Cross Model Validation As A Tool For Population Pharmacokinetic/Pharmacodynamic Covariate Model Building
Jakob Ribbing and E. Niclas Jonsson
Division of Pharmacokinetics and Drug Therapy
One important part of population pharmacokinetic/pharmacodynamic analysis (pop-PK/PD) is the covariate model building, i.e. the identification of patient specific characteristics that accounts for part of the variability in the PK/PD parameters.
Important covariates are usually identified using one or more of three distinct strategies: graphical analysis, scientific plausibility and statistical significance. The latter is accomplished through the log-likelihood ratio (LLR) test of nested models.
Another, appealing, strategy is to include covariates based on their ability to predict data that is not used in the estimation of the coefficients. One way of doing this is through data splitting but an approach that utilizes the available data more efficiently is cross validation.
In the present work we have implemented and tested cross model validation (CMV) as a tool for covariate model building in pop-PK/PD. The algorithm randomly divides the original data into a number of groups, for example 10. For each 9/10ths, a covariate model is built in a stepwise manner, based on the drop in the objective function value (OFV)provided by NONMEM. Covariates are included as long as the model is estimable. In other words, no statistical testing is performed. For each model size (each added parameter), the remaining 1/10ths of the data is predicted and the sum of the 10 predicted OFVs, for each model size, are added (OFVp). The number of covariate parameters supported by the whole dataset is given by the model size with the lowest OFVp. Then, using the whole data set, the final model is developed in a stepwise fashion, again based on the OFV, until the supported model size is reached.
The advantages of the proposed method is that it avoids multiple comparisons based on p-values, uses an intuitively reasonable criteria for model selection and is objective in the sense that it can be automated.