A multiple imputation approach for MNAR mechanisms compatible with Heckman's model

Galimard, Jacques‐Emmanuel; Chevret, Sylvie; Protopopescu, Camélia; Resche-Rigon, Matthieu

doi:10.1002/sim.6902

Cited by 47 publications

(53 citation statements)

References 40 publications

(81 reference statements)

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“…In the presence of missing data on more than one variable (including the outcome), multiple imputation (MI) appears to be one of the most flexible and easiest method to apply due to the numerous types of variables handled and the extensive development of statistical packages dedicated to its implementation [17]. Galimard et al [18] previously developed an approach based on a conditional imputation model for an MNAR mechanism using a Heckman’s model and a two-step estimator to impute MNAR missing continuous outcomes. This approach allows imputing MAR missing covariates and MNAR missing outcomes within a multiple imputation by chained equations (MICE) procedure [18].…”

Section: Introductionmentioning

confidence: 99%

“…Galimard et al [18] previously developed an approach based on a conditional imputation model for an MNAR mechanism using a Heckman’s model and a two-step estimator to impute MNAR missing continuous outcomes. This approach allows imputing MAR missing covariates and MNAR missing outcomes within a multiple imputation by chained equations (MICE) procedure [18]. MICE specifies a suitable conditional imputation model for each incomplete variable and iteratively imputes the missing values until convergence.…”

Section: Introductionmentioning

confidence: 99%

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

Galimard

Chevret

Curis

et al. 2018

BMC Med Res Methodol

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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.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Galimard

Chevret

Curis

et al. 2018

BMC Med Res Methodol

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“…In PubMed, 16 studies in total have been found using this model, and 4 of these have been used for estimating HIV prevalence. Galimard et al (2016) has used Heckman's model in a randomise controlled clinical trial on seasonal influenza patients as an imputation method. 9 McGovern et al (2015) and Clark and Houle (2014) have used Heckman's model to estimate HIV prevalence and they have stated that this model gives more consistent estimations for HIV prevalence.…”

Section: Discussionmentioning

confidence: 99%

“…Galimard et al (2016) has used Heckman's model in a randomise controlled clinical trial on seasonal influenza patients as an imputation method. 9 McGovern et al (2015) and Clark and Houle (2014) have used Heckman's model to estimate HIV prevalence and they have stated that this model gives more consistent estimations for HIV prevalence. 5,14 DeMaris (2014) in his study, to consider also the effect of unmeasured confounding, has examined the association between being married and subjective well-being with Heckman's model.…”

Section: Discussionmentioning

confidence: 99%

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Usage of Heckman Sample Selection Model in Health Studies: An Application of Prostate Cancer Patients

Pasin¹,

Ankaralı²,

Yeşilyurt³

2017

Turkiye Klinikleri J Med Sci

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A AB BS ST TR RA AC CT T O Ob bj je ec ct ti iv ve e: : The objective of this study is to introduce theoretical characteristics of Heckman sample selection regression model,to clarify when it is required to be used and to show its usage in health area. M Ma at te er ri ia al l a an nd d M Me et th ho od ds s: : Heckman selection model, which is an appropriate tool for addressing the sample selection bias, was used for determining the risk factors of Gleason score for three datasets which have 2000 observations obtained from simulation study. The data was about the prostate cancer patients. In the data, there were benign tumor structures or stage 1 tumors in the study besides malign tumors but Gleason score was not calculated when tumor is benign. So sample selection bias is a matter for nonresponse Gleason score answers in our data. Also the model was performed for the datasets that have 0.30; 0.50 and 0.70 of censored proportion (nonresponse Gleason score) individual number by considering actual structures between variables with the help of simulation. R Re es su ul lt ts s: : There was no significant relationship between Gleason score and smoking, family history. But we found that age, PSA(prostate specific antigen) and weight variables have significant relationship with Gleason score (p<0.001). Adjusted standard error value was the highest in dataset with 0.50 censored proportion, and the lowest in data set with highest censor proportion (0.70). Among models the lowest log likelihood value has been determined in model with 0.50 censor proportion. C Co on nc cl lu us si io on n: : When there is sample selection bias on dependent variable, Heckman sample selection regression model can be suggested. In addition, researchers can have more accurate results by increasing the use of these models in health sciences. K Ke ey yw wo or rd ds s: : Models, statistical; neoplasm grading; prostatic neoplasms; selection bias Ö ÖZ ZE ET T A Am ma aç ç: : Bu çalışmanın amacı, Heckman seçim regresyon modelinin teorik özelliklerini tanıt-mak, hangi durumlarda kullanılması gerektiğini ve sağlık alanında kullanımını göstermektir. G Ge er re eç ç v ve e Y Yö ön nt te em ml le er r: : Çalışmada örnek seçim yanlılığını gideren uygun bir model olan Heckman seçim modeli, Gleason skoruna etki eden risk faktörlerini araştırmak amacıyla simülasyon çalışmasından elde edilen 2000 gözleme sahip üç veri seti için kullanılmıştır. Veri setleri prostat kanserli hastaları içermektedir. Gleason skoru prostat kanseri hastalarında tümörün çeşidi malign olduğunda hesaplanan bir skor olmasına rağmen, çalışmamızda tümor yapısı olarak iyi huylu veya 1. evre tümörler de mevcut olduğundan, Gleason skoru hesaplanamayan birçok kişi sebebiyle örnek seçim yanlılığı söz konusudur. Model, gerçek yapıları dikkate alarak simülasyon yoluyla elde edilen sansür oranları (Gleason skoru hesaplanamayan) sırasıyla 0.30; 0.50 ve 0.70 olan üç farklı veri seti için kurulmuştur. B Bu ul lg gu ul la ar r: : Gleason skoru ile sigara içme durumu ve aile öyküsü değişkenleri ara...

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

Gomes

Radice

Brenes

et al. 2018

Statistics in Medicine

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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. In such cases, the data are said to be missing not at random (MNAR), and nonresponse must be modeled together with the substantive model for the observed data.Selection models have been commonly used to handle MNAR data in clinical and epidemiological research, 4-6 by jointly modeling the outcome and missingness models and typically assuming bivariate normality. Heckman 7 was one of the first to propose such model (Heckman selection model) using a simultaneous equation approach, where the error terms were assumed to follow a bivariate Gaussian. At that time, to circumvent some of the difficulties associated with direct likelihood maximization, Heckman proposed a two-stage least-squares estimation procedure. 8 This involved combining a probit model for the probability of observing the outcome (first stage) with a linear regression model for the outcome (second stage), which was a function of the estimates obtained in the first stage. Although this approach (method of moments estimator) is somehow robust to deviations from normality, it relies crucially on the availability of exclusion restrictions, ie, variables that predict missingness but are unrelated to the outcome of interest. 9 An alternative approach to estimating selection models is the single-step full-information maximum likelihood (FIML), which jointly estimates the outcome and missing data equations. For example, Diggle and Kenward 10 combined a marg...

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A multiple imputation approach for MNAR mechanisms compatible with Heckman's model

Cited by 47 publications

References 40 publications

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

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

Usage of Heckman Sample Selection Model in Health Studies: An Application of Prostate Cancer Patients

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

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