OBJECTIVES:

Piecewise models have been suggested as a flexible alternative to standard parametric models for modeling complex hazard profiles, for example of immune-oncology therapies. However, the selection of cut-point(s) is often a point of contention. Therefore, this case study aimed to compare the accuracy of the long-term survival estimates of piecewise models of various cut-points with those of standard parametric models.

METHODS:

Overall survival Kaplan-Meier (KM) data from the 25.2-month data-cut of KEYNOTE-024 for pembrolizumab were digitized and fitted with six standard parametric models and piecewise models with standard parametric tails. For the piecewise models, 3-, 8- and 14-months were chosen as cut-points by inspecting smoothed hazard, cumulative hazard, and log cumulative hazard plots. From the cut-points onwards, parametric tails were fitted to the remaining KM data and adjoined to the KM curves. The realized life years (LYs) from the KEYNOTE-024 59.9-month data-cut were compared with the estimated LYs from each model over the same time horizon to determine long-term survival estimate accuracy.

RESULTS:

The realized LYs from the KEYNOTE-024 59.9-month data-cut were 2.71. Average mean LYs across the standard parametric models were 2.70. Average mean LYs varied across piecewise models with different cut-points; at 3-, 8- and 14-month cut-points, piecewise models produced average mean LYs of 2.72, 2.68, and 2.82, respectively. Accuracy of piecewise models generally decreased at longer cut-points, with the 14-month cut-point performing worst. The top three models ranked by accuracy were the 8-month cut-point log-normal, standard generalized gamma, and standard log-logistic.

CONCLUSIONS:

Despite being more flexible, the piecewise models in this case study did not on average perform better than standard parametric models in estimating long-term survival, although the 3- and 8-month cut-point models performed similarly to standard parametric models. Reduced piecewise model accuracy for later cut-points likely reflected reduced numbers at risk on which to fit the parametric tails.