Covariate screening models

Covariate screening methods are used when there are a large number of covariates, such that evaluating every possible combination in a model is prohibitive. With this methodology, EBEs of the random effects are treated as data and then exploratory methods are used to assess the relationship between the random effects and the covariate of interest. In other words, each individual s pharmacokinetic parameter, clearance for example, is estimated and treated as a being without measurement error. These Bayes estimates are then compared against subject-specific covariates for a relationship using either manual or automated methods. 

A new type of covariate screening method is to use partially linear mixed effects models (Bonate, 2005). Briefly, the time component in a structural model is modeled using a penalized spline basis function with knots at usually equally spaced time intervals. Under this approach, the knots are treated as random effects and linear mixed effects models can be used to find the optimal smoothing parameter. Further, covariates can be introduced into the model to improve the goodness of fit. The LRT between a full and reduced model with and without the covariate of interest can be used to test for the inclusion of a covariate in a model. The advantage of this method is that the exact structural model (i.e., a 1-compartment or 2-compartment model with absorption) does not have to be determined and it is fast and efficient at covariate identification. 

Wu and Wu (2002) compared three different covariate screening methods nonlinear least-squares based method (NL-based), EBE-based method, and direct covariate screening by inclusion in the model and LRT. In the NL-based method, the same model is fit to each individual using nonlinear regression and the parameter estimates for that subject are obtained. Correlation tests or regression-based models between the individual parameter estimates and individual covariates may then be used to determine whether a significant relationship exists between the variables. This method is difficult to implement in practice because it requires rich data for each subject. For Phase 3 studies where sparse pharmacokinetic data are often collected, this method is impractical since many subjects will have insufficient data to support even simple pharmacokinetic... 

In summary, the choice of covariate screening method is capricious. Modelers mostly use what they are comfortable with and may not even compare the results from different screening methods. The most reliable method would be screening covariates directly in NONMEM, but this method is also the slowest. Further,... 

The next covariate screening approach would be to use a regression-based method and take a more rigorous statistical approach to the problem. Using the generalized additive model (GAM) procedure in SAS, a LOESS smooth was applied to the continuous covariates wherein the procedure was allowed to identify the optimal smoothing parameter for each covariate tested. Two dependent variables were examined t, and the EBE for CL. To avoid possible skewness in the residuals,... 

Objective The objective of this analysis was to develop a population pharmacokinetic model for NS2330 and its major metabolite Ml, based on data from a 14-week proof of concept study in Alzheimer s disease patients, including a screening for covariates that might influence the pharmacokinetic characteristics of the drug and/or its metabolite. Subsequently, several simulations should be performed to assess the influence of the covariates on the plasma concentration-time profiles of NS2330 and its metabolite. 

One may think of an iterative model for the preclinical discovery screening cycle. A large number of compounds are to be mined for compounds that are active for example, that bind to a particular target. The compounds may come from different sources such as vendor catalogues, corporate collections, or combinatorial chemistry projects. In fact, the compounds need only to exist in a virtual sense, because in silico predictions in the form of a model can be made in a virtual screen (Section 8) which can then be used to decide which compounds should be physically made and tested. A mapping from the structure space of compounds to the descriptor space or property space provides covariates or explanatory variables that can be used to build predictive models. These models can help in the selection process, where a subset of available molecules is chosen for the biological screen. The experimental results of the biological screen (actives and inactives, or numeric potency values) are then used to learn more about the structure-activity relationship (SAR) which leads to new models and a new selection of compounds as the cycle renews. 

K. G. Kowalski and M. M. Hutmacher, Efficient screening of covariates in population models using Wald s approximation to the likelihood ratio test. J Clin Pharmacol 28 253-275 (2001). 

With the base model fit in hand, any of a number of different strategies may be employed to evaluate the influence of the exposure variables and covariates on the response. As with other population PK (and PK/PD or PD) analyses, many different techniques and processes have been advocated for efficiently and effectively screening and selecting covariates for inclusion in a model (17-19). For the purposes of this chapter, the model including the effect of exposure (AUC) on the response is illustrated, as is the final model, including other covariate effects (presumably derived following the application of some technique to screen all potential covariates). 

FIGURE 39.2 Relationship between BSA and total clearance demonstrated by graphical presentation from post hoc estimates of a base model without size. Note that BSA was not a significant covariate in the univariate screen when included in isolation size effects on parameters despite the obvious relationship between BSA and clearance. 

Step 4 may be redundant if the covariates were tested directly in the nonlinear mixed effects model. If the covariates were screened using some external method, e.g., regression models, then these covariates are included in the model in a forward stepwise manner. Improvement in the goodness of fit in the model is tested using either the LRT or T-test. In addition, reduction in parameter variability is expected as well. Further discussion of this topic will be made later in the chapter. 

Wahlby, Jonsson, and Karlsson (2002) compared covariate identification by GAM screening to screening of covariates directly within NONMEM (NM-NM method). Within her analysis she examined two different GAM relationships one between the EBE of the parameter itself and the covariate of interest (GAM(EBE)-NM method) and one between an estimate of the random effect (r ) and the covariate of interest (GAM(t )-NM method). For simulated data sets, the GAM(t )-NM method and NM-NM method gave identical covariate models, although the GAM(EBE) method was not as sensitive at covariate detection as the GAM(t ) method. When some parameters were fixed during fitting and not allowed to optimize within the NM-NM procedure, the sensitivity at covariate detection was diminished for that method. 

In practice, using a normal chemistry panel and complete blood count it is not unusual to have 30 potential covariates, everything from sodium ion concentration to alkaline phosphatase activity. Early in PopPK analyses it was not unusual to screen every single covariate for their impact on the model. But a model might end up having a volume of distribution as a function of chloride ion concentration or clearance that is a function of glucose concentration. Physiologically, these covariates are nonsensical. Ideally at the end of model... 

Kowalski, K.G. Screening covariate models using Wald s approximation An evaluation of the WAM algorithm on several data sets. Presented at the 9th Annual Midwest User s Forum Population Data Analysis (MUFPADA), 2001. 

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