Statistics and Its Interface

Volume 16 (2023)

Number 4

Fine-tuned sensitivity analysis for non-ignorable missing data mechanism in linear regression models

Pages: 617 – 627

DOI: https://dx.doi.org/10.4310/22-SII748

Authors

Rong Zhu (Medical Research Council Biostatistics Unit, School of Clinical Medicine, University of Cambridge, United Kingdom)

Peng Yin (Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China)

Jian Qing Shi (Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen, China; and National Center for Applied Mathematics, Shenzhen, China)

Abstract

Missing data is a widespread problem in many fields, such as statistical analysis in medical research. The missing data mechanism (MDM) is overly complicated in many cases, and the most complex one is the non-ignorable missingness. In this paper, we analyse the incomplete data bias of maximum likelihood estimates on the inference of linear regression models with non-ignorable missing covariate specifically, where the working model always has a small departure from the true model. The incomplete data bias has been divided into two parts because of two types of uncertainties, one is the misspecified distribution between covariates, the other is the misspecified MDM.We identify the key sensitivity parameters in MDM and further propose generative MDM models, leading to a non-implausible set which quantify a smaller range of possible solutions comparing to the conventional sensitivity analysis and worst-case study. Our analysis focuses the sensitivity of MDM modelling in the missing covariate problems. Numerical examples are presented in both simulation studies and a real data example.

Keywords

bias analysis, model uncertainty, non-ignorable missing data, incomplete data bias, sensitivity analysis

2010 Mathematics Subject Classification

Primary 62Dxx, 62J05. Secondary 62F25.

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Rong Zhu and Jian Qing Shi (corresponding author) acknowledge financial support from the Medical Research Council [grant number: MR/M025152/2].

Peng Yin acknowledges financial support from the National Natural Science Foundation of China (NNSFC) [grant number: 11801542].

Received 24 August 2021

Accepted 13 July 2022

Published 14 April 2023