LETTERS

MASTERS ET AL. RESPOND

in study. We contend that mortality selection and age-related survey selection severely bias estimates from survival models that do not account for these selection processes. Once we accounted for these processes the obesity-mortality association was found to grow stronger with increasing age. Overall then, disagreement exists about the reasons behind the estimated age patterns of the obesity---mortality association. To determine if the age-specific hazard ratios (HRs) presented in our article accurately reflects the US obesity--mortality association, one must test all these competing explanations. We have done so through a number of analyses, but to the specific issues raised by Wang and Yu, we respond with the following 2 points:

We thank the editor for the opportunity to respond to the comments of Wang and Yu. The central issue raised in both letters is the age pattern of the US obesity---mortality association. Most research suggests that the effect of obesity on mortality risk grows weaker with increasing age, consistent with Wang’s Figure 1. Conversely, some research suggests that the agediminishing effect of obesity on mortality risk reflects biases from unaccounted for factors in survival models.1---4 Yu, for example, believes it reflects cohort variation in the obesitymortality association.4 Others3 argue that it reflects “reverse causality” and that the obesity---mortality association changes across time

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1. Using results from our article, Wang has estimated HRs associated with obesity that decline across age. However, Wang misinterpreted the results from the RoystonParmar (RP) survival models we fitted,5 and he miscalculated the hazard ratios from the coefficients presented in our supplementary Tables B and C. 2. Yu cited results from her own work to suggest that cohort variation in the obesity--mortality association explains the declining effects of obesity on mortality risk across age.4 However, her work is limited in a crucial way: Yu never fitted models that allowed the obesity-mortality association to vary simultaneously by attained age and birth cohort and, thus, never directly

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Note. Grade 1 obesity was defined as a body mass index of 30–34.9 kg/m2.

FIGURE 1—Estimated hazard ratios from the fitted cohort-specific models for grade 1 obesity for (a) Black women, (b) White women, (c) Black men, and (d) White men.

April 2014, Vol 104, No. 4 | American Journal of Public Health

Letters | e5

LETTERS

tested the sources of variation against one another. To point 1, Wang calculated the HRs for each BMI level by setting the coefficients associated with attained age dependency to zero and then exponentiating the summed coefficients associated with age at survey. He should not have done this. To show the proper procedures for calculating HRs from RoystonParmar survival models we direct readers to Appendix 1 (available as a supplement to this letter at http://www.ajph.org). To point 2, Yu contends that cohort variation in the obesity---mortality association explains the declining effect of obesity on mortality risk across age. She cites her own work showing that the estimated age patterns of the obesity--mortality association do not decline once cohort variation in the obesity---mortality association is included in her model. However, Yu is simply exchanging one source of variation for the other. We direct readers to equations 2, 3, and 4 in Yu’s article.4 In no model did Yu allow the effect of obesity on mortality risk to vary by both age and cohort, and thus, in no model did Yu simultaneously test these sources of variation. The simultaneous inclusion of both sources of variation in one analytic model is precisely the contribution made by our article. Indeed, in supplemental analyses conducted during the review process, we investigated cohort-based temporal variation in the effect of grade 1 and grade 2/3 obesity, while also permitting the effects to vary by attained age. Estimated hazard ratios from the fitted cohort-specific models for class 1 obesity are presented in Figure 1, along with the estimated hazard ratios from the fully fitted models we presented in our article (noted by “average” black line). Two points are especially worth noting. One, the results provide no evidence supporting Yu’s contention that the substantive effect of grade 1 obesity on mortality risk has significantly changed across cohorts. For all 4 groups, the average effects of grade 1 obesity on mortality risk estimated by our models (black line) do not deviate in any significant way from the individual cohort patterns. This is especially true among white men and women; higher cohort-based variation in the Black male and female samples likely reflects

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smaller counts of death and, thus, less stable estimates. Second, we see significant agebased variation in the obesity---mortality association within cohorts. This evidence directly counters Yu’s claim that intercohort variation in the obesity---mortality association accounts for the observed age-based variation in the obesity---mortality association. In short, intercohort variation (of which we find no convincing evidence) cannot explain intracohort age-based variation in the obesity---mortality association. j Ryan K. Masters, PhD Eric N. Reither, PhD Daniel A. Powers, PhD Y. Claire Yang, PhD Andrew E. Burger, MS Bruce G. Link, PhD

About the Authors At the time of the study, Ryan K. Masters was with Robert Wood Johnson Foundation Health and Society Scholars Program, Columbia University, New York, NY. Eric N. Reither and Andrew E. Burger were with Department of Sociology, Social Work, and Anthropology, Utah State University, Logan. Daniel A. Powers was with Department of Sociology, University of Texas at Austin. Y. Claire Yang was with Department of Sociology and Lineberger Comprehensive Cancer Center, University of North Carolina, Chapel Hill. Bruce G. Link was with Department of Epidemiology and Department of Sociomedical Sciences, Columbia University. Correspondence should be sent to Ryan K. Masters, University of Colorado at Boulder, Department of Sociology, UCB 327 Ketchum 214, Boulder, CO 80309 (e-mail: ryan. [email protected]). Reprints can be ordered at http://www.ajph.org by clicking the “Reprints” link. This letter was accepted January 30, 2014. doi:10.2105/AJPH.2014.301916

Contributors All authors contributed equally to the letter.

References 1. Masters RK, Powers DA, Link BG. Obesity and US mortality risk over the adult life course. Am J Epidemiol. 2013;177(5):431---442. 2. Banack HR, Kaufman JS. The “obesity paradox” explained. [letter] Epidemiology. 2013;24(3):461---462. 3. Mehta NK, Stokes A. Obesity and US mortality risk over the adult life course. [letter] Am J Epidemiol. 2013;178(2):320. 4. Yu Y. Reexamining the declining effect of age on mortality differentials associated with excess body mass: evidence of cohort distortions in the United States. Am J Public Health. 2012;102(5):915---922. 5. Lambert PC, Royston P. Further development of flexible parametric models for survival analysis. Stata J. 2009;9(2):265---290.

American Journal of Public Health | April 2014, Vol 104, No. 4

Masters et al. respond.

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