Selection Bias in Pre-Specified Covariate Models
Vijay D Ivaturi , Andrew C Hooker, Mats O Karlsson
Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden
Objectives: Often covariate parameter relations are chosen a priori such as in the full model approach or the partial stepwise covariate model building (SCM) approach where covariates are investigated for some parameters only. The relations chosen may overlook true relations, which exist between an available covariate and a parameter of the model. The objective of this work was to investigate the risk of bias of parameter estimates and inflated Type I error, when a true covariate relation is ignored. A secondary objective was to explore potential base-model predictors which can be used to predict risk of parameter bias and false positive relations in such situations.
Methods: Sparse and rich data were simulated from PK and PD models with a true covariate parameter relationship. Estimation models where the true effect was ignored and the covariate was included on other parameters were fit to these data. Type 1 error and bias in parameter estimates of covariate relations were assessed for these estimation models where the true covariate relation was ignored. The predictors evaluated for Type I error inflation included: richness of the data, correlation between estimates, shrinkage, magnitude of covariate effects and sample size. These methods were also evaluated on real datasets.
Results: In general when a true effect was ignored, but the covariate was included on another parameter, there was a substantial bias in the estimated covariate relation. There was also an increased Type I error for the estimated covariate parameter relation. No explanatory variables were selected as reliable predictors of this increased false positive risk but in general, sparseness of data and correlation between the false and true thetas correlated positively with risk of bias and false positives. These results were consistent when evaluated on real datasets.
Conclusions: When choosing covariate relations a priori such as in the full model or the partial SCM approach, there is an increased risk of bias on covariate effects or false positives respectively. In case of the full model approach a way to avoid risk of bias could be to always include covariates of interest on all parameters of the model. For the partial SCM, it is relatively easy to extend the scope of models to test after the initial search. In that second search covariates found on some parameters should then be tested on those not explored during the initial partial SCM.
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