Missing Not At Random Research Articles

Evaluation of Multiple Imputation with Large Proportions of Missing Data: How Much Is Too Much?

Background:Multiple Imputation (MI) is known as an effective method for handling missing data in public health research. However, it is not clear that the method will be effective when the data contain a high percentage of missing observations on a variable.Methods:Using data from “Predictive Study of Coronary Heart Disease” study, this study examined the effectiveness of multiple imputation in data with 20% missing to 80% missing observations using absolute bias (|bias|) and Root Mean Square Error (RMSE) of MI measured under Missing Completely at Random (MCAR), Missing at Random (MAR), and Not Missing at Random (NMAR) assumptions.Results:The |bias| and RMSE of MI was much smaller than of the results of CCA under all missing mechanisms, especially with a high percentage of missing. In addition, the |bias| and RMSE of MI were consistent regardless of increasing imputation numbers from M=10 to M=50. Moreover, when comparing imputation mechanisms, MCMC method had universally smaller |bias| and RMSE than those of Regression method and Predictive Mean Matching method under all missing mechanisms.Conclusion:As missing percentages become higher, using MI is recommended, because MI produced less biased estimates under all missing mechanisms. However, when large proportions of data are missing, other things need to be considered such as the number of imputations, imputation mechanisms, and missing data mechanisms for proper imputation.

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.

Identifying treatment effects using trimmed means when data are missing not at random.

Patients often discontinue from a clinical trial because their health condition is not improving or they cannot tolerate the assigned treatment. Consequently, the observed clinical outcomes in the trial are likely better on average than if every patient had completed the trial. If these differences between trial completers and non-completers cannot be explained by the observed data, then the study outcomes are missing not at random (MNAR). One way to overcome this problem-the trimmed means approach for missing data due to study discontinuation-sets missing values as the worst observed outcome and then trims away a fraction of the distribution from each treatment arm before calculating differences in treatment efficacy (Permutt T, Li F. Trimmed means for symptom trials with dropouts. Pharm Stat. 2017;16(1):20-28). In this paper, we derive sufficient and necessary conditions for when this approach can identify the average population treatment effect. Simulation studies show the trimmed means approach's ability to effectively estimate treatment efficacy when data are MNAR and missingness due to study discontinuation is strongly associated with an unfavorable outcome, but trimmed means fail when data are missing at random. If the reasons for study discontinuation in a clinical trial are known, analysts can improve estimates with a combination of multiple imputation and the trimmed means approach when the assumptions of each hold. We compare the methodology to existing approaches using data from a clinical trial for chronic pain. An R package trim implements the method. When the assumptions are justifiable, using trimmed means can help identify treatment effects notwithstanding MNAR data.

Data Missing Not at Random in Mobile Health Research: Assessment of the Problem and a Case for Sensitivity Analyses.

BackgroundMissing data are common in mobile health (mHealth) research. There has been little systematic investigation of how missingness is handled statistically in mHealth randomized controlled trials (RCTs). Although some missing data patterns (ie, missing at random [MAR]) may be adequately addressed using modern missing data methods such as multiple imputation and maximum likelihood techniques, these methods do not address bias when data are missing not at random (MNAR). It is typically not possible to determine whether the missing data are MAR. However, higher attrition in active (ie, intervention) versus passive (ie, waitlist or no treatment) conditions in mHealth RCTs raise a strong likelihood of MNAR, such as if active participants who benefit less from the intervention are more likely to drop out.ObjectiveThis study aims to systematically evaluate differential attrition and methods used for handling missingness in a sample of mHealth RCTs comparing active and passive control conditions. We also aim to illustrate a modern model-based sensitivity analysis and a simpler fixed-value replacement approach that can be used to evaluate the influence of MNAR.MethodsWe reanalyzed attrition rates and predictors of differential attrition in a sample of 36 mHealth RCTs drawn from a recent meta-analysis of smartphone-based mental health interventions. We systematically evaluated the design features related to missingness and its handling. Data from a recent mHealth RCT were used to illustrate 2 sensitivity analysis approaches (pattern-mixture model and fixed-value replacement approach).ResultsAttrition in active conditions was, on average, roughly twice that of passive controls. Differential attrition was higher in larger studies and was associated with the use of MAR-based multiple imputation or maximum likelihood methods. Half of the studies (18/36, 50%) used these modern missing data techniques. None of the 36 mHealth RCTs reviewed conducted a sensitivity analysis to evaluate the possible consequences of data MNAR. A pattern-mixture model and fixed-value replacement sensitivity analysis approaches were introduced. Results from a recent mHealth RCT were shown to be robust to missing data, reflecting worse outcomes in missing versus nonmissing scores in some but not all scenarios. A review of such scenarios helps to qualify the observations of significant treatment effects.ConclusionsMNAR data because of differential attrition are likely in mHealth RCTs using passive controls. Sensitivity analyses are recommended to allow researchers to assess the potential impact of MNAR on trial results.

Bayesian sensitivity analyses for longitudinal data with dropouts that are potentially missing not at random: A high dimensional pattern-mixture model.

Randomized clinical trials with outcome measured longitudinally are frequently analyzed using either random effect models or generalized estimating equations. Both approaches assume that the dropout mechanism is missing at random (MAR) or missing completely at random (MCAR). We propose a Bayesian pattern-mixture model to incorporate missingness mechanisms that might be missing not at random (MNAR), where the distribution of the outcome measure at the follow-up time , conditional on the prior history, differs across the patterns of missing data. We then perform sensitivity analysis on estimates of the parameters of interest. The sensitivity parameters relate the distribution of the outcome of interest between subjects from a missing-data pattern at time with that of the observed subjects at time . The large number of the sensitivity parameters is reduced by treating them as random with a prior distribution having some pre-specified mean and variance, which are varied to explore the sensitivity of inferences. The missing at random (MAR) mechanism is a special case of the proposed model, allowing a sensitivity analysis of deviations from MAR. The proposed approach is applied to data from the Trial of Preventing Hypertension.

Bevacizumab biosimilar (MB02) and reference bevacizumab in patients with stage IIIB/IV non-squamous non-small cell lung cancer (NSCLC) (STELLA study): Multiple Imputation analysis.

e15003 Background: Stella Trial is a phase III, multinational, double-blind and randomized study to confirm clinical similarity between MB02 and EU-bevacizumab in patients with stage IIIB/IV no squamous NSCLC. 627 subjects with newly diagnosed or recurrent stage IIIb/IV NSCLC were randomized 1:1 to receive either MB02 or EU-bevacizumab plus chemotherapy (paclitaxel and carboplatin) every 3-week cycle for six cycles (week 18) followed by MB02/bevacizumab in blinded monotherapy until disease progression, treatment intolerance, death, patient withdrawal or end of study (w52). An approach targeting the MI of the continuous sum of target diameters (mm), and subsequent categorization of Overall Response (OR) was performed as sensitivity analysis for the assessment of the primary endpoint. Multiple Imputation (MI) has emerged as a credible method to assess the effects of missing data (MD), an inescapable problem with a potential ability to undermine research results' strength and validity in a clinical study, providing the user with a valuable toolset to sufficiently account for the varying types of MD and appropriately adjust the assumptions. Methods: The primary endpoint of the study was Objective Response Rate (ORR) at week 18 per an Independent Radiological Committee (IRC) in the Intention to treat set (ITT). The ORR was analysed with a Cochran-Mantel-Haenszel model, including the stratification factors of sex, smoking status, disease diagnosis and disease stage, comparing the stratified estimates risk difference (RD). In addition, these results were analysed implementing a pattern-mixture MI process accounting for missing at random (MAR) and missing not at random (MNAR) data based on the sum of target diameters in subjects without tumour response data or falling into the categories NonCR/NonPD or non-evaluable (NE). Results: The clinical equivalence of MB02 with EU-bevacizumab is demonstrated by the efficacy data provided through the primary endpoint and the MI sensitive analysis applied. The MI (MAR and MNAR) represents an added value that supports the biosimilarity of MB02 and EU-bevacizumab. The results for the primary analysis of the RD in ORR at w18 in the ITT set were entirely contained within the boundaries of predefined margins (±12): -4.02 [95% CI: -11.76 to 3.71]). Under MI, the ORR RD showed similarity at 95% CIs (-1.92; 95% CI: -10.02 to 6.19) and using the multiple imputations for subjects without tumour response data (missing, NonCR/NonPD or NE), the ORR RD was -2.22 with 95% CI of (-10.54 to 6.10) at w18 in the ITT. Conclusions: The clinical equivalence of MB02 with EU-bevacizumab is demonstrated by the efficacy data provided through the primary endpoint and the MI sensitive analysis applied. The MI (MAR and MNAR) represent an added value that supports the biosimilarity of MB02 and EU-bevacizumab. Clinical trial information: NCT03296163.

Tripartite Collaborative Filtering with Observability and Selection for Debiasing Rating Estimation on Missing-Not-at-Random Data

Most collaborative filtering (CF) models estimate missing ratings with an implicit assumption that the ratings are missing-at-random, which may cause the biased rating estimation and degraded performance since recent deep exploration shows that ratings may likely be missing-not-at-random (MNAR). To debias MNAR rating estimation, we introduce item observability and user selection to depict the generation of MNAR ratings and propose a tripartite CF (TCF) framework to jointly model the triple aspects of rating generation: item observability, user selection, and ratings, and to estimate the MNAR ratings. An item observability variable is introduced to a complete observability model to infer whether an item is observable to a user. TCF also conducts a complete rating model for rating generation and utilizes a user selection model dependent on the item observability and rating values to model user selection of the observable items. We further elaborately instantiate TCF as a Tripartite Probabilistic Matrix Factorization model (TPMF) by leveraging the probabilistic matrix factorization. Besides, TPMF introduces multifaceted dependency between user selection and ratings to model the influence of user selection on ratings. Extensive experiments on synthetic and real-world datasets show that modeling item observability and user selection effectively debias MNAR rating estimation, and TPMF outperforms the state-of-the-art methods in estimating the MNAR ratings.

Bayesian semi-parametric G-computation for causal inference in a cohort study with MNAR dropout and death.

Causal inference with observational longitudinal data and time-varying exposures is often complicated by time-dependent confounding and attrition. The G-computation formula is one approach for estimating a causal effect in this setting. The parametric modeling approach typically used in practice relies on strong modeling assumptions for valid inference, and moreover depends on an assumption of missing at random, which is not appropriate when the missingness is missing not at random (MNAR) or due to death. In this work we develop a flexible Bayesian semi-parametric G-computation approach for assessing the causal effect on the subpopulation that would survive irrespective of exposure, in a setting with MNAR dropout. The approach is to specify models for the observed data using Bayesian additive regression trees, and then use assumptions with embedded sensitivity parameters to identify and estimate the causal effect. The proposed approach is motivated by a longitudinal cohort study on cognition, health, and aging, and we apply our approach to study the effect of becoming a widow on memory. We also compare our approach to several standard methods.

Parametric Fractional Imputation for Longitudinal Data with Intermittent Missing Values

Longitudinal data analysis had been widely developed in the past three decades. Longitudinal data are common in many fields such as public health, medicine, biological and social sciences. Longitudinal data have special nature as the individual may be observed during a long period of time. Hence, missing values are common in longitudinal data. The presence of missing values leads to biased results and complicates the analysis. The missing values have two patterns: intermittent and dropout. The missing data mechanisms are missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). The appropriate analysis relies heavily on the assumed mechanism and pattern. The parametric fractional imputation is developed to handle longitudinal data with intermittent missing pattern. The maximum likelihood estimates are obtained and the Jackkife method is used to obtain the standard errors of the parameters estimates. Finally a simulation study is conducted to validate the proposed approach. Also, the proposed approach is applied to a real data.

Examining Nonnormal Latent Variable Distributions for Non-Ignorable Missing Data.

Missing not at random (MNAR) modeling for non-ignorable missing responses usually assumes that the latent variable distribution is a bivariate normal distribution. Such an assumption is rarely verified and often employed as a standard in practice. Recent studies for "complete" item responses (i.e., no missing data) have shown that ignoring the nonnormal distribution of a unidimensional latent variable, especially skewed or bimodal, can yield biased estimates and misleading conclusion. However, dealing with the bivariate nonnormal latent variable distribution with present MNAR data has not been looked into. This article proposes to extend unidimensional empirical histogram and Davidian curve methods to simultaneously deal with nonnormal latent variable distribution and MNAR data. A simulation study is carried out to demonstrate the consequence of ignoring bivariate nonnormal distribution on parameter estimates, followed by an empirical analysis of "don't know" item responses. The results presented in this article show that examining the assumption of bivariate nonnormal latent variable distribution should be considered as a routine for MNAR data to minimize the impact of nonnormality on parameter estimates.

Bridging gaps in demographic analysis with phylogenetic imputation.

Phylogenetically informed imputation methods have rarely been applied to estimate missing values in demographic data but may be a powerful tool for reconstructing vital rates of survival, maturation, and fecundity for species of conservation concern. Imputed vital rates could be used to parameterize demographic models to explore how populations respond when vital rates are perturbed. We used standardized vital rate estimates for 50 bird species to assess the use of phylogenetic imputation to fill gaps in demographic data. We calculated imputation accuracy for vital rates of focal species excluded from the data set either singly or in combination and with and without phylogeny, body mass, and life-history trait data. We used imputed vital rates to calculate demographic metrics, including generation time, to validate the use of imputation in demographic analyses. Covariance among vital rates and other trait data provided a strong basis to guide imputation of missing vital rates in birds, even in the absence of phylogenetic information. Mean NRMSE for null and phylogenetic models differed by <0.01 except when no vital rates were available or for vital rates with high phylogenetic signal (Pagel's λ > 0.8). In these cases, including body mass and life-history trait data compensated for lack of phylogenetic information: mean normalized root mean square error (NRMSE) for null and phylogenetic models differed by <0.01 for adult survival and <0.04 for maturation rate. Estimates of demographic metrics were sensitive to the accuracy of imputed vital rates. For example, mean error in generation time doubled in response to inaccurate estimates of maturation time. Accurate demographic data and metrics, such as generation time, are needed to inform conservation planning processes, for example through International Union for Conservation of Nature Red List assessments and population viability analysis. Imputed vital rates could be useful in this context but, as for any estimated model parameters, awareness of the sensitivities of demographic model outputs to the imputed vital rates is essential.

A comparative study of evaluating missing value imputation methods in label-free proteomics

The presence of missing values (MVs) in label-free quantitative proteomics greatly reduces the completeness of data. Imputation has been widely utilized to handle MVs, and selection of the proper method is critical for the accuracy and reliability of imputation. Here we present a comparative study that evaluates the performance of seven popular imputation methods with a large-scale benchmark dataset and an immune cell dataset. Simulated MVs were incorporated into the complete part of each dataset with different combinations of MV rates and missing not at random (MNAR) rates. Normalized root mean square error (NRMSE) was applied to evaluate the accuracy of protein abundances and intergroup protein ratios after imputation. Detection of true positives (TPs) and false altered-protein discovery rate (FADR) between groups were also compared using the benchmark dataset. Furthermore, the accuracy of handling real MVs was assessed by comparing enriched pathways and signature genes of cell activation after imputing the immune cell dataset. We observed that the accuracy of imputation is primarily affected by the MNAR rate rather than the MV rate, and downstream analysis can be largely impacted by the selection of imputation methods. A random forest-based imputation method consistently outperformed other popular methods by achieving the lowest NRMSE, high amount of TPs with the average FADR < 5%, and the best detection of relevant pathways and signature genes, highlighting it as the most suitable method for label-free proteomics.

A Bayesian Latent Variable Selection Model for Nonignorable Missingness

Missing data are exceedingly common across a variety of disciplines, such as educational, social, and behavioral science areas. Missing not at random (MNAR) mechanism where missingness is related to unobserved data is widespread in real data and has detrimental consequence. However, the existing MNAR-based methods have potential problems such as leaving the data incomplete and failing to accommodate incomplete covariates with interactions, non-linear terms, and random slopes. We propose a Bayesian latent variable imputation approach to impute missing data due to MNAR (and other missingness mechanisms) and estimate the model of substantive interest simultaneously. In addition, even when the incomplete covariates involves interactions, non-linear terms, and random slopes, the proposed method can handle missingness appropriately. Computer simulation results suggested that the proposed Bayesian latent variable selection model (BLVSM) was quite effective when the outcome and/or covariates were MNAR. Except when the sample size was small, estimates from the proposed BLVSM tracked closely with those from the complete data analysis. With a small sample size, when the outcome was less predictable from the covariates, the missingness proportions of the covariates and the outcome were larger, and the missingness selection processes of the covariates and the outcome were more MNAR and MAR, the performance of BLVSM was less satisfactory. When the sample size was large, BLVSM always performed well. In contrast, the method with an MAR assumption provided biased estimates and undercoverage confidence intervals when the missingness was MNAR. The robustness and the implementation of BLVSM in real data were also illustrated. The proposed method is available in the Blimp software application, and the paper includes a data analysis example illustrating its use.

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.

Bayesian Estimation of Log-Normal Distribution Under Ranked Set Sampling With Missing Data

In this paper, joint Bayesian estimation of two parameters of a log-normal distribution is obtained based on simple random sampling (SRS) and ranked set sampling (RSS) with complete and missing data. For the missing data case, two missing mechanisms are considered: missing at random (MAR) and missing not at random (MNAR). A logistic regression model is specified for the MNAR mechanism. The results based on SRS and RSS with three different types of prior information are compared via simulation studies with both complete and missing data. It is shown that the results obtained under RSS are significantly better than those obtained under SRS. In the simulation studies, the Gibbs sampling method, Metropolis-Hastings algorithm and importance sampling method are used to sample posterior distributions to estimate the unknown parameters of the log-normal distribution.

Development of a Models of Interpersonal Competencies as a Complex System

Competencies represent a dynamic combination of cognitive and metacognitive skills, knowledge and understanding, interpersonal and practical skills, and ethical values. Since there are many entities, as well as many activities between entities, according to system theory, the whole system belongs to complex systems. The paper develops a conceptual and computational model of interpersonal competences for the process of optimization and methodology design, using simulation modeling. The developed model enables: faster data collection, more accurate results, avoiding human error in data entry and processing, survey time can be measured and more easily restricted, NMAR (Not Missing at Random) data is avoided and socially desirable responses are more easily avoided.

Imputation-based semiparametric estimation for INAR(1) processes with missing data

In applied problems parameter estimation with missing data has risen as a hot topic. Imputation for ignorable incomplete data is one of the most popular methods in integer-valued time series. For data missing not at random (MNAR), estimators directly derived by imputation will lead results that is sensitive to the failure of the effectiveness. In view of the first-order integer-valued autoregressive (INAR(1)) processes with MNAR response mechanism, we consider an imputation based semiparametric method, which recommends the complete auxiliary variable of Yule-Walker equation. Asymptotic properties of relevant estimators are also derived. Some simulation studies are conducted to verify the effectiveness of our estimators, and a real example is also presented as an illustration.

An application of the mixed-effects model and pattern mixture model to treatment groups with differential missingness suspected not-missing-at-random.

Likelihood-based, mixed-effects models for repeated measures (MMRMs) are occasionally used in primary analyses for group comparisons of incomplete continuous longitudinal data. Although MMRM analysis is generally valid under missing-at-random assumptions, it is invalid under not-missing-at-random (NMAR) assumptions. We consider the possibility of bias of estimated treatment effect using standard MMRM analysis in a motivational case, and propose simple and easily implementable pattern mixture models within the framework of mixed-effects modeling, to handle the NMAR data with differential missingness between treatment groups. The proposed models are a new form of pattern mixture model that employ a categorical time variable when modeling the outcome and a continuous time variable when modeling the missingness-data patterns. The models can directly provide an overall estimate of the treatment effect of interest using the average of the distribution of the missingness indicator and a categorical time variable in the same manner as MMRM analysis. Our simulation results indicate that the bias of the treatment effect for MMRM analysis was considerably larger than that for the pattern mixture model analysis under NMAR assumptions. In the case study, it would be dangerous to interpret only the results of the MMRM analysis, and the proposed pattern mixture model would be useful as a sensitivity analysis for treatment effect evaluation.

Imputation and low-rank estimation with Missing Not At Random data

Missing values challenge data analysis because many supervised and unsupervised learning methods cannot be applied directly to incomplete data. Matrix completion based on low-rank assumptions are very powerful solution for dealing with missing values. However, existing methods do not consider the case of informative missing values which are widely encountered in practice. This paper proposes matrix completion methods to recover Missing Not At Random (MNAR) data. Our first contribution is to suggest a model-based estimation strategy by modelling the missing mechanism distribution. An EM algorithm is then implemented, involving a Fast Iterative Soft-Thresholding Algorithm (FISTA). Our second contribution is to suggest a computationally efficient surrogate estimation by implicitly taking into account the joint distribution of the data and the missing mechanism: the data matrix is concatenated with the mask coding for the missing values; a low-rank structure for exponential family is assumed on this new matrix, in order to encode links between variables and missing mechanisms. The methodology that has the great advantage of handling different missing value mechanisms is robust to model specification errors. The performances of our methods are assessed on the real data collected from a trauma registry (TraumaBase $$^{\textregistered }$$ ) containing clinical information about over twenty thousand severely traumatized patients in France. The aim is then to predict if the doctors should administrate tranexomic acid to patients with traumatic brain injury, that would limit excessive bleeding.

Masked Data Analysis based on the Generalized Linear Model

In this paper, we consider the estimation problem in the presence of masked data for series systems. A missing indicator is proposed to describe masked set of each failure time.Moreover, a Generalized Linear model (GLM) with appropriate link function is used to model masked indicator in order to involve masked information into likelihood function. Both maximum likelihood and Bayesian methods were considered.The likelihood function with both missing at random (MAR) and missing not at random (MNAR) mechanismsare derived.Using an auxiliary variable, a Bayesian approach is expanded to obtain posterior estimations of the model parameters.The proposed methods have been illustrated through a real example.