Robust estimation of causal effects of binary treatments in unconfounded studies with dichotomous outcomes

The estimation of causal effects has been the subject of extensive research. In unconfounded studies with a dichotomous outcome, Y, Cangul, Chretien, Gutman and Rubin (2009) demonstrated that logistic regression for a scalar continuous covariate X is generally statistically invalid for testing null treatment effects when the distributions of X in the treated and control populations differ and the logistic model for Y given X is misspecified. In addition, they showed that an approximately valid statistical test can be generally obtained by discretizing X followed by regression adjustment within each interval defined by the discretized X. This paper extends the work of Cangul et al. 2009 in three major directions. First, we consider additional estimation procedures, including a new one that is based on two independent splines and multiple imputation; second, we consider additional distributional factors; and third, we examine the performance of the procedures when the treatment effect is non-null. Of all the methods considered and in most of the experimental conditions that were examined, our proposed new methodology appears to work best in terms of point and interval estimation.