Date Available


Year of Publication


Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation


Arts and Sciences



First Advisor

Dr. Jianrong Wu

Second Advisor

Dr. Arnold Stromberg


A challenge arising in cancer immunotherapy trial design is the presence of non-proportional hazards (NPH) patterns in survival curves. We considered three different NPH patterns caused by delayed treatment effect, cure rate and responder rate of treatment group in this dissertation. These three NPH patterns would violate the proportional hazard model assumption and ignoring any of them in an immunotherapy trial design will result in substantial loss of statistical power.

In this dissertation, four models to deal with NPH patterns are discussed. First, a piecewise proportional hazards model is proposed to incorporate delayed treatment effect into the trial design consideration. Second, we consider a piecewise proportional hazard model with cure rate to deal with both delayed treatment effect and cure rate. Third, we extended the second model as a general random delayed cure rate model in cancer immunotherapy trials design. Fourth, we proposed a piecewise proportional hazard responder rate model to deal with both delayed treatment effect and responder rate. Sample size formulas are derived for weighted log-rank tests under a fixed alternative hypothesis under various models. The accuracy of sample size calculation using the new formulas are assessed and compared with the existing methods via simulation studies. The sensitivities for mis-specifying the random delay time are also studied through simulations. What is more, a real immunotherapy trial is used to illustrate the study design along with practical consideration of balance between sample size and follow-up time in second model.

Digital Object Identifier (DOI)