Date of Award


Document Type

Open Access Thesis


Epidemiology and Biostatistics


The Norman J. Arnold School of Public Health

First Advisor

Jiajia Zhang


With the development of advanced medical technology, a significant proportion of patients can be cured of many chronic diseases. Because a substantial fraction of patients have censored information, the standard survival model, such as the proportional hazards (PH) model cannot capture the cured information of patients. Thus PH mixture cure model is developed to handle the survival data with potential cured information. A corresponding sample size formula based on log rank test has been proposed by Wang et al. (2012) and the probability of death in their formula is only contributed by the control arm. However, to calculate the sample size and power, the hazard ratio and odds ratio are prespecified, which can also contribute to increase the accuracy of probability of death, by accounting for both the control and treatment arm. Therefore, we modify this formula by improving the estimation of the probability of death based on both the control and treatment arm using two approaches. The Schoenfeld and Ewell method adjusts the probability of death by averaging the death from both groups. The modified approach is verified by extensive simulation under exponential, weibull and lognormal distribution. The performance of the three methods has been compared under each setting with parametric and nonparametric estimation. Furthermore, the sample size calculation has been extended to PH mixture cure model with nonbinary covariates and evaluated by simulation studies. These modifications have been implemented in the R package and applied to the real data sets.

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Biostatistics Commons