Statistical inference on survival data in group-parallel clinical trials with treatment switching

Usually patients are allowed to switch their treatments in clinical trials out of an ethical consideration. This complicates the modeling of the trial, as well as the analyzing process of the collected data. For group-parallel clinical trials which contain two groups (one is the test and the other is the control) and where all patients may switch their treatments, some statistical inferences on patients’ survival data are conducted. The median survival times for two treatments are estimated by the maximum likelihood method. Furthermore, the hypothesis test on equality, superiority/non-inferiority and equivalence of two median survival times as well as the confidence interval estimation for the difference of two medians are also discussed. The sample size required in designing each hypothesis test is derived. Also a numerical study is conducted to assess the performance of the proposed approaches.