"Efron's Rules" for Inference after Imputation and Model Selection

• Activity Number: 565 - Data Science in Statistical Genomics: Challenges and Solutions
• Type: Topic Contributed
• Date/Time: Wednesday, August 2, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Genomics and Genetics
• Author(s): Karen Messer* and Lin Liu and Loki Natarajan
• Companies: UCSD Biostatistics and UCSD Biostatistics and UCSD Biostatistics
• Keywords: model selection ; imputation ; model averaging

Abstract

We address the practical problem of model selection in the presence of imputation for missing data. Our focus is on valid inference, in particular on confidence intervals that incorporate both the imputation mechanism and the model selection mechanism. We investigate commonly used resampling-based approaches - multiple imputation and the bootstrap - and incorporate Efron's 2014 computationally efficient variance estimate for bootstrap-smoothed estimates. We compare the resulting `Efron's rules' estimator to a 'Rubin's rules' estimator based on multiple imputation. These turn out to be versions of frequentist model averaged estimators, and are compared to an un-averaged selection estimator using the framework of Claeskens and Hjort. Simulation and real data examples are drawn from the related literature. Practical recommendations are given, including circumstances where the new Efron's rules estimator is seen to work well.