Estimating the causal effects of treatment

Objective - To provide a relatively non-technical review of recent statistical research on the analysis and interpretation of the results of randomised controlled trials in which there are possibly all three of the following types of protocol violation: non-adherence to allocated treatment, contamination (that is, patients receiving treatments other than the one to which they were allocated) and attrition (missing outcome data). Methods - The estimation methods involve the use of potential outcomes (counterfactuals) in the definition of a causal effect of treatment and in drawing valid inferences concerning its size. Results - The methods are explained through the use of simple arithmetical expressions involving the counts from three-way contingency tables (Outcome by Treatment Received by Random Allocation). Illustration is provided through the use of a hypothetical data set. Conclusions - Recent advances in statistical methodology enable one to estimate treatment effects from the results of randomised trials in which the treatment actually received is not necessarily the one to which the patient was allocated. These methods allow one to make adjustments to allow for both non-compliance and loss to follow-up. Even for such a 'broken' randomised trial, inference concerning causal effects is safer than that from data arising from an observational study that never involved random allocation in the first place.