Assessing causal effects in the presence of treatment switching through principal stratification
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Clinical trials focusing on survival outcomes often allow patients in the control arm to switch to the treatment arm if their physical conditions are worse than certain tolerance levels. The Intention-To-Treat analysis provides valid causal estimates of the effect of assignment, but it does not measure the effect of the actual receipt of the treatment and ignores the information of treatment switching. Other existing methods propose to reconstruct the outcome a unit would have had if s/he had not switched under strong assumptions. We propose to re-define the problem of treatment switching using principal stratification focusing on principal causal effects for patients belonging to subpopulations defined by the switching behavior under control. We use a Bayesian approach to inference taking into account that (i) switching happens in continuous time generating infinitely many principal strata; (ii) switching time is not defined for units who never switch in a particular experiment; and (iii) survival time and switching time are subject to censoring. We illustrate our framework using a synthetic dataset based on the Concorde study, a randomized controlled trial aimed to assess causal effects on time-to-disease progression or death of immediate versus deferred treatment with zidovudine among patients with asymptomatic HIV infection.
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