Cost-effectiveness Analysis in R Using a Multi-state Modeling Survival Analysis Framework: A Tutorial

Abstract

This tutorial provides a step-by-step guide to performing cost-effectiveness analysis using a multi-state modeling approach. Alongside the tutorial, we provide easy-to-use functions in the statistics package R. We argue that this multi-state modeling approach using a package such as R has advantages over approaches where models are built in a spreadsheet package. In particular, using a syntax-based approach means there is a written record of what was done and the calculations are transparent. Reproducing the analysis is straightforward as the syntax just needs to be run again. The approach can be thought of as an alternative way to build a Markov decision-analytic model, which also has the option to use a state-arrival extended approach. In the state-arrival extended multi-state model, a covariate that represents patients' history is included, allowing the Markov property to be tested. We illustrate the building of multi-state survival models, making predictions from the models and assessing fits. We then proceed to perform a cost-effectiveness analysis, including deterministic and probabilistic sensitivity analyses. Finally, we show how to create 2 common methods of visualizing the results-namely, cost-effectiveness planes and cost-effectiveness acceptability curves. The analysis is implemented entirely within R. It is based on adaptions to functions in the existing R package mstate to accommodate parametric multi-state modeling that facilitates extrapolation of survival curves.

Keywords: Markov models; cost-effectiveness analysis; probabilistic sensitivity analysis; survival analysis.

Figure 1

Algorithm for health economic modeling using a multi-state modeling framework.

Figure 2

Transition diagram for multi-state model showing the 3 transitions: 1) progression-free to progression, 2) progression-free to death, and 3) progression to death.

Figure 3

Log-log plots for each transition. FC, fludarabine and cyclophosphamide; RFC, rituximab, fludarabine, and cyclophosphamide.

Figure 4

Cumulative hazard plots for each transition. FC, fludarabine and cyclophosphamide; RFC, rituximab, fludarabine, and cyclophosphamide.

Figure 5

Observed and predicted proportions for progression → death: trial observation period (RFC treatment only). KM, Kaplan-Meier; RFC, rituximab, fludarabine, and cyclophosphamide.

Figure 6

Observed and predicted proportions for progression → death: extrapolation to 15 years (RFC treatment only). KM, Kaplan-Meier; RFC, rituximab, fludarabine, and cyclophosphamide.

Figure 7

Cost-effectiveness plane. QALY, quality-adjusted life year; WTP, willingness to pay.

Figure 8

Cost-effectiveness acceptability curve.