Treatment switching in a randomized controlled trial is said to occur when a patient randomized to one treatment arm switches to another treatment arm during follow-up. This can occur at the point of disease progression, whereby patients in the control arm may be offered the experimental treatment. It is widely known that failure to account for treatment switching can seriously dilute the estimated effect of treatment on overall survival. In this paper, we aim to account for the potential impact of treatment switching in a re-analysis evaluating the treatment effect of NucleosideReverse Transcriptase Inhibitors (NRTIs) on a safety outcome (time to first severe or worse sign or symptom) in participants receiving a new antiretroviral regimen that either included or omitted NRTIs in the Optimized Treatment That Includes or OmitsNRTIs (OPTIONS) trial. We propose an estimator of a treatment causal effect under a structural cumulative survival model (SCSM) that leverages randomization as an instrumental variable to account for selective treatment switching. Unlike Robins accelerated failure time model often used to address treatment switching, the proposed approach avoids the need for artificial censoring for estimation. We establish that the proposed estimator is uniformly consistent and asymptotically Gaussian under standard regularity conditions. A consistent variance estimator is also given and a simple resampling approach provides uniform confidence bands for the causal difference comparing treatment groups overtime on the cumulative intensity scale. We develop an R package named ivsacim implementing all proposed methods, freely available to download from R CRAN. We examine the finite performance of the estimator via extensive simulations.
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