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“Selection Bias by Death” and Other Ways Collider Bias May Cause the Obesity Paradox

Schooling, C. Mary; Au Yeung, Shiu Lun

doi: 10.1097/EDE.0000000000000591
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CUNY Graduate School of Public Health and Health Policy, New York, NY, School of Public Health, Li Ka Shing Faculty of Medicine, The University of Hong Kong, Hong Kong, China, mary.schooling@sph.cuny.edu

School of Public Health, Li Ka Shing Faculty of Medicine, The University of Hong Kong, Hong Kong, China

The authors report no conflicts of interest.

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To the Editor:

Use of more formal methods, including directed acyclic graphs, has helped resolve several long-standing epidemiologic paradoxes. The obesity paradox, where obesity is negatively associated with mortality in certain population sub-groups, remains something of an enigma. Elegantly, Sperrin et al.1 show analytically that collider stratification bias, due to selection on a mediator (M) of the obesity (A) mortality (Y) relation in the presence of an unmeasured mediator outcome confounder (U) (Figure A), only partially explains the obesity paradox.

FIGURE. Diffe

FIGURE. Diffe

Sperrin et al.1 do not consider other ways that collider stratification bias could generate the obesity paradox. Specifically, collider stratification bias may also occur through selection on a factor (S) dependent on the mediator (M) and the outcome (Y)2 (Figure A) or through selection on a factor (S) dependent on the mediator (M) and the exposure (A) (Figure C). Specifically, selection bias by death3 could occur if the exposure (A) causes ill-health (M), which causes selection (S), and ill-health causes mortality (Y), but people previously exposed have already died and so are not recruited into the study (Figure B) generating selection (S) on mortality (Y), as well as on ill-health (M). Notably the obesity paradox is more marked at older ages.

Conceptualizing the obesity paradox, as a problem arising from “selection bias by death”3 or missing the “already dead”2 or the “already ill” from the study also has implications for study design. Specifically, recruiting a population-representative sample may induce collider stratification bias because older people only represent part of their original cohort, and so harmful effects of exposures that caused deaths in the cohort before recruitment may be understated. This bias would be particularly marked for outcomes, such as death, to which older people are particularly prone. As such conceptualizing the obesity paradox as a problem of “selection bias by death” or of the “already dead” casts doubt on the use of population representative samples and studies of older people. This conceptualization also explains paradoxes, such as the cross-over paradox that occurs in the association of race/ethnicity with mortality in the very old,4 where those surviving to older ages from disadvantaged groups are more strongly selected survivors than others.

Sperrin et al.1 show analytically, with the bias quantified, why one explanation for the obesity paradox may be inadequate.1 Consideration of other more nuanced and parsimonious explanations for the obesity paradox may not only resolve it but shed light on other paradoxes.

C. Mary Schooling

CUNY Graduate School of Public Health and Health Policy

New York, NY

School of Public Health

Li Ka Shing Faculty of Medicine

The University of Hong Kong

Hong Kong, China

mary.schooling@sph.cuny.edu

Shiu Lun Au Yeung

School of Public Health

Li Ka Shing Faculty of Medicine

The University of Hong Kong

Hong Kong, China

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REFERENCES

1. Sperrin M, Candlish J, Badrick E, Renehan A, Buchan I. Collider bias is only a partial explanation for the obesity paradox. Epidemiology. 2016;27:525–530.
2. Schooling CM, Cowling BJ, Jones HE. Selection bias in cohorts of cases. Prev Med. 2013;57:247–248.
3. Hernán MA, Alonso A, Logroscino G. Cigarette smoking and dementia: potential selection bias in the elderly. Epidemiology. 2008;19:448–450.
4. Sautter JM, Thomas PA, Dupre ME, George LK. Socioeconomic status and the Black-White mortality crossover. Am J Public Health. 2012;102:1566–1571.
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