Estimating parameters of proportional hazards model based on expert knowledge and statistical data

Proportional hazards model (PHM) is a convenient statistical tool that can be successfully applied in industrial problems, such as in accelerated life testing and condition-based maintenance, or in biomedical sciences. Estimation of PHM requires lifetime data, as well as condition monitoring data, which often is incomplete or missing, and necessitates the use of expert knowledge to compensate for it. This paper describes the methodology for elicitation of expert's beliefs and experience necessary to estimate the parameters of a PHM with time-dependent covariates. The paper gives a background of PHM and review of the literature related to the knowledge elicitation problem and gives a foundation for the proposed methodology. The knowledge elicitation process is based on case analyses and comparisons. This method results in a set of inequalities, which in turn define a feasible space for the parameters of the PHM. By sampling from the feasible space an empirical prior distribution of the parameters can be estimated. Then, using Bayes rule and statistical data the posterior distribution can be obtained. This technique can also provide reliable outcomes when no statistical data are available. The technique has been tested several times in laboratory experiments and in a real industrial case and has shown promising results.