The Book of Why: The New Science of Cause and Effect (Penguin Science)

by Judea Pearl

For many researchers, the most (perhaps only) familiar method of predicting the effect of an intervention is to “control” for confounders using the adjustment formula. This is the method to use if you are confident that you have data on a sufficient set of variables (called deconfounders) to block all the back-door paths between the intervention and the outcome. To do this, we measure the average causal effect of an intervention by first estimating its effect at each “level,” or stratum, of the deconfounder. We then compute a weighted average of those strata, where each stratum is weighted according to its prevalence in the population. If, for example, the deconfounder is gender, we first estimate the causal effect for males and females. Then we average the two, if the population is (as usual) half male and half female. If the proportions are different—say, two-thirds male and one-third female—then to estimate the average causal effect we would take a correspondingly weighted average.