Estimating treatment effects on duration with disease: a principal stratification framework

In clinical research, estimating the average treatment effect is a common goal. However, when treatment effects vary substantially across individuals, it is often more informative to evaluate the treatment effect within subgroups. This paper focuses on causal inference for a duration outcome in a principal stratum-defined as the subgroup of individuals who would experience a positive duration under one treatment. Motivated by the Danish Vulva Cancer Recurrence Study (DaVulvaRec), which compares intensive versus standard follow-up in women treated for vulvar cancer, we examine the effect of intensive follow-up on the time with a cancer recurrence diagnosis. The principal stratum is in this example women who would be diagnosed with cancer recurrence under the intensive follow-up. We present a framework for identifying and estimating the average treatment effect in the principal stratum under a monotonicity assumption and introduce a sensitivity parameter to evaluate the impact of potential violations of this assumption. Using a multi-state model with pseudo-observations, we account for censoring and demonstrate that this approach offers greater statistical power than conventional comparisons between treatment groups. We illustrate the methodology to sample size calculation, the final analysis of the DaVulvaRec study using a simulated data set and an application to data from a randomized study on colon cancer.