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Copula selection models for non‐Gaussian outcomes that are missing not at random

Gomes, M; Radice, R; Brenes, JC; Marra, G; (2018) Copula selection models for non‐Gaussian outcomes that are missing not at random. Statistics in Medicine 10.1002/sim.7988. (In press). Green open access

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Abstract

Missing not at random (MNAR) data pose key challenges for statistical inference because the substantive model of interest is typically not identifiable without imposing further (eg, distributional) assumptions. Selection models have been routinely used for handling MNAR by jointly modeling the outcome and selection variables and typically assuming that these follow a bivariate normal distribution. Recent studies have advocated parametric selection approaches, for example, estimated by multiple imputation and maximum likelihood, that are more robust to departures from the normality assumption compared with those assuming that nonresponse and outcome are jointly normally distributed. However, the proposed methods have been mostly restricted to a specific joint distribution (eg, bivariate t‐distribution). This paper discusses a flexible copula‐based selection approach (which accommodates a wide range of non‐Gaussian outcome distributions and offers great flexibility in the choice of functional form specifications for both the outcome and selection equations) and proposes a flexible imputation procedure that generates plausible imputed values from the copula selection model. A simulation study characterizes the relative performance of the copula model compared with the most commonly used selection models for estimating average treatment effects with MNAR data. We illustrate the methods in the REFLUX study, which evaluates the effect of laparoscopic surgery on long‐term quality of life in patients with reflux disease. We provide software code for implementing the proposed copula framework using the R package GJRM.

Type: Article
Title: Copula selection models for non‐Gaussian outcomes that are missing not at random
Open access status: An open access version is available from UCL Discovery
DOI: 10.1002/sim.7988
Publisher version: https://doi.org/10.1002/sim.7988
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: copula, missing not at random, multiple imputation, non-Gaussian outcomes, selection model, simultaneous equation modeling
UCL classification: UCL
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Population Health Sciences > Institute of Epidemiology and Health
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Population Health Sciences > Institute of Epidemiology and Health > Applied Health Research
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10059067
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