530 Letters to the Editor
ACKNOWLEDGMENTS
The author was supported by the National Health and Medical
Research Council of Australia (research fellowship APP1042343).
Conflict of interest: none declared.
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. Mehta NK, Stokes A. Re: “Obesity and US mortality risk over
the adult life course” [letter]. Am J Epidemiol. 2013;178(2):320.
3. Masters RK, Powers DA, Link BG. The authors reply. Am J
Epidemiol. 2013;178(2):321–323.
Zhiqiang Wang (e-mail: [email protected])
Center for Chronic Disease, School of Medicine,
University of Queensland, Brisbane, Australia
DOI: 10.1093/aje/kwt329; Advance Access publication: January 12, 2014
2.00
Hazard Ratio
term equals 0 or, in other words, age-at-survey equals mean
age. It makes no biological sense to estimate hazard ratios
under this assumption for most age groups. For example, it
is impossible to interpret hazard ratios for men aged 35–44
years by assuming their age-at-survey is 47.31 years (mean
age).
I have recalculated hazard ratios on the basis of all relevant
numbers in their final models according to the above formula.
These recalculated hazard ratios are approximate estimates
because I did not use the original raw data. Nevertheless,
the trend is clear (Figure 1 and Table 1). The obesitymortality association actually weakened substantially with
increasing age, which contradicts their conclusion of growing
stronger with age. When multiple regression techniques are
used to control for confounders, particularly with interaction
terms involving the exposure of interest, authors should interpret their findings in the context of complete relevant information generated by the model rather than focusing only on
interpreting coefficients of main effect estimates.
1.00
Class 1 obese
Class 2/3 obese
0.50
53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85
Age, years
Figure 1. Mortality hazard ratios, estimated from age 50–84 years
smoothed hazards in the class 1 and class 2/3 obese samples relative
to the normal/overweight sample, National Health Interview Survey
Linked Mortality Files, 1986–2006.
age does not preclude partitioning age-related variation into
these 2 distinct sources (3, 4). Moreover, if the goal is to separate these sources of variation, it is inappropriate to reintroduce the very source of variation for which one is controlling
(i.e., age-at-survey). That said, we recognize Dr. Wang’s
point that it is biologically implausible to standardize ageat-survey on the mean (47.31 years) for those participants
in the National Health Interview Survey (NHIS) whose
attained age was less than the mean.
Second, to address Dr. Wang’s point, we refit survival
models on the National Health Interview Survey Linked
Mortality Files (NHIS-LMF), stratified by body mass
index, for women with attained age of 50–84 years and standardized age-at-survey of 50 years (obese classes 2 and 3
were combined because of small counts of death at individual
ages). Consistent with the results presented in our paper (2),
Figure 1 illustrates the relative decline in the obesitymortality association across attained age from survival models that do not account for variation from age-at-survey,
whereas Figure 2 illustrates that the obesity-mortality association grows substantially stronger across attained age after
standardizing by birth cohort and age-at-survey. Thus, the
2.00
We thank Dr. Wang (1) for commenting on our paper (2),
as well as for raising important points regarding the fitting of
survival models and the interpretation of their results. Our response is 3-fold. First, we stand by our use of age-at-survey as
a proxy for likely confounders of the US obesity-mortality
association (i.e., cohort differences in mortality risk and agegraded survey selection). We accounted for these factors by
modeling effects of respondents’ 5-year birth cohort and
age-at-survey, as well as 2-way effects between body mass
index (weight (kg)/height (m)2) and age-at-survey. Dr. Wang
is correct that age-at-survey and attained age are collinear.
However, collinearity between age-at-survey and attained
Hazard Ratio
THE AUTHORS REPLY
1.00
Class 1 obese
Class 2/3 obese
0.50
53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85
Age, years
Figure 2. Mortality hazard ratios, estimated from age 50–84 years
smoothed hazards in the class 1 and class 2/3 obese samples relative
to normal/overweight sample, standardizing by age-at-survey (50
years), National Health Interview Survey Linked Mortality Files,
1986–2006.
Am J Epidemiol. 2014;179(4):529–532
0.20
0.18
Normal/overweight
Class 1 obese
0.16
Class 2/3 obese
0.14
1999 qx
0.12
0.10
0.08
0.06
0.04
0.02
0.00
53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85
Age, years
Figure 3. Smoothed mortality hazards for US women aged 50–84
years, by body mass index (weight (kg)/height (m)2) in the National
Health Interview Survey Linked Mortality Files, 1986–2006, versus official 1999 US female qx.
Mortality Hazard
results presented in our paper (2) are replicated on a subsample of data for which the age range appropriately conforms to
ages-at-survey and attained ages.
Finally, we end by making an important distinction between 1) fitting models to describe data and 2) fitting models
to help describe important processes in the population of interest. We believe that our ultimate goal as mortality researchers is the latter. Dr. Wang, conversely, seems most concerned
about the former. To show the importance of this distinction,
we compare the smoothed hazards from the NHIS-LMF
samples of US women with the qx in the official 1999 US
female life tables (1999 is the average year of death in the
NHI-LMF) (5).
Results presented in Figures 3–5 help to illustrate the importance of our distinction between points 1 and 2 above. Specifically, survival models that do not account for age-at-survey
estimate hazards that are both 1) unrealistically high for the normal/overweight sample and 2) suspiciously low for the class 1
and class 2/3 obese samples (Figure 3). The estimates are, in
fact, mathematically impossible because qx must be an average
of the mortality experiences of the underweight, normal weight,
overweight, and obese populations, yet qx is substantially lower
than all hazards estimated in the NHIS-LMF data. Furthermore,
0.20
0.18
Normal/overweight
Class 1 obese
0.16
Class 2/3 obese
0.14
1999 qx
0.12
0.10
0.08
0.06
0.04
0.02
0.00
53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85
Age, years
Figure 4. Smoothed mortality hazards for US women aged 50–84
years, by body mass index (weight (kg)/height (m)2) in the National
Health Interview Survey Linked Mortality Files, 1986–2006, standardizing by age-at-survey (50 years) versus official 1999 US female qx.
Am J Epidemiol. 2014;179(4):529–532
0.02
Absolute Hazard Difference
Mortality Hazard
Letters to the Editor 531
0.01
1999 vs. Normal/overweight
1999 vs. Normal/overweight, accounting for selection
0.00
–0.01
–0.02
–0.03
–0.04
53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85
Age, years
Figure 5. Differences between official 1999 US female qx and
smoothed hazards for the normal/overweight sample in the National
Health Interview Survey Linked Mortality Files, 1986–2006.
the older US female population is overwhelmingly composed
of the normal weight or overweight populations (6). Thus, the
age-specific hazards for the normal/overweight sample should
approximate the official qx. As seen in Figure 3, this is not
the case. Further still, the difference between the normal/
overweight hazard and qx grows larger with increasing age
(Figure 5), despite the fact that the older population becomes
less obese with age. This model, although presumably preferred
by Dr. Wang because it most accurately describes patterns in the
NHIS-LMF data, poorly describes the population of interest.
Contrast these hazards with those in Figure 4, which are
based on models fitted to the normal/overweight, class 1
obese, and class 2/3 obese samples while accounting for
5-year birth cohort and standardizing age-at-survey. The estimated hazards from these models are much closer to the empirical patterns in the US female population.
We conclude by emphasizing that our interest should not
be in describing the data—especially if we believe those
data to be biased—but rather we should use theory, data,
and models to accurately describe population processes of interest. Evidence suggests that our models, which are attentive
to cohort differences in mortality risk and age-related selection processes, comply more with empirical mortality patterns in the US population than do models that ignore these
sources of variation. When we use these models to investigate
the US obesity-mortality association, we find no evidence
that the obesity-mortality association weakens with age.
Rather, evidence points to a stronger association with increasing age.
ACKNOWLEDGMENTS
Financial support was provided by the Robert Wood Johnson Foundation’s Health and Society Scholars Program. Funding was also provided by the Eunice Kennedy Shriver National Institute of Child
Health and Human Development (grant 5 R24 HD042849-9 to the
Population Research Center at the University of Texas at Austin).
Conflict of interest: none declared.
REFERENCES
1. Wang Z. Re: “Obesity and US mortality risk over the adult life
course” [letter]. Am J Epidemiol. 2014;179(4):529–530.
532 Letters to the Editor
2. Masters RK, Powers DA, Link BG. Obesity and US mortality
risk over the adult life course. Am J Epidemiol. 2013;177(5):
431–442.
3. Masters RK, Powers DA, Link BG. The authors reply. Am J
Epidemiol. 2013;178(2):321–323.
4. Singer JD, Willett JB. Applied Longitudinal Data Analysis:
Modeling Change and Event Occurrence. New York, NY:
Oxford University Press, Inc.; 2003.
5. Anderson RN, DeTurk PB. United States Life Tables, 1999.
National Vital Statistics Reports. Hyattsville, MD: National
Center for Health Statistics; 2002;50(6).
6. Flegal KM, Carroll MD, Ogden CL, et al. Prevalence and trends
in obesity among US adults, 1999–2000. JAMA. 2002;288(14):
1723–1727.
Ryan K. Masters1, Daniel A. Powers2, and Bruce G. Link3
(e-mail: [email protected])
1
Department of Sociology and the Institute of Behavioral
Science, University of Colorado at Boulder, Boulder, CO
2
Department of Sociology and the Population Research
Center, University of Texas at Austin, Austin, TX
3
Departments of Epidemiology and Sociomedical Sciences,
Mailman School of Public Health, Columbia University,
New York, NY
DOI: 10.1093/aje/kwt331; Advance Access publication: January 12, 2014
Am J Epidemiol. 2014;179(4):529–532