Survival Models in Health Economic Evaluations: Balancing Fit and Parsimony to Improve Prediction

Abstract

Health economic decision models compare costs and health effects of different interventions over the long term and usually incorporate survival data. Since survival is often extrapolated beyond the range of the data, inaccurate model specification can result in very different policy decisions. However, in this area, flexible survival models are rarely considered, and model uncertainty is rarely accounted for. In this article, various survival distributions are applied in a decision model for oral cancer screening. Flexible parametric models are compared with Bayesian semiparametric models, in which the baseline hazard can be made arbitrarily complex while still enabling survival to be extrapolated. A fully Bayesian framework is used for all models so that uncertainties can be easily incorporated in estimates of long-term costs and effects. The fit and predictive ability of both parametric and semiparametric models are compared using the deviance information criterion in order to account for model uncertainty in the cost-effectiveness analysis. Under the Bayesian semiparametric models, some smoothing of the hazard function is required to obtain adequate predictive ability and avoid sensitivity to the choice of prior. We determine that one flexible parametric survival model fits substantially better than the others considered in the oral cancer example.

Survival Analysis for Economic Evaluations Alongside Clinical Trials—Extrapolation with Patient-Level Data

“…If standard models appear unsuitable, the use of more flexible parametric models (such as the generalized gamma and generalized F models), piecewise modeling, and other novel survival modeling methods such as those demonstrated by Royston and Parmar 20 and Jackson and others 19 should be considered. The fit of alternative models should be assessed systematically, including consideration of the fit to the observed data (internal validity) and the plausibility The model selection process algorithm presents a step-by-step process through which appropriate survival models can be identified.…”

Weibull regression with Bayesian variable selection to identify prognostic tumour markers of breast cancer survival

“…When q = 0 the PDF is: $$f(t)=\frac{1}{\sqrt{2\pi }\sigma t}\mathit{\text{exp}}\left\{-\frac{1}{2{\sigma }^2}{\left(\mathit{\text{log}}\left(t\right)-\mu \right)}^2\right\}$$ When q = 1, the Generalised gamma reduces to the Weibull with k = 1/ σ and λ = exp (− µ ). For a more detailed description of the Generalized gamma and its relationship with other survival models, we recommend referring to Cox et al58 and Jackson et al59 To capture associations between predictors and outcome, the parameter µ may be substituted for the standard linear predictor. Therefore, to induce associations between the covariates and outcome in the simulated data, we drew survival times from a Generalised gamma distribution with $$\mu =\alpha +\mathit{\beta }\mathit{\text{X}}$$ where the covariate matrix X is that of the real data from the first imputation chain, and β is a vector of 119 tumour marker effects on survival.…”

Estimating Lifetime Costs of Social Care: A Bayesian Approach Using Linked Administrative Datasets from Three Geographical Areas

“…We preferred an alternative approach described by Jackson et al (2010a), which estimates the probability that each model has the lowest DIC of all the available models on replicate datasets. These probabilities were determined using a Bayesian bootstrap algorithm (Jackson et al, 2010b). This algorithm avoids some of the computational expense associated with the classical bootstrap, in which the data would be resampled and the models refitted.…”