Sieve based full likelihood approach for the Cox proportional hazards model with applications to immunotherapies trials

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In clinical studies, the time-to-event outcomes are widely used to evaluate a new treatment efficacy. When complete randomization is not possible or successful the Cox proportional hazards model can be used to adjust for the confounding effects and to increase statistical power. Phase II studies usually have relatively small number, so the survival analysis results are not very reliable or do not have enough power to detect a positive result of the experimental treatment. This project aims to provide better survival analysis results compared to existing methods for small sample studies. Sieve method has becoming a popular approach in survival analysis, we propose to use the sieve maximum likelihood estimations to improve survival analysis results for small studies and provide corresponding computing tools for public use.