Estimators based on unconventional likelihoods with nonignorable missing data and its application to a children's mental health study

ABSTRACT

Nonignorable missing data is common in studies where the outcome is relevant to the subject's behaviour. Ibrahim, Lipsitz, and Horton [(2001), ‘Using Auxiliary Data for Parameter Estimation with Non-ignorably Missing Outcomes’, Journal of the Royal Statistical Society: Series C (Applied Statistics), 50, 361–373] fitted a logistic regression for a binary outcome subject to nonignorable missing data, and they proposed to replace the outcome in the mechanism model with an auxiliary variable that is completely observed. They had to correctly specify a model for the auxiliary variable; unfortunately the outcome variable subject to nonignorable missingness is still involved. The correct specification of this model is mysterious. Instead, we propose two unconventional likelihood-based estimation procedures where the nonignorable missingness mechanism model could be completely bypassed. We apply our proposed methods to the children's mental health study and compare their performance with existing methods. The large sample properties of the proposed estimators are rigorously justified, and their finite sample behaviours are examined via comprehensive simulation studies.

KEYWORDS:

• Nonignorable missing data
• missingness mechanism
• unconventional likelihood
• pseudo likelihood
• conditional likelihood
• asymptotic normality

Acknowledgments

The authors would like to thank the editor, the associate editor and two anonymous referees for their constructive comments, which have led to a significantly improved paper. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Jiwei Zhao  http://orcid.org/0000-0002-9298-9412

Additional information

Funding

This work was supported by the National Center for Advancing Translational Sciences of the National Institutes of Health [grant number UL1TR001412].