OBJECTIVES

: Estimates of mean survival time are required for cost effectiveness analysis (CEA) of oncology treatments. NICE DSU-TSD-14 guidelines recommend six parametric models for extrapolating mean survival time from trial data: Exponential, Weibull, Gompertz, Log-logistic, Lognormal and Generalized Gamma. If none of these models fit the data well, the uncertainty in the extrapolated means and, hence, CEA increases. In these cases flexible modeling approaches are needed. We postulated that difficult-to-fit survival data often arises from having a sample that represents a mixture of distributions, such as a mixture of rapidly progressing patients and patients with durable responses.

A finite mixture model (FMM) is a flexible approach that may produce better fit than the recommend models. However, fitting FMMs can be computationally difficult and there is a tendency for convergence to local maximum likelihood estimates (MLEs). So, we introduce a novel algorithm to address these weaknesses of FMM.

METHODS

: The EM-algorithm used to fit FMM is initiated at a random starting point depending on the software. To ensure Global MLEs are obtained, many starting points need to be explored. Our algorithm first estimates the model parameters using quantile regression and these estimates provide a data-driven starting point for the EM algorithm, increasing the likelihood of converging to global MLEs. We compared the fit of a two-component Weibull FMM to the commonly used parametric models using data from an immuno-oncology melanoma trial that had “heavy-tailed” and difficult-to-fit KM-curves.

RESULTS

A two-component Weibull FMM fit better than the best fitting of the six recommended models (AIC 319 vs 574, respectively). Further, the proposed algorithm substantially improved the likelihood of converging to global MLEs.

CONCLUSIONS

: The FMM algorithm produces better fit and better estimates of mean survival times than standard parametric approaches; reducing uncertainty in CEA that depend on these estimates.