Bayes linear kinematics in a dynamic survival model

Bayes linear kinematics and Bayes linear Bayes graphical models provide an extension of Bayes linear methods so that full conditional updates may be combined with Bayes linear belief adjustment. In this paper we investigate the application of this approach to survival analysis with time-dependent covariate effects, a more complicated problem than previous applications. We use a piecewise-constant hazard function with a prior in which covariate effects are correlated over time. The need for computationally intensive methods is avoided and the relatively simple structure facilitates interpretation. Our approach eliminates the problem of non-commutativity which was observed in earlier work by Gamerman. We apply the technique to data on survival times for leukemia patients. We demonstrate the use Bayes linear kinematics in a more complicated problem.We use a realistically complicated case study in semi-parametric survival analysis.The previously-observed problem of non-commutativity is overcome.Attention is given to the specification of prior beliefs and its effects.