Sensitivity analysis of progression-free survival with dependent withdrawal

We develop a sensitivity analysis method for comparing treatment-specific distributions where the endpoint is progression-free survival (PFS). The censoring process may be informative due to selective patient withdrawal, which occurs whenever disease evaluation has been discontinued without progression being documented. The sensitivity analysis explores the effects of the dependence between patient withdrawal and progression time using a conditional probability model which incorporates a set of sensitivity parameters. We propose an EM algorithm for estimation of PFS under the model for dependence and construct log-rank-type score statistics from the estimated distributions. Bootstrap procedures are used to estimate the variance of the score statistic. We also extend the methodology to incorporate additional survival information, which may be available on the cases who were withdrawn. An Eastern Cooperative Oncology Group (ECOG) advanced lung cancer clinical trial (E1594) is used to illustrate the methodology.