Survival Modeling for the Estimation of Transition Probabilities in Model-Based Economic Evaluations in the Absence of Individual Patient Data: A Tutorial

Abstract

Survival modeling techniques are increasingly being used as part of decision modeling for health economic evaluations. As many models are available, it is imperative for interested readers to know about the steps in selecting and using the most suitable ones. The objective of this paper is to propose a tutorial for the application of appropriate survival modeling techniques to estimate transition probabilities, for use in model-based economic evaluations, in the absence of individual patient data (IPD). An illustration of the use of the tutorial is provided based on the final progression-free survival (PFS) analysis of the BOLERO-2 trial in metastatic breast cancer (mBC). An algorithm was adopted from Guyot and colleagues, and was then run in the statistical package R to reconstruct IPD, based on the final PFS analysis of the BOLERO-2 trial. It should be emphasized that the reconstructed IPD represent an approximation of the original data. Afterwards, we fitted parametric models to the reconstructed IPD in the statistical package Stata. Both statistical and graphical tests were conducted to verify the relative and absolute validity of the findings. Finally, the equations for transition probabilities were derived using the general equation for transition probabilities used in model-based economic evaluations, and the parameters were estimated from fitted distributions. The results of the application of the tutorial suggest that the log-logistic model best fits the reconstructed data from the latest published Kaplan-Meier (KM) curves of the BOLERO-2 trial. Results from the regression analyses were confirmed graphically. An equation for transition probabilities was obtained for each arm of the BOLERO-2 trial. In this paper, a tutorial was proposed and used to estimate the transition probabilities for model-based economic evaluation, based on the results of the final PFS analysis of the BOLERO-2 trial in mBC. The results of our study can serve as a basis for any model (Markov) that needs the parameterization of transition probabilities, and only has summary KM plots available.