Prostate cancer survival estimates: An application with piecewise hazard function derivation

The hazard function is defined as time-dependent. However, it is an overlooked area of research about the estimation of hazard function within the frame of time. The possible explanation could be carried by estimating function through the changes of time points. It is expected that it will provide us the overall idea of survival trend. This work is dedicated to propose a method to work with piecewise hazard rate. It is a data-driven method and provides us the estimates of hazard function with different time points.

The proposed method is explored with prostate cancer patients, registered in the Surveillance, Epidemiology, and End Results Program and having aged at diagnosis with range 40-80 years and above. A total of 610,814 patients are included in this study. The piecewise hazard rate is formulated to serve the objective. The measurement of piecewise hazard rate is compared with Wald-type test statistics, and corresponding R function is provided. The duration of follow-ups is split into different intervals to obtain the piecewise hazard rate estimates.

The maximum duration of follow-up observed in this study is 40 years. The piecewise hazard rate changes at different intervals of follow-ups are observed almost same except few later intervals in the follow-up. The likelihood of hazard in earlier aged patients observed lower in comparison to older patients. The hazard rates in different grades of prostate cancer also observed separately.

The application of piecewise hazard helps to generate statistical inference in a deeper manner. This analysis will provide us the better understanding of a requirement of effective treatment toward prolonged survival benefit for different aged patients.