Pauline Traynard (1), Geraldine Ayral (1), Jonathan Chauvin (1)
(1) Lixoft, Antony, France
Objectives: Time-to-event data are often analyzed using non-parametric or semi-parametric (e.g Cox models) approaches. These approaches are simple but also have limitations. Parametric approaches offer a powerful alternative, which enables the use of frailty, mixture or even joint PK-TTE or PD-TTE models. They also allow to perform simulations for new treatments, or new populations with different covariate distributions. We illustrate the use of parametric models using the MonolixSuite, on two typical data sets: a TTE data set of survival in lung cancer patients [1], and a PD-TTE data set of serum bilirubin and liver transplant in primary biliary cirrhosis patients [2]. To simplify the testing of several models, a library of typical TTE models has been implemented for the MonolixSuite.
Methods: The developed library of TTE models contains the most common parametric TTE models, i.e exponential, Weibull, log-logistic, uniform, Gompertz, gamma and generalized gamma models, with or without delay and for single or repeated events. The library is used to find appropriate models for two data sets: survival in lung cancer and liver transplant.
Results: We first use the Mlxplore application from the MonolixSuite to perform a sensitivity analysis of the influence of each parameter. A summary is presented to guide the users in their choice of an appropriate model for their data. The lung cancer data set is then stepwise modeled. All models from the library are tested and compared using the likelihood ratio test and a visual assessment of the Visual Predictive Check for time-to-event data implemented in Monolix. The Gompertz model shows the best agreement with the data. Available covariates are then tested using a backward strategy. Sex and the ECOG performance score appear as significant covariates. The model is then used to perform a variety of simulations and predict the survival in cohorts with particular distributions of covariates. The uncertainty of the predicted survival is also assessed with simulation replicates. For the PD-TTE data set on liver transplant, a continuous model is first developed for the serum bilirubin. A joint PD-TTE model is then implemented, in which the bilirubin concentration impacts the hazard of transplantation in a proportional way. The model shows reliable parameter estimation and a good agreement with the data.
Conclusion: The choice of a parametric model for time-to-event data is more complicated than for continuous outcomes because no direct model representation exists. The provided visual summary of the typical survival functions corresponding to typical time-to-event models is a useful guide for modelers. Using this guide and the diagnostic plots provided by Monolix, appropriate parametric models can be found for both experimental data sets. The MonolixSuite and the new TTE library allow an efficient modeling and diagnostic of parametric models for TTE or joint continuous-TTE data. The TTE model library has been made available in the 2018R1 MonolixSuite release.
References:
[1] Therneau and Grambsch (2000). Modeling Survival Data: Extending the Cox Model. Springer, New York.
[2] Mbogning et al. (2015). Journal of Statistical Computation and Simulation, 85(8), 1512-1528.
Reference: PAGE 27 (2018) Abstr 8623 [www.page-meeting.org/?abstract=8623]
Poster: Methodology - Model Evaluation