Estimation and completion of survival data with piecewise linear models and S-distributions

摘要

Survival processes are often validly represented with the default Weibull or lognormal distributions, but in some cases they exhibit lighter or heavier tails and different degrees or types of skewness. It is, therefore, desirable to develop parametric survival models with an expanded range of plasticity in distributional shape. The four-parameter S-distribution is a viable candidate for this purpose. It is flexible enough to model a wide variety of unimodal shapes and has a number of advantages for computational data analysis and classification. In the past, the parameters of S-distributions have been estimated directly with methods of non-linear regression or maximum likelihood. Here, it is shown how the distribution can be identified from a piecewise linear, continuous approximation of the hazard function, which is often more informative than the survival function itself. The method is illustrated with an analysis of the survival of tuberculosis infected guinea pigs as well as a number of simulations with different types of censored and uncensored survival processes. The results suggest that the piecewise linear hazard model and the S-distribution provide effective tools for representing and completing survival data, even if they are heavily censored.