When investigating relationships between education and health, one has to take age into account. Conditioning on age entails conditioning on surviving, which has been argued to lead to a potential selection bias. In this note, I argue that surviving should be considered as a necessary precondition for the relationships of interest and, therefore, not as a possible source of bias. I criticize models of health trajectories that do not condition on surviving.
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Additional problems occur when cohorts are based on a broad range of birth years; for some discussion, see Lauderdale (2001).
This model, of course, is extremely simplified. Real individual health trajectories show a wide variety of different, generally nonlinear, and often nonmonotonic forms.
The plot is inspired by aging-vector graphs as used by Kim and Durden (2007).
For discussion of this question, see also Kurland et al. (2009). They considered the hierarchical growth curve model as an unconditional model (with regard to surviving), which requires values of the dependent variable for deceased persons as well. This model is contrasted with a partly conditional model, which relates to the surviving members of a cohort and is basically equal to Eq. (6).
Of course, it is possible for omitted variables to distort an assessment of the relationship between education and health: for example, if an omitted variable affects both health and mortality such that, conditional on surviving, its correlation with education changes. However, this problem cannot be avoided by hypothetically dismissing the conditioning on survival.
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Rohwer, G. A Note on the Dependence of Health on Age and Education. Demography 53, 325–335 (2016). https://doi.org/10.1007/s13524-016-0457-y
- Age trajectories of health
- Mortality selection
- Growth curve modeling
- Hierarchical models