title: Estimating the causal effects of treatment.
abstract: 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 randomized 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.
authors.affiliation: Biostatistics Group, School of Epidemiology & Health Sciences, University of Manchester, Manchester, United Kingdom. g.dunn@man.ac.uk
authors.forename: Graham
authors.initials: G
authors.lastname: Dunn
mesh_terms: D006801:Humans; D001523:Mental Disorders / Q000628:therapy; D015233:Models, Statistical; D010349:Patient Compliance; D016032:Randomized Controlled Trials as Topic; D016896:Treatment Outcome