. . Growth trajectories, breast size, and breast-tissue composition in a British prebirth cohort of young women . Am J Epidemiol . 2018 ; 187 ( 6 ): 1259 – 1268 . Google Scholar Crossref Search ADS PubMed 3 De Stavola BL , Nitsch D , dos Santos Silva I , et al. . Statistical issues in life course epidemiology . Am J Epidemiol . 2006 ; 163 ( 1 ): 84 – 96 . Google Scholar Crossref Search ADS PubMed 4 VanderWeele TJ . Mediation analysis: a practitioner’s guide . Annu Rev Public Health . 2016 ; 37 : 17 – 32 . Google Scholar Crossref Search ADS PubMed 5 Howe LD , Tilling K , Matijasevich A , et al. . Linear spline multilevel models for summarising childhood growth trajectories: a guide to their application using examples from five birth cohorts . Stat Methods Med Res . 2016 ; 25 ( 5 ): 1854 – 1874 . Google Scholar Crossref Search ADS PubMed © The Author(s) 2018. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model)

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American Journal of EpidemiologyOxford University Press

Published: Sep 1, 2018

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