The Kaplan-Meier Mean Covariate plot (KMMC): a new diagnostic for covariates in time-to-event models.
Andrew C. Hooker and Mats O. Karlsson
Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden
Objectives: When building time-to-event (TTE) models it is often difficult to screen for covariates (or predictors) and it can be especially challenging to understand, and illustrate, how covariates should be included in the model. For example, to understand the influence of a continuous covariate, one might stratify the covariate and plot multiple Kaplan-Meier visual predictive check (VPC) plots along the various strata. Time-varying covariates represent another challenge that is not well handled by present graphical diagnostics. In this work we present a new graphical tool that can overcome these problems; the Kaplan-Meier Mean Covariate (KMMC) plot.
Methods: The plot is created by computing the mean (or any other function) of a covariate for all of the individuals still in a study at every inflection point of a Kaplan-Meier survival curve. This "running" mean of a covariate that is influential on survival would be expected to increase or decrease as a study progresses. Simulating from a model numerous times will give numerous simulated KMMC curves, and a VPC of the KMMC can thus be created, allowing for comparison between model predictions and the true data. The plot is easily created using the latest versions of PsN [1] and Xpose [2].
Results: KMMC plots for both before and after a covariate is included in a TTE model are shown to identify the covariate effect and show when a model adequately describes that effect.
Conclusions: From a base TTE model all covariates can be screened right away using the KMMC plot. The plot works well for continuous as well as categorical covariates and can easily handle both time-constant and time-varying covariates. The KMMC plot can filter out or stratify individuals that are censored in the study so that covariates influencing both censoring and event can be visualized.
Acknowledgement: This work was part of the DDMoRe project.
References:
[1] Perl Speaks NONMEM (PsN), http://www.psn.sf.net/.
[2] Xpose, http://www.xpose.sf.net/.
