# Bayesian survival modelling in health economic evaluation

## Introduction

Survival analysis is an essential component of the health economic evaluation of new interventions. In fact, many of the technical appraisals performed by bodies such as NICE involve evaluations based on some form of time-to-event analysis, for instance when dealing with cancer drugs. More specifically, cost-effectiveness analyses (CEAs) require estimating the difference in *mean* survival times between arms (rather than median, which is more common in “standard” biostatistics analysis), in order to quantify the long term economic benefits of a new intervention. New treatments and drugs often impact life expectancy and/or quality of life for periods longer in duration than the randomised clinical trials (RCTs) from which the experimental data are obtained. Hence, obtained survival curves are usually
right-censored and inadequate to determine long term costs and outcomes. In health-economic evaluations, curves must be extrapolated to a much longer time horizon in order to compute the mean time-to-event.

Often, the process of survival analysis is rendered even more complicated by the fact that the data may not be informative enough to estimate long-term extrapolation, as well as the need to perform parametric estimates, without clear guidance as to which, in a set of suitable candidates, is the “best” model (not only in terms of the fit to the observed data, but over the entire extrapolation period).

This work will explore several issues, including the expansion of standard three-stage Markov models for cancer drugs using underlying *partitioned survival analysis* within a full Bayesian approach, to provide improvements in the modelling, estimation and economic evaluation. The work will be closely linked with the development and improvement of survHE.