Heckman imputation models for binary or continuous MNAR outcomes and MAR predictors

Abstract

BackgroundMultiple imputation by chained equations (MICE) requires specifying a suitable conditional imputation model for each incomplete variable and then iteratively imputes the missing values. In the presence of missing not at random (MNAR) outcomes, valid statistical inference often requires joint models for missing observations and their indicators of missingness. In this study, we derived an imputation model for missing binary data with MNAR mechanism from Heckman’s model using a one-step maximum likelihood estimator. We applied this approach to improve a previously developed approach for MNAR continuous outcomes using Heckman’s model and a two-step estimator. These models allow us to use a MICE process and can thus also handle missing at random (MAR) predictors in the same MICE process.MethodsWe simulated 1000 datasets of 500 cases. We generated the following missing data mechanisms on 30% of the outcomes: MAR mechanism, weak MNAR mechanism, and strong MNAR mechanism. We then resimulated the first three cases and added an additional 30% of MAR data on a predictor, resulting in 50% of complete cases. We evaluated and compared the performance of the developed approach to that of a complete case approach and classical Heckman’s model estimates.ResultsWith MNAR outcomes, only methods using Heckman’s model were unbiased, and with a MAR predictor, the developed imputation approach outperformed all the other approaches.ConclusionsIn the presence of MAR predictors, we proposed a simple approach to address MNAR binary or continuous outcomes under a Heckman assumption in a MICE procedure.Electronic supplementary materialThe online version of this article (10.1186/s12874-018-0547-1) contains supplementary material, which is available to authorized users.

Preventing bias from selective non-response in population-based survey studies: findings from a Monte Carlo simulation study

“…One example is the ‘brlrmr’ package for treating MNAR in the outcome of logistic regression models [12]. Another R package, miceMNAR, [13, 14], allows combining selection modeling with multiple imputation (MI) for treating MNAR in continuous and binary outcomes. Other important contributions in recent years are simulation studies performed for better understanding and improvement of criteria for selecting the true missingness model under MNAR [8], and comparison of different imputation methods for different missing mechanisms [15].…”

Multiple Imputation of Binary Multilevel Missing not at Random Data

“…This imputation algorithm extends the work of Galimard et al . (). We have implemented it in a way that the algorithm can be used within the mice() function of the R package mice.…”

“…For this, like Galimard et al . () we use a selection‐model‐based approach. Combined with the binary variable Y to be imputed, this yields a two‐equation system: one equation for the selection process and one equation describing Y .…”

“…Besides these methods, which take into account the multilevel structure of the data, we also evaluate the procedure of Galimard et al . () that handles MNAR by using a selection model approach but is only designed for single‐level data (MNAR Galimard). As a benchmark scenario, we present the results of a complete‐case analysis (CCA), which in the case at hand (only missing values in y ) is also valid under MAR (Von Hippel, ).…”

“…Very recently, Galimard et al . () presented a variant of their model that applies to binary missing not at random data. Their basic idea is to use a bivariate probit model to specify the response probability and the binary outcome of a single‐level model jointly.…”