Abstract
In research on the determinants of change in health status, a crucial analytic decision is whether to adjust for baseline health status. In this paper, the authors examine the consequences of baseline adjustment, using for illustration the question of the effect of educational attainment on change in cognitive function in old age. With data from the US-based Assets and Health Dynamics Among the Oldest Old survey (n = 5,726; born before 1924), they show that adjustment for baseline cognitive test score substantially inflates regression coefficient estimates for the effect of schooling on change in cognitive test scores compared with models without baseline adjustment. To explain this finding, they consider various plausible assumptions about relations among variables. Each set of assumptions is represented by a causal diagram. The authors apply simple rules for assessing causal diagrams to demonstrate that, in many plausible situations, baseline adjustment induces a spurious statistical association between education and change in cognitive score. More generally, when exposures are associated with baseline health status, this bias can arise if change in health status preceded baseline assessment or if the dependent variable measurement is unreliable or unstable. In some cases, change-score analyses without baseline adjustment provide unbiased causal effect estimates when baseline-adjusted estimates are biased.
Highlights
Introduction to using directed acyclic graph (DAG)In Directed acyclic graphs (DAGs), arrows between variables represent the investigator’s a priori assumptions about the causal relations among the potential covariates, the exposure, and the outcome
We have shown that baseline adjustment substantially alters coefficient estimates in analyses of the effect of education on cognitive change
Any of several causal structures could account for a discrepancy between baseline-adjusted and baseline-unadjusted models
Summary
In DAGs, arrows between variables represent the investigator’s a priori assumptions about the causal relations among the potential covariates, the exposure, and the outcome When these assumptions are represented in a DAG, a simple rule (described below) can be applied to select a set of covariates to include in a regression model. We informally introduce the rules for identifying the conditional independencies implied by a DAG, that is, determining whether the causal assumptions represented in the DAG necessarily imply that two variables are statistically independent conditional on a proposed covariate set To relate this discussion to more common epidemiology terms, note that regression coefficients, t statistics, odds ratios, and the like are examples of measures of statistical dependence between variables. Covariate adjustment in a regression model is a type of conditioning, as are stratification and matching
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