Nonparametric and Semiparametric Models
Survival data are conveniently summarized through estimates of the survival function and hazard function. Methods of estimating these functions from a sample of survival data are said to be nonparametric or distribution-free since they do not require specific assumptions to be made about the underlying distribution of the survival times. An initial step in the analysis of survival data is to present numerical or graphical summaries of the survival times for individuals in a particular group. Such summaries may be of interest in their own right, or as a precursor to a more detailed analysis of the data. Once the estimated survival function has been found, the median and other percentiles of the distribution of survival times can be estimated. When the survival times of two groups of patients are being compared, an informal comparison of the survival experience of each group of individuals can be made using the estimated survival functions. However, there are more formal procedures that enable two groups of survival data to be compared. Nonparametric procedure for comparing two or more groups of survival times is the logrank test which is the most powerful test against the alternatives that the hazard functions are proportional.