Structural cumulative survival models for estimation of treatment effects accounting for treatment switching in randomized experiments

Treatment switching in a randomized controlled trial occurs when a patient in one treatment arm switches to another 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 bias the estimated treatment causal effect. In this paper, we aim to account for the potential impact of treatment switching in a reanalysis evaluating the treatment effect of nucleoside reverse 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 omits NRTIs trial. We propose an estimator of a treatment causal effect for a censored time to event outcome under a structural cumulative survival model that leverages randomization as an instrumental variable to account for selective treatment switching. We establish that the proposed estimator is uniformly consistent and asymptotically Gaussian, with a consistent variance estimator and confidence intervals given, whose finite‐sample performance is evaluated via extensive simulations. An R package ‘ivsacim’ implementing all proposed methods is freely available on R CRAN. Results indicate that adding NRTIs versus omitting NRTIs to a new optimized treatment regime may increase the risk for a safety outcome.