The Irrelevance of Getting Stronger or Weaker with Age

In this issue, Wang and colleagues (1) discuss two previous papers in which Masters et al. sought to control for survivor bias in the association between obesity and mortality (2, 3). In their adjusted models for the effect of obesity on mortality, Masters et al. obtained increasing effect sizes with increasing age, in contrast to the prior literature showing an attenuation of the effect magnitudes over the life course. Their ad hoc correction method has since been refuted (4), but the authors still insist that it remains qualitatively valid (5). This new paper (1) offers some further elaboration on this methodological debate, demonstrating that when modeled more appropriately, the effect estimates do indeed weaken with age. According to Wang et al., the error of the previous papers was to ignore interaction between obesity and age by controlling age at baseline to a single value. In the new analyses, both with hazard ratios estimated from the fitted flexible survival model and matched analyses in which participants with obesity were paired to participants without obesity, these authors found a pattern of diminishing hazard ratios as the participants aged. Although this reanalysis shows how easy it is to reverse an overall pattern of results with an alternative model specification, it does little to resolve any etiologic questions of interest. The associations estimated in these models lack a causal interpretation for a variety of reasons, none of which are resolved in this new article. Fundamentally, obesity is poorly defined as an exposure, since it lacks any unambiguous onset in these data and does not correspond to any specific intervention (6). Aging cohorts are increasingly selected over time by differential mortality that is partly a function of exposure, making the effect estimates in the survivors problematic to interpret (7). It has been shown that exposures that are harmful to every individual in the population can generate protective hazard ratios when the cohort is selectively pruned in this way and, furthermore, that hazard ratios are never causally interpretable when failures are common because they are explicitly conditioned on past survival (8). Most important, however, is the simple fact that ratio contrasts that diminish in magnitude over the life course do not imply weaker effects with age. This is because the denominator is also changing with age. For example, consider a hazard ratio of 3 at a young age, composed of a numerator rate in the exposed of 15 per 1,000 person years (PYs) and a denominator rate in the unexposed of 5 per 1,000 PYs. At an older age, the numerator and denominator are 40 and 20 per 1,000 PYs, so that the hazard ratio of 2 is smaller. Nonetheless, among each 1,000 people followed for a year, 10 are dead because of exposure at the younger age, whereas 20 are dead because of exposure at the older age. The hazard ratio has decreased, but the strength of the effect has increased. If the authors can reverse the direction of the trend over age by using something as simple and arbitrary as taking the difference of the hazards instead of the ratio of the hazards, then the pattern obviously has no deeper significance for the underlying etiology. The prospects for this whole research question look rather discouraging when approached by using cohort data in which people of various ages report a baseline BMI at the time of interview and are then followed up for mortality over subsequent decades. The older people at the time of the interview have already been purged of the most susceptible people in the population through differential mortality and, moreover, may have already lost weight because of illness. One might improve upon this last concern somewhat by using highest attained weight, as suggested recently (9), and by considering for follow-up only those younger than, say, age 50 at baseline to minimize left-censoring of the earlier birth cohorts. Even so, the causal parameter remains difficult to interpret, and the counterfactual balance across BMI groups is difficult to accept with any credibility. As with most observational epidemiology, thinking in terms of a “target trial” would go a long way to illuminating most of the deficiencies of these existing studies (10), although it is not obvious that these can be surmounted with any ethical or feasible design. Rather, we could probably make more progress by focusing on the study of specific interventions like weight loss programs or bariatric surgery. It's not hazard ratios but rather epidemiologic designs that really need to get stronger over time.

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