Missing At Random Assumption Research Articles

EFFICIENCY IN ESTIMATION UNDER MONOTONIC ATTRITION

Attrition is monotonic when agents leaving multi-period studies do not return. Under a general missing at random (MAR) assumption, we study efficiency in estimation of parameters defined by moment restrictions on the distributions of the counterfactuals that were unrealized due to monotonic attrition. We discuss novel issues related to overidentification, usability of sample units, and the information content of various MAR assumptions for estimation of such parameters. We propose a standard doubly robust estimator for these parameters by equating to zero the sample analog of their respective efficient influence functions. Our proposed estimator performs well and vastly outperforms other estimators in our simulation experiment and empirical illustration.

Simultaneous alleviation of verification and reference standard biases in a community-based tuberculosis screening study using Bayesian latent class analysis.

Estimation of prevalence and diagnostic test accuracy in tuberculosis (TB) prevalence surveys suffer from reference standard and verification biases. The former is attributed to the imperfect reference test used to bacteriologically confirm TB disease. The latter occurs when only the participants screening positive for any TB-compatible symptom or chest X-ray abnormality are selected for bacteriological testing (verification). Bayesian latent class analysis (LCA) alleviates the reference standard bias but suffers verification bias in TB prevalence surveys. This work aims to identify best-practice approaches to simultaneously alleviate the reference standard and verification biases in the estimates of pulmonary TB prevalence and diagnostic test performance in TB prevalence surveys. We performed a secondary analysis of 9869 participants aged ≥15 years from a community-based multimorbidity screening study in a rural district of KwaZulu-Natal, South Africa (Vukuzazi study). Participants were eligible for bacteriological testing using Xpert Ultra and culture if they reported any cardinal TB symptom or had an abnormal chest X-ray finding. We conducted Bayesian LCA in five ways to handle the unverified individuals: (i) complete-case analysis, (ii) analysis assuming the unverified individuals would be negative if bacteriologically tested, (iii) analysis of multiply-imputed datasets with imputation of the missing bacteriological test results for the unverified individuals using multivariate imputation via chained equations (MICE), and simultaneous imputation of the missing bacteriological test results in the analysis model assuming the missing bacteriological test results were (iv) missing at random (MAR), and (v) missing not at random (MNAR). We compared the results of (i)-(iii) to the analysis based on a composite reference standard (CRS) of Xpert Ultra and culture. Through simulation with an overall true prevalence of 2.0%, we evaluated the ability of the models to alleviate both biases simultaneously. Based on simulation, Bayesian LCA with simultaneous imputation of the missing bacteriological test results under the assumption that the missing data are MAR and MNAR alleviate the reference standard and verification biases. CRS-based analysis and Bayesian LCA assuming the unverified are negative for TB alleviate the biases only when the true overall prevalence is <3.0%. Complete-case analysis produced biased estimates. In the Vukuzazi study, Bayesian LCA with simultaneous imputation of the missing bacteriological test results under the MAR and MNAR assumptions produced overall PTB prevalence of 0.9% (95% Credible Interval (CrI): 0.6-1.9) and 0.7% (95% CrI: 0.5-1.1) respectively alongside realistic estimates of overall diagnostic test sensitivity and specificity with substantially overlapping 95% CrI. The CRS-based analysis and Bayesian LCA assuming the unverified were negative for TB produced 0.7% (95% CrI: 0.5-0.9) and 0.7% (95% CrI: 0.5-1.2) overall PTB prevalence respectively with realistic estimates of overall diagnostic test sensitivity and specificity. Unlike CRS-based analysis, Bayesian LCA of multiply-imputed data using MICE mitigates both biases. The findings demonstrate the efficacy of these advanced techniques in alleviating the reference standard and verification biases, enhancing the robustness of community-based screening programs. Imputing missing values as negative for bacteriological tests is plausible under realistic assumptions.

Addressing missing outcome data in randomised controlled trials: A methodological scoping review

BackgroundMissing outcome data is common in trials, and robust methods to address this are needed. Most trial reports currently use methods applicable under a missing completely at random assumption (MCAR), although this strong assumption can often be inappropriate. ObjectiveTo identify and summarise current literature on the analytical methods for handling missing outcome data in randomised controlled trials (RCTs), emphasising methods appropriate for data missing at random (MAR) or missing not at random (MNAR). Study design and settingWe conducted a methodological scoping review and identified papers through searching four databases (MEDLINE, Embase, CENTRAL, and CINAHL) from January 2015 to March 2023. We also performed forward and backward citation searching. Eligible papers discussed methods or frameworks for handling missing outcome data in RCTs or simulation studies with an RCT design. ResultsFrom 1878 records screened, our search identified 101 eligible papers. 90 (89%) papers described specific methods for addressing missing outcome data and 11 (11%) described frameworks for overall methodological approach. Of the 90 methods papers, 30 (33%) described methods under the MAR assumption, 48 (53%) explored methods under the MNAR assumption and 11 (12%) discussed methods under a hybrid of MAR and MNAR assumptions. Control-based methods under the MNAR assumption were the most common method explored, followed by multiple imputation under the MAR assumption. ConclusionThis review provides guidance on available analytic approaches for handling missing outcome data, particularly under the MNAR assumption. These findings may support trialists in using appropriate methods to address missing outcome data.

Predicting absolute risk for a person with missing risk factors.

We compared methods to project absolute risk, the probability of experiencing the outcome of interest in a given projection interval accommodating competing risks, for a person from the target population with missing predictors. Without missing data, a perfectly calibrated model gives unbiased absolute risk estimates in a new target population, even if the predictor distribution differs from the training data. However, if predictors are missing in target population members, a reference dataset with complete data is needed to impute them and to estimate absolute risk, conditional only on the observed predictors. If the predictor distributions of the reference data and the target population differ, this approach yields biased estimates. We compared the bias and mean squared error of absolute risk predictions for seven methods that assume predictors are missing at random (MAR). Some methods imputed individual missing predictors, others imputed linear predictor combinations (risk scores). Simulations were based on real breast cancer predictor distributions and outcome data. We also analyzed a real breast cancer dataset. The largest bias for all methods resulted from different predictor distributions of the reference and target populations. No method was unbiased in this situation. Surprisingly, violating the MAR assumption did not induce severe biases. Most multiple imputation methods performed similarly and were less biased (but more variable) than a method that used a single expected risk score. Our work shows the importance of selecting predictor reference datasets similar to the target population to reduce bias of absolute risk predictions with missing risk factors.

Quantifying bias due to missing data in quality of life surveys of advanced-stage cancer patients.

Many studies on cancer patients investigate the impact of treatment on health-related quality of life (QoL). Typically, QoL is measured longitudinally, at baseline and at predefined timepoints thereafter. The question is whether, at a given timepoint, patients who return their questionnaire (available cases, AC) have a different QoL than those who do not return their questionnaire (non-AC). We employed augmented inverse probability weighting (AIPW) to estimate the average QoL of non-AC in two studies on advanced-stage cancer patients. The AIPW estimator assumed data to be missing at random (MAR) and used machine learning (ML)-based methods to estimate answering probabilities of individuals at given timepoints as well as their reported QoL, as a function of auxiliary variables. These auxiliary variables were selected by medical oncologists based on domain expertise. We aggregated results both by timepoint and by time until death and compared AIPW estimates to the AC averages. Additionally, we used a pattern mixture model (PMM) to check sensitivity of our AIPW estimates against violation of the MAR assumption. Our study included 1927 patients with advanced pancreatic and 797 patients with advanced breast cancer. The AIPW estimate for average QoL of non-AC was below the average QoL of AC when aggregated by timepoint. The difference vanished when aggregated by time until death. PMM estimates were below AIPW estimates. Our results indicate that non-AC have a lower average QoL than AC. However, estimates for QoL of non-AC are subject to unverifiable assumptions about the missingness mechanism.

How to deal with missing data? Multiple imputation by chained equations: recommendations and explanations for clinical practice

The presence of missing data, a constant problem in medical research, has several consequences: systematic loss of power, associated or not with a reduction in the representativeness of the sample analyzed. There are three types of missing data: 1) missing completely at random (MCAR); 2) missing at random (MAR); 3) missing not at random (MNAR). Multiple imputation by chained equations allows for the correct handling of missing data under the MCAR and MAR assumptions. It allows to simulate for each missing data j, a number m of simulated values which seem plausible with regard to the other variables. A random effect is included in this simulation to express the uncertainty. Several data sets are thus created and analyzed individually, in an identical way. Then the estimators of each data set are combined to obtain a global estimator. Multiple imputation increases power, corrects for some biases and has the advantage of being applicable to many types of variables. Complete case analysis should no longer be the norm. The objective of this guide is to help the reader in conducting an analysis with multiple imputed data. We cover the following points: the different types of missing data, the different historical approaches to handling them, and then we detail the multiple imputation method using chained equations. We provide a code example for the mice package of R®.

Composite quantile regression analysis of survival data with missing cause-of-failure information and its application to breast cancer clinical trial

The analysis of survival data can be challenging due to the presence of missing data. This paper proposes weighted composite quantile regression (CQR) for estimating a lot of quantile regression (QR) of survival data based on single-index coefficient model (SICM), which is a very general and flexible tool for exploring the relationship between response variable and a set of predictors. The statistical inference for SICM is considered when cause-of-failure information (censored or non-censored) is always observed. However, the cause-of-failure information may be missing at random (MAR) for various reasons. Regression calibration, imputation and inverse probability weighted approaches are applied to deal with the MAR assumption. The asymptotic normalities of the proposed estimators are established. Meanwhile, the oracle property of the variable selection based on adaptive LASSO penalty procedure is conducted. To assess the finite sample performance of the proposed estimators, simulation study with normal error and heavy-tail error are considered. As expected, the CQR estimators perform as good as the least-square estimators for normal error, and are more robust to heavy-tailed error. Finally, a breast cancer real data analysis is carried out to illustrate the proposed methodologies.

Bias reduction in the logistic model parameters with the LogF(1,1) penalty under MAR assumption

In this paper, we present a novel validated penalization method for bias reduction to estimate parameters for the logistic model when data are missing at random (MAR). Specific focus was given to address the data missingness problem among categorical model covariates. We penalize a logit log-likelihood with a novel prior distribution based on the family of the LogF(m,m) generalized distribution. The principle of expectation-maximization with weights was employed with the Louis' method to derive an information matrix, while a closed form for the exact bias was derived following the Cox and Snell's equation. A combination of simulation studies and real life data were used to validate the proposed method. Findings from the validation studies show that our model's standard errors are consistently lower than those derived from other bias reduction methods for the missing at random data mechanism. Consequently, we conclude that in most cases, our method's performance in parameter estimation is superior to the other classical methods for bias reduction when data are MAR.

The Data-Adaptive Fellegi-Sunter Model for Probabilistic Record Linkage: Algorithm Development and Validation for Incorporating Missing Data and Field Selection.

BackgroundQuality patient care requires comprehensive health care data from a broad set of sources. However, missing data in medical records and matching field selection are 2 real-world challenges in patient-record linkage.ObjectiveIn this study, we aimed to evaluate the extent to which incorporating the missing at random (MAR)–assumption in the Fellegi-Sunter model and using data-driven selected fields improve patient-matching accuracy using real-world use cases.MethodsWe adapted the Fellegi-Sunter model to accommodate missing data using the MAR assumption and compared the adaptation to the common strategy of treating missing values as disagreement with matching fields specified by experts or selected by data-driven methods. We used 4 use cases, each containing a random sample of record pairs with match statuses ascertained by manual reviews. Use cases included health information exchange (HIE) record deduplication, linkage of public health registry records to HIE, linkage of Social Security Death Master File records to HIE, and deduplication of newborn screening records, which represent real-world clinical and public health scenarios. Matching performance was evaluated using the sensitivity, specificity, positive predictive value, negative predictive value, and F1-score.ResultsIncorporating the MAR assumption in the Fellegi-Sunter model maintained or improved F1-scores, regardless of whether matching fields were expert-specified or selected by data-driven methods. Combining the MAR assumption and data-driven fields optimized the F1-scores in the 4 use cases.ConclusionsMAR is a reasonable assumption in real-world record linkage applications: it maintains or improves F1-scores regardless of whether matching fields are expert-specified or data-driven. Data-driven selection of fields coupled with MAR achieves the best overall performance, which can be especially useful in privacy-preserving record linkage.

Score test for missing at random or not under logistic missingness models.

Missing data are frequently encountered in various disciplines and can be divided into three categories: missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). Valid statistical approaches to missing data depend crucially on correct identification of the underlying missingness mechanism. Although the problem of testing whether this mechanism is MCAR or MAR has been extensively studied, there has been very little research on testing MAR versus MNAR. A critical challenge that is faced when dealing with this problem is the issue of model identification under MNAR. In this paper, under a logistic model for the missing probability, we develop two score tests for the problem of whether the missingness mechanism is MAR or MNAR under a parametric model and a semiparametric location model on the regression function. The implementation of the score tests circumvents the identification issue as it requires only parameter estimation under the null MAR assumption. Our simulations and analysis of human immunodeficiency virus data show that the score tests have well-controlled type I errors and desirable powers.

Testing the missingness mechanism in longitudinal surveys: a case study using the Health and Retirement Study

ABSTRACT Imputation or likelihood-based approaches to handle missing data assume the data are missing completely at random (MCAR) or missing at random (MAR). However, little research has examined the missingness pattern before using these imputation/likelihood methods. Three missingness mechanisms – MCAR, MAR, and not missing at random (NMAR) – can be tested using information on research design, disciplinary knowledge, and appropriate methods. This study summarized six commonly used statistical methods to test the missingness mechanism and discussed their application conditions. We further applied these methods to a two-wave longitudinal dataset from the Health and Retirement Study (N = 18,747). Health measures met the MAR assumptions although we could not completely rule out NMAR. Demographic variables provided auxiliary information. The logistic regression method demonstrated applicability to a wide range of scenarios. This study provides a useful guide to choose methods to test missingness mechanisms depending on the research goal and nature of the data.

Fast model‐based clustering of partial records

Partially recorded data are frequently encountered in many applications and usually clustered by first removing incomplete cases or features with missing values, or by imputing missing values, followed by application of a clustering algorithm to the resulting altered dataset. Here, we develop clustering methodology through a model‐based approach using the marginal density for the observed values, assuming a finite mixture model of multivariate t distributions. We compare our approximate algorithm to the corresponding full expectation–maximization (EM) approach that considers missing values in the incomplete dataset and makes a missing at random (MAR) assumption, as well as case deletion and imputation methods. Since only the observed values are utilized, our approach is computationally more efficient than imputation or full EM. Simulation studies demonstrate that our approach has favourable recovery of the true cluster partition compared to case deletion and imputation under various missingness mechanisms and is at least competitive with the full EM approach, even when MAR assumptions are violated. Our methodology is demonstrated on a problem of clustering gamma‐ray bursts and is implemented at https://github.com/emilygoren/MixtClust.

Impact of missing outcome data in meta-analyses of lifestyle interventions during pregnancy to reduce postpartum weight retention: An overview of systematic reviews with meta-analyses and additional sensitivity analyses.

High risk of bias associated with missing outcome data (MOD) in meta-analyses (MAs) of the effects of lifestyle interventions during pregnancy on postpartum weight retention (PPWR) casts doubt on whether such interventions can be relied upon as truly effective. This systematic overview of three MAs (19 RCTs), each with high MOD rates in the subset of RCTs included, examined how MOD were addressed in the estimation of summary intervention effects. All MAs reported beneficial and statistically significant intervention effects estimated based on complete case analyses, deemed valid if MOD was missing at random (MAR). Therefore, we conducted sensitivity analyses using pattern mixture models and informative missingness parameters (describing how the outcome in the missing participants may be related to the outcome in the completers), to ascertain the robustness of the estimates to reasonable deviations from the MAR assumption. In plausible scenarios where the response in intervention group participants with versus without MOD was worse (by just 0.5kg), effect estimates were attenuated in all MAs and no longer statistically significant in two MAs. Statistical significance was retained when all 19 RCTs identified across MAs were examined together in a broader meta-analysis: -0.63 kg (95%CI -0.17, -0.08), but the clinical relevancy of effects of this magnitude remains unclear.

1463Impact of missing outcome data in meta-analyses of lifestyle interventions during pregnancy to reduce postpartum-weight-retention

Abstract Background High risk of bias associated with missing outcome data (MOD) in meta-analyses (MAs) of the effects of lifestyle interventions during pregnancy on postpartum weight retention (PPWR), casts doubt on whether such interventions can be relied upon as truly effective, since estimates are deemed valid only if MOD was missing at random (MAR). Methods We conducted a systematic overview of MAs to examine the impact of MOD on the estimation of meta-analytic summary intervention effects and conducted sensitivity analyses using pattern mixture models and informative missingness parameters (describing how the outcome in the missing participants may be related to the outcome in the completers), to ascertain the robustness of the estimates to reasonable deviations from the MAR assumption. Results Three relevant MAs were identified, all with high MOD rates in the RCTs included (median&amp;gt;30%), and all reporting beneficial intervention effects on PPWR (in kg) estimated based on complete case analyses: [-0.78 (95%CI: -1.39,-0.16), -0.81 (-1.57,-0.06), and -0.94 (-1.52,-0.37)] in MAs of any lifestyle, exercise, or diet + exercise interventions, respectively. In plausible scenarios where the outcome for the intervention group in participants with vs without MOD was worse (by 0.5kg), effect estimates were attenuated in all and no longer significant in 2 of the MAs [-0.58 (-1.29,0.13), -0.70 (-1.50,0.10) and -0.88 (-1.73,-0.02)]. Conclusions Statistical significance was retained when all 19 RCTs identified across MAs were meta-analysed: -0.63 (-0.17,-0.08). Key messages The clinical relevancy of effects of this magnitude remains unclear.

Effect of Missing Data Treatment on the Predictive Accuracy of C4.5 Classifier

Missing data is a common problem confronted by researchers in machine learning applications. Missing values affect both the performance of analysis tools, as well as the quality of the drawn decisions. This research aims to analyze the impact of four missing data treatment methods on the predictive accuracy of the C4.5 decision tree algorithm. It also investigates the imputation accuracy of each imputation method using a single dataset with missing values presented in a single variable. The work was performed under three missing data assumptions, namely, Missing Completely At Random (MCAR), Missing At Random (MAR) and Missing Not At Random (MNAR) with three missingness’ rates: 5%, 10%, and 15%. The methods used to treat the missing data are: lite-wise deletion, mean/mode imputation, K-nearest neighbor imputation, and decision tree imputation. The results of the experiments showed that the C4.5 classifier achieved better performance under the MCAR assumption. While the mean/mode imputation has the highest C4.5 predictive accuracy under MAR and MNAR assumptions. The k-nearest neighbor method obtained the most accurate imputation result under the MCAR assumption, whereas mean/mode imputation was the most accurate method under the MAR assumption. On the other hand, the lowest imputation accuracy levels were achieved under the MNAR assumption attributed to the mean/mode imputation method.

Strategies for assessing the impact of loss to follow-up on estimates of neurodevelopmental impairment in a very preterm cohort at 2 years of age

BackgroundLoss to follow-up is a major challenge for very preterm (VPT) cohorts; attrition is associated with social disadvantage and parents with impaired children may participate less in research. We investigated the impact of loss to follow-up on the estimated prevalence of neurodevelopmental impairment in a VPT cohort using different methodological approaches.MethodsThis study includes births < 32 weeks of gestational age (GA) from 4 regions in the UK and Portugal participating in a European birth cohort (N = 1737 survivors). Data on maternal characteristics, pregnancy complications, neonatal outcomes and neighborhood deprivation were collected at baseline. Neurodevelopment was assessed at 2 years of corrected age (CA) using standardized parent-report measures. We applied (1) multiple imputation (MI) and (2) inverse probability weighting (IPW) to estimate the impact of non-response on the prevalence of moderate to severe neurodevelopmental impairment and assessed violations of the missing at random (MAR) assumption using the delta method.Results54.2% of children were followed-up. Follow-up was less likely when mothers were younger, multiparous, foreign-born, did not breastfeed and came from deprived areas. The prevalence of neurodevelopmental impairment was 18.4% (95% confidence interval (CI):15.9–21.1) and increased to 20.4% (95%CI: 17.3–23.4) and 20.0% (95%CI:16.9–23.1) for MI and IPW models, respectively. Simulating strong violations of MAR (children with impairments being 50% less likely to be followed-up) raised estimates to 23.6 (95%CI:20.1–27.1)ConclusionsIn a VPT cohort with high loss to follow-up, correcting for attrition yielded modest increased estimates of neurodevelopmental impairment at 2 years CA; estimates were relatively robust to violations of the MAR assumption.

Missing not at random in end of life care studies: multiple imputation and sensitivity analysis on data from the ACTION study

BackgroundMissing data are common in end-of-life care studies, but there is still relatively little exploration of which is the best method to deal with them, and, in particular, if the missing at random (MAR) assumption is valid or missing not at random (MNAR) mechanisms should be assumed. In this paper we investigated this issue through a sensitivity analysis within the ACTION study, a multicenter cluster randomized controlled trial testing advance care planning in patients with advanced lung or colorectal cancer.MethodsMultiple imputation procedures under MAR and MNAR assumptions were implemented. Possible violation of the MAR assumption was addressed with reference to variables measuring quality of life and symptoms. The MNAR model assumed that patients with worse health were more likely to have missing questionnaires, making a distinction between single missing items, which were assumed to satisfy the MAR assumption, and missing values due to completely missing questionnaire for which a MNAR mechanism was hypothesized. We explored the sensitivity to possible departures from MAR on gender differences between key indicators and on simple correlations.ResultsUp to 39% of follow-up data were missing. Results under MAR reflected that missingness was related to poorer health status. Correlations between variables, although very small, changed according to the imputation method, as well as the differences in scores by gender, indicating a certain sensitivity of the results to the violation of the MAR assumption.ConclusionsThe findings confirmed the importance of undertaking this kind of analysis in end-of-life care studies.

Testing the Missing Mechanism of Demographic and Health Variables in the Health and Retirement Study

Studies using data from longitudinal health survey of older adults usually assumed the data were missing completely at random (MCAR) or missing at random (MAR). Thus subsequent analyses used multiple imputation or likelihood-based method to handle missing data. However, little existing research actually examines whether the data met the MCAR/MAR assumptions before performing data analyses. This study first summarized the commonly used statistical methods to test missing mechanism and discussed their application conditions. Then using two-wave longitudinal data from the Health and Retirement Study (HRS; wave 2014-2015 and wave 2016-2017; N=18,747), this study applied different approaches to test the missing mechanism of several demographic and health variables. These approaches included Little’s test, logistic regression method, nonparametric tests, false discovery rate, and others. Results indicated the data did not meet the MCAR assumption even though they had a very low rate of missing values. Demographic variables provided good auxiliary information for health variables. Health measures (e.g., self-reported health, activity of daily life, depressive symptoms) met the MAR assumptions. Older respondents could drop out and die in the longitudinal survey, but attrition did not significantly affect the MAR assumption. Our findings supported the MAR assumptions for the demographic and health variables in HRS, and therefore provided statistical justification to HRS researchers about using imputation or likelihood-based methods to deal with missing data. However, researchers are strongly encouraged to test the missing mechanism of the specific variables/data they choose when using a new dataset.

Comparison of exclusion, imputation and modelling of missing binary outcome data in frequentist network meta-analysis

BackgroundMissing participant outcome data (MOD) are ubiquitous in systematic reviews with network meta-analysis (NMA) as they invade from the inclusion of clinical trials with reported participant losses. There are available strategies to address aggregate MOD, and in particular binary MOD, while considering the missing at random (MAR) assumption as a starting point. Little is known about their performance though regarding the meta-analytic parameters of a random-effects model for aggregate binary outcome data as obtained from trial-reports (i.e. the number of events and number of MOD out of the total randomised per arm).MethodsWe used four strategies to handle binary MOD under MAR and we classified these strategies to those modelling versus excluding/imputing MOD and to those accounting for versus ignoring uncertainty about MAR. We investigated the performance of these strategies in terms of core NMA estimates by performing both an empirical and simulation study using random-effects NMA based on electrical network theory. We used Bland-Altman plots to illustrate the agreement between the compared strategies, and we considered the mean bias, coverage probability and width of the confidence interval to be the frequentist measures of performance.ResultsModelling MOD under MAR agreed with exclusion and imputation under MAR in terms of estimated log odds ratios and inconsistency factor, whereas accountability or not of the uncertainty regarding MOD affected intervention hierarchy and precision around the NMA estimates: strategies that ignore uncertainty about MOD led to more precise NMA estimates, and increased between-trial variance. All strategies showed good performance for low MOD (<5%), consistent evidence and low between-trial variance, whereas performance was compromised for large informative MOD (> 20%), inconsistent evidence and substantial between-trial variance, especially for strategies that ignore uncertainty due to MOD.ConclusionsThe analysts should avoid applying strategies that manipulate MOD before analysis (i.e. exclusion and imputation) as they implicate the inferences negatively. Modelling MOD, on the other hand, via a pattern-mixture model to propagate the uncertainty about MAR assumption constitutes both conceptually and statistically proper strategy to address MOD in a systematic review.

Dealing with missing outcome data in meta-analysis.

Missing data result in less precise and possibly biased effect estimates in single studies. Bias arising from studies with incomplete outcome data is naturally propagated in a meta‐analysis. Conventional analysis using only individuals with available data is adequate when the meta‐analyst can be confident that the data are missing at random (MAR) in every study—that is, that the probability of missing data does not depend on unobserved variables, conditional on observed variables. Usually, such confidence is unjustified as participants may drop out due to lack of improvement or adverse effects. The MAR assumption cannot be tested, and a sensitivity analysis to assess how robust results are to reasonable deviations from the MAR assumption is important. Two methods may be used based on plausible alternative assumptions about the missing data. Firstly, the distribution of reasons for missing data may be used to impute the missing values. Secondly, the analyst may specify the magnitude and uncertainty of possible departures from the missing at random assumption, and these may be used to correct bias and reweight the studies. This is achieved by employing a pattern mixture model and describing how the outcome in the missing participants is related to the outcome in the completers. Ideally, this relationship is informed using expert opinion. The methods are illustrated in two examples with binary and continuous outcomes. We provide recommendations on what trial investigators and systematic reviewers should do to minimize the problem of missing outcome data in meta‐analysis.