Covariate Screening Methods

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. 

Alternatively, instead of using the EBE of the parameter of interest as the dependent variable, an estimate of the random effect (t ) can be used as the dependent variable, similar to how partial residuals are used in stepwise linear regression. Early population pharmacokinetic methodology advocated multiple linear regression using either forward, backwards, or stepwise models. A modification of this is to use multiple simple linear models, one for each covariate. For categorical covariates, analysis of variance is used instead. If the p-value for the omnibus F-test or p-value for the T-test is less than some cut-off value, usually 0.05, the covariate is moved forward for further examination. Many reports in the literature use this approach. 

Because of the criticisms against linear models and GAMs there are those within the pharmacokinetic community who advocate a simple examination of the sca- 

It should also be recognized that regression-based methods, whether they are linear models or GAMs, do not take into account whether a covariate is time dependent nor do they reflect the potentially correlated behavior of the parameters. These methods compare the value of a single dependent variable against the value of a single independent variable. If the independent variable varies with time then some summary of the independent variable must be used. For example, the baseline, the median value, or the value at the midpoint of the time interval on which the variable was collected are sometimes used. 

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. 

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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,... 

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 a subsequent study, the DemixC method was appHed to a mixture of D-glucose, L-histidine, L-lysine, serotonin hydrochloride, D-sorbitol as well as to the venom of the walking stick insect Anisomorpha buprestoides, which consists of at least six compounds [84]. The H—H TOCSY spectra of 2048 X 512 points were recorded in a screening setup at 600 MHz with a 1 mm probehead. With the help of databases, the mixture was deconvolved and the venom identified. Thus, automated mixture deconvolution in screening mode using covariance processed H—H TOCSY experiments was found feasible. 

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