The stated goal of observational studies is to elucidate a "cause and effect" relationship by comparing the responses of groups of treated (exposed) and control (unexposed) subjects; for example, to determine whether exposure to radiation due to fallout from nuclear testing is responsible for higher risk of childhood leukemia. Because assignment of subjects to these "treatment" groups is not random, a concern is that subjects of a particular type (e.g. with "higher response," "greater risk") may be over-represented in some groups. The model for causal inference based on counterfactuals, discussed in the previous talk (10/7/99), formalizes why this issue compromises attempts to make causal inference through estimation of the "average causal effect." A popular approach that is hoped to address this problem is to "adjust" in the analysis for the effects of "confounding factors" that may be associated both with the treatment and response. The counterfactual model also makes explicit under what conditions such "adjustment" should provide unbiased estimates of the average causal effect. In particular, such adjustment may allow such inference under the assumption of "strongly ignorable treatment assignment," also known as the "no unmeasured confounders" assumption in epidemiology.This material was discussed briefly in the last talk. Here, we will review it and then discuss in greater detail different approaches to implementing such adjustments, such as matching, stratification, and regression modeling. We will show explicitly how and why such adjustments are expected to work when strong ignorability holds. Because the number of confounding factors may be large, such methods may be unwieldy. Rosenbaum and Rubin (1983) proposed a way to reduce the dimensionality in such problems via use of the propensity score. We will exhibit theoretically exactly why the use of propensity score should achieve such adjustment. We will then discuss specific methods of implementing such adjustment, including stratification on the propensity score, inverse weighting methods, and regression methods that exploit the propensity score proposed by Robins et al.
A natural concern is that the strong ignorability assumption may not hold for observed confounders but rather it may hold only when unobserved confounders are taken into account. Alternatively, one may be tempted adjust for variables that are themselves affected by exposure, although the theory requires adjustment only on confounders (by definition not affected by exposure). We will briefly discuss the consequences of these issues.
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