Confidence intervals for causal parameters

Abstract

Consider an unbiased follow-up study designed to investigate the causal effect of a dichotomous exposure on a dichotomous disease outcome. Under a deterministic outcome model, a standard '95 per cent binomial confidence interval' may fail to cover the causal parameter of interest at the nominal rate when we take the causal parameter to be a parameter associated with the observed study population (regardless of whether the observed study population was sampled from a larger superpopulation). I propose new interval estimators that, in this setting, improve upon the performance of the standard 'binomial confidence interval.'