Analytical Strategies for Failure Time Data with a Cured Fraction

Background: Some failure time data comes from a population that consists of some subjects that are susceptible to and others that are non-susceptible to the event of interest. The data typically have heavy censoring at the end of the follow-up period, and a traditional survival analysis would not always be appropriate. Yet it is commonly seen in literatures. Methods: We carry out simulation studies to compare the performances of Cox’s PH model with proportional hazards mixture cure (PHMC) model and accelerated failure model (AFT model) with AFT mixture cure (AFTMC) model respectively. Then we apply the models to the datasets of Lung Cancer and Eastern Cooperative Oncology Group (ECOG) phase III clinical trial E1684. Results: When the cured rate is 0, the estimated bias, confidence interval capture rate, and K index of PHMC and AFTMC model are close to Cox’s PH and AFT model respectively. The MSE of PHMC model is slightly larger than Cox’s PH model and of AFTMC model are similar to AFT model. When survival data has a substantial proportion of subjects being cured, the absolute value of Bias and MSE in PHMC and AFTMC model are always smaller than Cox’s PH and AFT model respectively. The confidence interval capture rate of PHMC and AFTMC model are always closer to the acceptable range than Cox’s PH and AFT model. The K index of PHMC and AFTMC model are always greater than Cox’s PH and AFT model. Conclusions: The PHMC and AFTMC model do not have obvious advantages for time-to-event data without a cured fraction. In this case, it is recommended to utilize Cox’s PH or AFT model for analysis. If some subjects are non-susceptible to the event of interest in the data, it is recommended to utilize PHMC or AFTMC model for analysis, however, which may need a sufficient sample size. Keywords: Cox’s PH model, PHMC model, AFT model, AFTMC model, cure model