Pseudo conditional likelihood inference for repeated binary outcomes in two-arm experimental studies with non-compliance

A causal model is proposed for two-arm experimental studies with possible non-compliance in which the effect of the treatment is measured by a binary response variable, the value of which is available even before the treatment. A pseudo conditional likelihood method is proposed for the estimation of the model and, in particular, of the causal effect of the treatment over control in the subpopulation of compliers. The estimator is very simple to use and represents an extension of the conditional logistic estimator. Its asymptotic properties are studied by exploiting the general theory on maximum likelihood estimation of misspecified models. Finite-sample properties of the estimator are illustrated by simulation. The extension of the model and the estimation method to the case of missing responses is outlined. The approach is illustrated by an application to a dataset deriving from a study on the efficacy of a training course on the attitude to practise breast self examination.