Computational Intelligence in Survival Analysis

Survival analysis, often called time-to-event analysis, is a set of methods focused on failure time prediction. Such methods are developed in a variety of research domains like medicine, sociology, economics or engineering, and are used to analyze different types of failures. For example, in business applications the failure may denote bankruptcy or loan default. One of the most important characteristics of survival data is censoring. Censored observations contain incomplete information of failure occurrence. It means that for a number of companies we do not observe the event of interest, we only know that the failure did not occur before some specified time. Since the percentage of censored observation is usually high, they should be taken into account in the prediction process. Considering statistical methods for analysis of survival data, the most common approach is Cox’s proportional hazards model (Cox, 1972). This semi-parametric model is usually used for determining risk factors – variables, that influence the risk of failure. Its application is limited by additional assumptions concerning proportional hazards and known functional form of independent variables effect. Other methods, accelerated failure time models (Marubini & Valsecci, 1995), may be used only when the failure time distribution is specified. Since the assumptions are often difficult to fulfill, other assumption-free models are developed. Many of them are based on computational intelligence techniques, mainly on artificial neural networks and survival trees. In the chapter I would like to introduce the problem of survival analysis and to describe the possibilities of the use of computational intelligence techniques for analysis of survival data. Although the term “computational intelligence” covers many different techniques, we will narrow the examples of their applications to the most common approaches artificial neural networks, survival trees, and ensembles of tree-based models.