Date of Graduation


Document Type


Degree Name

Master of Science in Statistics and Analytics (MS)

Degree Level



Statistics and Analytics


Qingyang Zhang

Committee Member

Avishek Chakraborty

Second Committee Member

Mark Arnold


Clinical trials, MaxCombo test, Survival data


In oncology clinical trials, when a treatment is administered to the patient population, a certain subset of patients may respond to the treatment while the other does not. The positive responders with long-term survival are considered “statistically cured” and can be referred to as cured patients or long-term survivors. When a proportion of patients achieve long-term survival, the hazard functions of two arms (control vs. treatment) are no longer proportional. As a result, the traditional log-rank test, which is the most popular test to evaluate the effectiveness of a treatment in clinical trials, tends to lose its power. In this thesis, we first design a simulation study to compare the empirical statistical power of the log-rank test and two recently proposed tests for non-proportional data, namely the MaxCombo test, and the RMST difference test, while considering the fact that long-term survivors also have a certain risk of events. Under exponential mixture cure model, our simulation studies show that the power of the three tests can be affected by several factors, including the short-term median survival, the long-term median survival, and cured proportion difference between two arms. In chapter 3, we propose a restricted EM algorithm to estimate the parameters of the exponential mixture cure model, which has been extensively used to model the survival data in the presence of cured proportions. We derive both unrestricted and restricted versions of EM algorithm for survival data with right-censored observations. Furthermore, we conduct a simulation study to compare the performance of both methods in terms of parameter estimate accuracy and computational efficiency. The results show that our proposed restricted EM method performs significantly better than the unrestricted one, particularly when the median survival time of the long-term survivors is considerably greater than that of the short-term survivors.

Available for download on Monday, February 17, 2025