Kernel-based visual hazard comparison (kbVHC): a simulation-free diagnostic for parametric repeated time-to-event models
Sebastiaan C. Goulooze (1), Pyry A. J. Välitalo (1), Elke H. J. Krekels (1), Catherijne A. J. Knibbe (1,2)
(1) Division of Pharmacology, Cluster Systems Pharmacology, Leiden Academic Centre for Drug Research, Leiden, The Netherlands (2) Department of Clinical Pharmacy, St. Antonius Hospital, Nieuwegein, The Netherlands
Objectives: Repeated time-to-event models are the preferred method to characterize the repeated occurrence of clinical events [1]. Commonly used diagnostics for parametric repeated time-to-event models (e.g. Kaplan-Meier VPC) require simulations, which may be difficult to generate in situations with dose titration or informative dropout [2]. Here, we present a novel simulation-free diagnostic tool for parametric hazard models, the kernel-based visual hazard comparison (kbVHC). The kbVHC relies on the visual comparison of the predicted mean hazard rate of a parametric model with a non-parametric kernel estimator of the hazard rate [3,4] with a mismatch between the two suggesting misspecification of the parametric model.
Methods: The degree of smoothing of the kernel estimator is determined by its bandwidth. Here, the local kernel bandwidth is set to the lowest value that results in a bootstrap coefficient of variation of the hazard rate that is equal to or lower than a user-defined CVtarget. Bootstrapping was used to determine the 95% confidence interval of the kernel estimator. The predicted mean hazard of the parametric model was calculated from the individual post-hoc estimates. The kbVHC was evaluated by simulating various scenarios with different number of subjects (50-500), hazard rates, CVtarget values, and hazard models (Weibull, Gompertz, and circadian-varying hazard). The kbVHC was compared with the Kaplan-Meier VPC in terms of its sensitivity to detect hazard model misspecification [5].
Results: The kbVHC was able to distinguish between Weibull and Gompertz hazard models, even when the hazard rate was relatively low (< 2 events per subject), performing comparable to the Kaplan-Meier VPC. Additionally, it was more sensitive than the Kaplan-Meier VPC to detect circadian variation of the hazard rate. Interpretation of the kbVHC depends on the degree of smoothing of the kernel hazard rate. Ranges for appropriate CVtarget values are provided, based on the number of events in the dataset.
Conclusions: The kbVHC has a good sensitivity for model misspecification, even outperforming the existing Kaplan-Meier VPC for circadian-varying hazard models. Because the kbVHC does not require simulations, it can also be used in situations where appropriate simulations are difficult to generate. An additional useful feature of the kernel estimator, is that it can already be generated prior to model development to explore the shape of the hazard rate function.
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