A framework for automatic modelling of survival using fuzzy inference

Survival analysis describes the analysis of data that corresponds to the time from when an individual enters a study until the occurrence of some particular event or end-point. It is most commonly used in the context of modelling survival (or disease-free interval time) in medical contexts, often concerned with the comparison of survival for different combinations of risk factors and/or treatments. Analytical methods which are transparent to the clinicians in understanding and explaining individual inference need to be considered when dealing with such medical data. In this paper, we present a framework for modelling survival utilising the application of the ANFIS fuzzy inference system. In this framework, alternative methods of partitioning the input space can be selected to define the membership functions, for example by using expert knowledge, equalizer partitioning, fuzzy c-means clustering, or the combination of these techniques. Further, the rule base can be established by enumerating all possible combinations of membership functions of all inputs. After the initialisation of the fuzzy inference structure, the replication data (until time to event) will be subject to be trained using the gradient descent and nonnegative least square algorithm to estimate the conditional event probability. This framework is validated over a novel dataset of patients following operative surgery for ovarian cancer. We demonstrate that the proposed framework can be successfully applied to estimate the hazard and survival curves between different prognostic factors, and model survival times, while providing models with explicit explanation capabilities.