390 Conditional Hazard Estimating Neural Networks Antonio Eleuteri Royal Liverpool University Hospital, UK Azzam Taktak Royal Liverpool University Hospital, UK Bertil Damato Royal Liverpool University Hospital, UK Angela Douglas Liverpool Women’s Hospital, UK Sarah Coupland Royal Liverpool University Hospital, UK Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited. INTRODUCTION Survival analysis is used when we wish to study the occurrence of some event in a population of subjects and the time until the event of interest. This time is called survival time or failure time. Survival analysis is often used in industrial life-testing experiments and in clinical follow-up studies. Examples of application include: time until failure of a light bulb, time until occurrence of an anomaly in an electronic circuit, time until relapse of cancer, time until pregnancy. In the literature we fnd many different modeling approaches to survival analysis. Conventional para- metric models may involve too strict assumptions on the distributions of failure times and on the form of the infuence of the system features on the survival time, assumptions which usually extremely simplify the experimental evidence, particularly in the case of medical data (Cox & Oakes, 1984). In contrast, semi- parametric models do not make assumptions on the distributions of failures, but instead make assumptions on how the system features infuence the survival time (the usual assumption is the proportionality of hazards); furthermore, these models do not usually allow for direct estimation of survival times. Finally, non-parametric models usually only allow for a qualitative description of the data on the population level. Neural networks have recently been used for survival analysis; for a survey on the current use of neural net- works, and some previous attempts at neural network survival modeling we refer to (Bakker & Heskes, 1999), (Biganzoli et al., 1998), (Eleuteri et al., 2003), (Lisboa et al., 2003), (Neal, 2001), (Ripley & Ripley, 1998), (Schwarzer et al. 2000). Neural networks provide effcient parametric es- timates of survival functions, and, in principle, the capability to give personalised survival predictions. In a medical context, such information is valuable both to clinicians and patients. It helps clinicians to choose appropriate treatment and plan follow-up effciently. Patients at high risk could be followed up more fre- quently than those at lower risk in order to channel valuable resources to those who need them most. For patients, obtaining information about their prognosis is also extremely valuable in terms of planning their lives and providing care for their dependents. In this article we describe a novel neural network model aimed at solving the survival analysis problem in a continuous time setting; we provide details about the Bayesian approach to modeling, and a sample ap- plication on real data is shown. BACKGROUND Let T denote an absolutely continuous positive random variable, with distribution function P, representing the time of occurrence of an event. The survival function, S(t), is defned as: