Evaluating methods for Lasso selective inference in biomedical research by a comparative simulation study
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Variable selection for regression models plays a key role in the analysis of biomedical data. However, inference after selection is not covered by classical statistical frequentist theory which assumes a fixed set of covariates in the model. We review two interpretations of inference after selection: the full model view, in which the parameters of interest are those of the full model on all predictors, and then focus on the submodel view, in which the parameters of interest are those of the selected model only. In the context of L1-penalized regression we compare proposals for submodel inference (selective inference) via confidence intervals available to applied researchers via software packages using a simulation study inspired by real data commonly seen in biomedical studies. Furthermore, we present an exemplary application of these methods to a publicly available dataset to discuss their practical usability. Our findings indicate that the frequentist properties of selective confidence intervals are generally acceptable, but desired coverage levels are not guaranteed in all scenarios except for the most conservative methods. The choice of inference method potentially has a large impact on the resulting interval estimates, thereby necessitating that the user is acutely aware of the goal of inference in order to interpret and communicate the results. Currently available software packages are not yet very user friendly or robust which might affect their use in practice. In summary, we find submodel inference after selection useful for experienced statisticians to assess the importance of individual selected predictors in future applications.
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