Computational Methods in Survival Analysis

Survival analysis is widely used in the fields of medical science, pharmaceutics, reliability and financial engineering, and many others to analyze positive random phenomena defined by event occurrences of particular interest. In the reliability field, we are concerned with the time to failure of some physical component such as an electronic device or a machine part. This article briefly describes statistical survival techniques developed recently from the standpoint of statistical computational methods focussing on obtaining the good estimates of distribution parameters by simple calculations based on the first moment and conditional likelihood for eliminating nuisance parameters and approximation of the likelihoods. The method of partial likelihood (Cox, 1972, 1975) was originally proposed from the view point of conditional likelihood for avoiding estimating the nuisance parameters of the baseline hazards for obtaining simple and good estimates of the structure parameters. However, in case of heavy ties of failure times calculating the partial likelihood does not succeed. Then the approximations of the partial likelihood have been studied, which will be described in the later section and a good approximation method will be explained. We believe that the better approximation method and the better statistical model should play an important role in lessening the computational burdens greatly.