Assessing Causal Effects on Survival Time in the Presence of Treatment Switching



In clinical trials focusing on survival outcomes for patients suffering from Acquired Immune Deficiency Syndrome (AIDS)-related illnesses and particularly painful cancers in advanced stages, patients in the control arm are often allowed to switch to the treatment arm if their physical conditions are worse than certain tolerance levels. The Intention-To-Treat analysis, comparing groups formed by randomization regardless of the treatment actually received, is often used; although it provides valid causal estimates of the effect of assignment, it does not give information about the effect of the actual receipt of the treatment and ignores the information of treatment switching in the control group. Other existing methods in the literature propose to reconstruct the outcome a unit would have had if s/he had not switched but they are usually based on strong assumptions, like that there exist no relation between patient’s prognosis and switching behaviour. Clearly, the switching status of the units in the control Group contains important post-treatment information and it is useful to characterize the heterogeneity of the treatment effect. We propose to re-define the problem of treatment switching using principal stratification and introduce new causal estimands, principal causal effects for patients belonging to subpopulations defined by the switching behavior under the control treatment, which appropriately adjust for the post-treatment information and characterize treatment effect heterogeneity. For inference, we use a Bayesian approach, which allows us to properly take into account that (i) switching happens in continuous time generating a continuum of principal strata; (ii) switching time is not defined for units who never switch in a particular experiment; and (iii) both survival time, the outcome of primary interest, and switching time are subject to censoring. We illustrate our framework using simulated data 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.

Joint work with Alessandra Mattei and Peng Ding.