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

by   Michael Kammer, et al.

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.


Selective Confidence Intervals for Martingale Regression Model

In this paper we consider the problem of constructing confidence interva...

Selective inference after variable selection via multiscale bootstrap

A general resampling approach is considered for selective inference prob...

Selective Inference for L_2-Boosting

We review several recently proposed post-selection inference frameworks ...

Selective Inference in Propensity Score Analysis

Selective inference (post-selection inference) is a methodology that has...

Exact Selective Inference with Randomization

We introduce a pivot for exact selective inference with randomization. N...

A Theory of Statistical Inference for Ensuring the Robustness of Scientific Results

Inference is the process of using facts we know to learn about facts we ...

Selective Inference for Sparse Multitask Regression with Applications in Neuroimaging

Multi-task learning is frequently used to model a set of related respons...

Please sign up or login with your details

Forgot password? Click here to reset