Dependent censoring in piecewise exponential survival models

There are often reasons to suppose that there is dependence between the time to event and time to censoring, or dependent censoring, for survival data, particularly when considering medical data. This is because the decision to treat or not is often made according to prognosis, usually with the most ill patients being prioritised. Due to identifiability issues, sensitivity analyses are often used to assess whether independent censoring can lead to misleading results. In this paper, a sensitivity analysis method for piecewise exponential survival models is presented. This method assesses the sensitivity of the results of standard survival models to small amounts of dependence between the time to failure and time to censoring variables. It uses the same assumption about the dependence between the time to failure and time to censoring as previous sensitivity analyses for both standard parametric survival models and the Cox model. However, the method presented in this paper allows the use of more flexible models for the marginal distributions whilst remaining computationally simple. A simulation study is used to assess the accuracy of the sensitivity analysis method and identify the situations in which it is suitable to use this method. The study found that the sensitivity analysis performs well in many situations, but not when the data have a high proportion of censoring.