A method to correct VPC bias due to non-random dropout via censored data addition, using the MonolixSuite
Monika Twarogowska
Simulations Plus
Objectives:
Non-random dropout is common in clinical studies focusing on tumor growth dynamics. This phenomenon results in an underestimation of the mean tumor size, which then manifests as a bias in the Visual Predictive Check (VPC) plot. In order to recover its diagnostic value, we present in this study a method to correct the VPC bias by adding censored observations after the time of dropout. When plotting the VPC, Monolix handles censored data by sampling simulated BLQ from the distribution conditional on the non-censored data and estimated parameters, which counteracts the effect of non-random dropout on the empirical percentiles.
Methods:
To correct a biased VPC, we add, for each individual, interval censored non-informative observations using the past inter-observation interval. Covariates and treatment are extended according to the last available value for each individual. This modified dataset is then used to generate a corrected VPC, keeping the population parameters as previously estimated.
To assess the efficiency of this method, we simulate a dataset with non-random dropout (e.g. by coupling a proportional time-to-event model), according to a known tumor growth model. In Monolix, we fit this reference model to the simulated data and consequently observe a bias in the VPC. Simultaneously, we also fit other models which are known to not capture the tumor growth data properly. We then apply the proposed method to obtain a modified dataset including added censored observations. For the “true” model, we check that the VPC bias is corrected. On the contrary, for the other “wrong” models, the bias-corrected VPC should still show a misspecification. This routine was implemented using different models, ranging from simple exponential tumor growth to more complex mechanistic models. We also investigate different bounds for the censoring interval, as well as different time intervals between the added observations.
Finally, to evaluate the impact of adding censored observations on the parameter estimation, we perform 100 replicates of Monolix runs using (1) the original dataset and (2) the dataset with added censored data, changing the random number seed between each replicate. We then perform a t-test to compare the means of the estimated parameters in case (1) and (2).
Results:
Adding censored observations using a large interval, e.g. (-∞,∞), allows us to efficiently correct the VPC bias when the “true” model is used. Moreover, when “wrong” models are used, the correction does not erase discrepancies between the model and the data, which are still visible in the VPC. Finally, we find that the parameters estimated with the data including the added censored observations are not statistically different from the parameters estimated with the original data. Consequently, it is possible to directly use the modified dataset for parameter estimation, and not only for VPC generation.
Conclusions:
The proposed method to recover the diagnostic value of a VPC presenting a bias due to non-random dropout is easy to implement and very efficient. An R function based on the MonolixSuite is available to modify the dataset automatically and generate a corrected VPC.