Introduction

As discussed in Chapter 8, ‘good decision analyses depend on both the veracity of the decision model and the validity of the individual data elements.’ The validity of each individual data element relies on the comprehensiveness of the literature search for the best and most appropriate study or studies, criteria for selecting the source studies, the design of the study or studies, and methods for synthesizing the data from multiple sources. Nonetheless, Sir Michael David Rawlins avers that ‘Decision makers have to incorporate judgements, as part of their appraisal of the evidence, in reaching their conclusions. Such judgements relate to the extent to which each of the components of the evidence base is “fit for purpose.” Is it reliable?’(1) Because the integration of a multitude of these ‘best available’ data elements forms the basis for model results, some individuals refer to decision analyses as black boxes, so this last question applies particularly to the overall model predictions. Consequently, assessing model validity becomes paramount. However, prior to assessing model validity, model construction requires attention to parameter estimation and model calibration. This chapter focuses on parameter estimation, calibration, and validation in the context of Markov and, more generally, state-transition models (Chapter 10) in which recurrent events may occur over an extended period of time. The process of parameter estimation, calibration, and validation is iterative: it involves both adjustment of the data to fit the model and adjustment of the model to fit the data.

Parameter estimation

Survival analysis involves determining the probability that an event such as death or disease progression will occur over time. The events modeled in survival analysis are called ‘failure’ events, because once they occur, they cannot occur again. ‘Survival’ is the absence of the failure event. The failure event may be death, or it may be death combined with a non-fatal outcome such as developing cancer or having a heart attack, in which case the absence of the event is referred to as event-free survival. Commonly used methods for survival analysis include life-table analysis, Kaplan–Meier product limit estimates, and Cox proportional hazards models. A survival curve plots the probability of being alive over time (Figure 11.1).