Power Piecewise Exponential Model for Interval-Censored Data

Longitudinal studies with periodic follow-ups and clinical trials generally have interval censoring. In order to analyze these data, there are some statistical models and methods: one of them is the semiparametric piecewise exponential (PE) model. In this paper, we introduce the power piecewise exponential distribution, more flexible than the PE distribution, for interval-censored data under two approaches: frequentist and Bayesian. For both approaches, we have performed simulation studies and realized that the power piecewise exponential model for interval-censored data has estimates close to the real values, decreasing standard deviation and relative bias, and coverage probability closer to the nominal level (95%), when the sample size increases. In practice, studies about HIV are widely known to have interval-censored, which is why we analyzed the hemophiliacs’ data using the model proposed in this paper under a frequentist approach. Another well-known clinical trial is about breast cancer, so we show the fit of the proposed model under the Bayesian approach for these data. In all the applications, the power piecewise exponential distribution presented the best adjustment.