Evaluating methods for Lasso selective inference in biomedical research: a comparative simulation study

Abstract

Abstract Background 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. This leads to over-optimistic selection and replicability issues. Methods We compared proposals for selective inference targeting the submodel parameters of the Lasso and its extension, the adaptive Lasso: sample splitting, selective inference conditional on the Lasso selection (SI), and universally valid post-selection inference (PoSI). We studied the properties of the proposed selective confidence intervals available via R software packages using a neutral 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. Results Frequentist properties of selective confidence intervals by the SI method were generally acceptable, but the claimed selective coverage levels were not attained in all scenarios, in particular with the adaptive Lasso. The actual coverage of the extremely conservative PoSI method exceeded the nominal levels, and this method also required the greatest computational effort. Sample splitting achieved acceptable actual selective coverage levels, but the method is inefficient and leads to less accurate point estimates. The choice of inference method had 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. Conclusions Despite violating nominal coverage levels in some scenarios, selective inference conditional on the Lasso selection is our recommended approach for most cases. If simplicity is strongly favoured over efficiency, then sample splitting is an alternative. If only few predictors undergo variable selection (i.e. up to 5) or the avoidance of false positive claims of significance is a concern, then the conservative approach of PoSI may be useful. For the adaptive Lasso, SI should be avoided and only PoSI and sample splitting are recommended. In summary, we find selective inference useful to assess the uncertainties in the importance of individual selected predictors for future applications.

Keywords

• Selective inference
• Penalized regression
• Linear model
• Variable selection
• Simulation study