Model selection and model averaging for analysis of truncated and censored data with measurement error

Li-Pang Chen,Grace Y Yi

doi:10.1214/20-ejs1762

Abstract

Model selection plays a critical role in statistical inference and a large literature has been devoted to this topic. Despite extensive research attention on model selection, research gaps still remain. An important but relatively unexplored problem concerns truncated and censored data with measurement error. Although analysis of left-truncated and right-censored (LTRC) data has received extensive interests in survival analysis, there has been no research on model selection for LTRC data with measurement error. In this paper, we take up this important problem and develop inferential procedures to handle model selection for LTRC data with measurement error in covariates. Our development employs the local model misspecification framework ([6]; [10]) and emphasizes the use of the focus information criterion (FIC). We develop valid estimators using the model averaging scheme and establish theoretical results to justify the validity of our methods. Numerical studies are conducted to assess the performance of the proposed methods.

Highlights

Model selection plays an important role in statistical inference, and various model selection criteria have been proposed, including the Akaike information criterion (AIC), Bayesian information criterion (BIC), and cross validation
We develop estimation methods using the focus information criterion (FIC) criterion to handle such data
The development here focuses on the case with continuous covariates subject to measurement error

Summary

Introduction

Model selection plays an important role in statistical inference, and various model selection criteria have been proposed, including the Akaike information criterion (AIC), Bayesian information criterion (BIC), and cross validation. Traditional statistical analysis often first builds the model by selecting important variables and based on the model, carries out statistical inferences This procedure, as pointed out by [7] and [8], among others, ignores the uncertainty induced from the variable selection process, producing estimators with invalid characterization of the associated variability. To mitigate this issue, researchers came up with the model averaging strategy based on averaging a set of candidate models with suitable weights attached and producing a compromise estimator of the model parameter . Detailed discussions can be found in [7]

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Conclusion