Estimating the survival functions for right-censored and interval-censored data with piecewise constant hazard functions

Study design of single-arm phase II immunotherapy trials with long-term survivors and random delayed treatment effect

In the traditional study design of a single-arm phase II cancer clinical trial, the one-sample log-rank test has been frequently used. A common practice in sample size calculation is to assume that the event time in the new treatment follows exponential distribution. Such a study design may not be suitable for immunotherapy cancer trials, when both long-term survivors (or even cured patients from the disease) and delayed treatment effect are present, because exponential distribution is not appropriate to describe such data and consequently could lead to severely underpowered trial. In this research, we proposed a piecewise proportional hazards cure rate model with random delayed treatment effect to design single-arm phase II immunotherapy cancer trials. To improve test power, we proposed a new weighted one-sample log-rank test and provided a sample size calculation formula for designing trials. Our simulation study showed that the proposed log-rank test performs well and is robust of misspecified weight and the sample size calculation formula also performs well.

Bayesian Inference For The Segmented Weibull Distribution

In this paper, we introduce a Bayesian approach for segmented Weibull distributions which could be a good alternative to analyze medical survival data in the presence of censored observations and covariates. With the obtained Bayesian estimated change-points we could get an excellent fit of the proposed model to any data sets. With the proposed methodology, it is also possible to identify survival times intervals where a covariate could have significantly different efects when compared to other lifetime intervals, an important point under a clinical view. The obtained Bayesian estimates are obtained using standard Markov Chain Monte Carlo methods. Some examples with real data sets illustrate the proposed methodology and its potential clinical value.