A Bayesian Framework for Patient-Level Partitioned Survival Cost-Utility Analysis

Abstract

Patient-level health economic data collected alongside clinical trials are an important component of the process of technology appraisal. For end-of-life treatments, the modeling of cost-effectiveness data may involve some form of partitioned survival analysis, in which measures of quality of life and survival for pre- and postprogression periods are combined to generate aggregate measures of clinical benefits (e.g., quality-adjusted survival). In addition, resource use data are often collected and costs are calculated for each type of health service (e.g., treatment, hospital, or adverse events costs). A critical problem in these analyses is that effectiveness and cost data present some complexities, such as nonnormality, spikes, and missingness, which should be addressed using appropriate methods to avoid biased results. This article proposes a general Bayesian framework that takes into account the complexities of trial-based partitioned survival cost-utility data to provide more adequate evidence for policy makers. Our approach is motivated by, and applied to, a working example based on data from a trial assessing the cost-effectiveness of a new treatment for patients with advanced non-small-cell lung cancer.[Box: see text].

Keywords: Bayesian statistics; STAN; economic evaluations; hurdle models; missing data; partitioned survival cost-utility analysis.

Figure 1

Joint distribution $p(\mathit{e},\mathit{c})$, expressed in terms of a marginal distribution for the effectiveness variables $\mathit{e}=(e^{\mathrm{PFS}},e^{\mathrm{PPS}})$ and a conditional distribution for the cost variables $\mathit{c}=(c^1,\dots ,c^K)$ given $\mathit{e}$, respectively, indicated with a solid red and blue box. The parameters indexing the corresponding distributions or modules are denoted with different Greek letters, whereas $i$ and $t$ denote the individual and treatment indices. The notation ${\mathbf{\beta }}_{·t}^1$ and ${\mathbf{\beta }}_{·t}^K$ indicates the set of the conditional mean cost regression parameters for $c^1$ and $c^K$, excluding the intercepts. The solid black and colored arrows show the dependence relationships between the parameters within and between different modules, respectively. The 3 large dots indicate the inclusion in the framework of the conditional distributions for the cost variables $c^k|\mathit{e},c^k,\dots ,c^{k-1}$, for $2<k<K$, omitted for clarity from the figure, whereas the small dots enclosed in the square brackets indicate the potential inclusion of other covariates at the mean level in each module.

Figure 2

Histograms of the distributions of the pre- and postprogression quality-adjusted survival (QAS) data, in the control (a, b) and intervention (c, d) group. About 50% of the individuals in both groups are associated with zero postprogression survival QAS (highest bars in panels b and d), while no actual zero is observed for progression-free survival QAS, which mainly lies between $[0.002,0.2]$ (highest bars in panels a and c).

Figure 3

Histograms of the distributions of the 3 cost components (drug, hospital, and adverse events) in the control (a–c) and intervention (d–f) groups (all costs are expressed in pounds).

Figure 4

Posterior means (squares), 50% (thick lines) and 95% (thin lines) highest posterior density credible intervals for the marginal means of pre- and postprogression quality-adjusted survival (a) and for the marginal means of the drug, hospital, and adverse events cost (b) in the control (red) and the intervention (blue) group in the TOPICAL trial.

Figure 5

(a) Cost-effectiveness plane and (b) cost-effectiveness acceptability curve (CEAC) graphs associated with the 2 interventions in the TOPICAL trial. In the CEP, the value of the incremental cost-effectiveness ratio is reported (darker green dot), while the portion of the plane on the right-hand side of the straight line passing through the origin (evaluated at k = £55,000) denotes the sustainability area; in the CEAC, the probability of cost-effectiveness is shown for willingness-to-pay threshold values up to £200,000.