Estimation of the causal effect of a time-varying exposure on the marginal mean of a repeated binary outcome

We provide sufficient conditions for estimating from longitudinal data the causal effect of a time-dependent exposure or treatment on the marginal probability of response for a dichotomous outcome. We then show how one can estimate this effect under these conditions using the g-computation algorithm of Robins. We also derive the conditions under which some current approaches to the analysis of longitudinal data, such as the generalized estimating equations (GEE) approach of Zeger and Liang, the feedback model techniques of Liang and Zeger, and within-subject conditional methods, can provide valid tests and estimates of causal effects. We use our methods to estimate the causal effect of maternal stress on the marginal probability of a child's illness from the Mothers' Stress and Children's Morbidity data and compare our results with those previously obtained by Zeger and Liang using a GEE approach.