A multiple imputation approach for MNAR mechanisms compatible with Heckman's model
Abstract
Standard implementations of multiple imputation (MI) approaches provide unbiased inferences based on an assumption of underlying missing at random (MAR) mechanisms. However, in the presence of missing data generated by missing not at random (MNAR) mechanisms, MI is not satisfactory. Originating in an econometric statistical context, Heckman's model, also called the sample selection method, deals with selected samples using two joined linear equations, termed the selection equation and the outcome equation. It has been successfully applied to MNAR outcomes. Nevertheless, such a method only addresses missing outcomes, and this is a strong limitation in clinical epidemiology settings, where covariates are also often missing.
We propose to extend the validity of MI to some MNAR mechanisms through the use of the Heckman's model as imputation model and a two‐step estimation process. This approach will provide a solution that can be used in an MI by chained equation framework to impute missing (either outcomes or covariates) data resulting either from a MAR or an MNAR mechanism when the MNAR mechanism is compatible with a Heckman's model. The approach is illustrated on a real dataset from a randomised trial in patients with seasonal influenza. Copyright © 2016 John Wiley & Sons, Ltd.
Citing Literature
Number of times cited according to CrossRef: 21
- Angelina Hammon, Sabine Zinn, Multiple imputation of binary multilevel missing not at random data, Journal of the Royal Statistical Society: Series C (Applied Statistics), 10.1111/rssc.12401, 69, 3, (547-564), (2020).
- Manuel Gomes, Michael G. Kenward, Richard Grieve, James Carpenter, Estimating treatment effects under untestable assumptions with nonignorable missing data, Statistics in Medicine, 10.1002/sim.8504, 39, 11, (1658-1674), (2020).
- Chiu‐Hsieh Hsu, Yulei He, Chengcheng Hu, Wei Zhou, A multiple imputation‐based sensitivity analysis approach for data subject to missing not at random, Statistics in Medicine, 10.1002/sim.8691, 39, 26, (3756-3771), (2020).
- Lihan Chen, Victoria Savalei, Mijke Rhemtulla, Two-stage maximum likelihood approach for item-level missing data in regression, Behavior Research Methods, 10.3758/s13428-020-01355-x, (2020).
- Kristin Gustavson, Espen Røysamb, Ingrid Borren, Preventing bias from selective non-response in population-based survey studies: findings from a Monte Carlo simulation study, BMC Medical Research Methodology, 10.1186/s12874-019-0757-1, 19, 1, (2019).
- Gustavo J. Canavire-Bacarreza, Alexander L. Lundberg, Alejandra Montoya-Agudelo, Survey Evidence on Black Market Liquor in Colombia, The Econometrics of Complex Survey Data, 10.1108/S0731-905320190000039016, (287-314), (2019).
- Xi Yang, Yeo Jin Kim, Farzaneh Khoshnevisan, Yuan Zhang, Min Chi, undefined, 2019 IEEE International Conference on Healthcare Informatics (ICHI), 10.1109/ICHI.2019.8904824, (1-3), (2019).
- Jamie M. Zoellner, Wen You, Jennie L. Hill, Donna-Jean P. Brock, Maryam Yuhas, Ramine C. Alexander, Bryan Price, Paul A. Estabrooks, A comparative effectiveness trial of two family-based childhood obesity treatment programs in a medically underserved region: Rationale, design & methods, Contemporary Clinical Trials, 10.1016/j.cct.2019.06.015, 84, (105801), (2019).
- Paulina Pankowska, Bart F M Bakker, Daniel L Oberski, Dimitris Pavlopoulos, How Linkage Error Affects Hidden Markov Model Estimates: A Sensitivity Analysis, Journal of Survey Statistics and Methodology, 10.1093/jssam/smz011, (2019).
- Stephanie Nicolian, Thibault Butel, Laetitia Gambotti, Manon Durand, Antoine Filipovic-Pierucci, Alain Mallet, Mamadou Kone, Isabelle Durand-Zaleski, Marc Dommergues, Cost-effectiveness of acupuncture versus standard care for pelvic and low back pain in pregnancy: A randomized controlled trial, PLOS ONE, 10.1371/journal.pone.0214195, 14, 4, (e0214195), (2019).
- Rachael A Hughes, Jon Heron, Jonathan A C Sterne, Kate Tilling, Accounting for missing data in statistical analyses: multiple imputation is not always the answer, International Journal of Epidemiology, 10.1093/ije/dyz032, (2019).
- Matthew Franklin, James Lomas, Simon Walker, Tracey Young, An Educational Review About Using Cost Data for the Purpose of Cost-Effectiveness Analysis, PharmacoEconomics, 10.1007/s40273-019-00771-y, (2019).
- Joost R. van Ginkel, Marielle Linting, Ralph C. A. Rippe, Anja van der Voort, Rebutting Existing Misconceptions About Multiple Imputation as a Method for Handling Missing Data, Journal of Personality Assessment, 10.1080/00223891.2018.1530680, (1-12), (2019).
- Manuel Gomes, Rosalba Radice, Jose Camarena Brenes, Giampiero Marra, Copula selection models for non‐Gaussian outcomes that are missing not at random, Statistics in Medicine, 10.1002/sim.7988, 38, 3, (480-496), (2018).
- Jacques-Emmanuel Galimard, Sylvie Chevret, Emmanuel Curis, Matthieu Resche-Rigon, Heckman imputation models for binary or continuous MNAR outcomes and MAR predictors, BMC Medical Research Methodology, 10.1186/s12874-018-0547-1, 18, 1, (2018).
- Sabine Zinn, Timo Gnambs, Modeling competence development in the presence of selection bias, Behavior Research Methods, 10.3758/s13428-018-1021-z, 50, 6, (2426-2441), (2018).
- Celeste Combrinck, Vanessa Scherman, David Maree, Sarah Howie, Multiple Imputation for Dichotomous MNAR Items Using Recursive Structural Equation Modeling With Rasch Measures as Predictors, SAGE Open, 10.1177/2158244018757584, 8, 1, (215824401875758), (2018).
- Dee D. Cetin-Berber, Walter L. Leite, A Comparison of One-Step and Three-Step Approaches for Including Covariates in the Shared Parameter Growth Mixture Model, Structural Equation Modeling: A Multidisciplinary Journal, 10.1080/10705511.2018.1428806, 25, 4, (588-599), (2018).
- Tierra D. Burrell, Kristin M. Voegtline, Kamila B. Mistry, An Association Between Maternal Intimate Partner Physical Violence and a Loaded Firearm in the Home, Journal of Interpersonal Violence, 10.1177/0886260518786503, (088626051878650), (2018).
- Jongho Im, Soeun Kim, Multiple imputation for nonignorable missing data, Journal of the Korean Statistical Society, 10.1016/j.jkss.2017.05.001, 46, 4, (583-592), (2017).
- Dale G. Blevins, Uptake, Translocation, and Function of Essential Mineral Elements in Crop Plants, Physiology and Determination of Crop Yield, undefined, (259-275), (1994).
