Estimating Causal Effects
The main purpose of a comparative study is to estimate a causal effect. We have defined a causal effect most generally as a distribution of individual response patterns in the study population. The response-pattern distribution can be viewed as the raw material from which any specific causal effect can be forged. This distribution could tell us everything we need to know about causal effects, but it cannot be observed directly. It is highly informative on a conceptual level, but is not directly useful for actually estimating an effect.
As explained in Chapter 2, the causal effects of interest typically take the form of a difference between (or ratio of) the values of two summary statistics. One of these statistics is a summary of the potential-outcome distribution for a group of exposed individuals; the other is the corresponding summary for the unexposed group. The difference of means and the ratio of proportions are by far the two most common summary measures of effect. The adoption of a particular measure of effect seems so natural and obvious that it is easy to overlook its significance. Implications that flow from the mathematical properties of a particular measure are sometimes interpreted incorrectly as properties of causal inference in general.
The empirical effect has the obvious advantage that its value can be calculated from potentially observable data. However, the empirical effect may have only an indirect relationship to the actual ...