数据缺失机制识别及处理的标准化流程及集成系统

目的 提出数据缺失机制识别及处理的标准化操作流程,并开发相应集成系统,为非统计专业背景的医学工作者处理缺失数据提供恰当、专业且简便的实现工具。方法 系统集成了完成者数据集法、K最近邻分类算法和链式方程多元插值法等缺失数据处理方法,并将其归纳到缺失机制识别及处理的统一框架下,为缺失数据处理提供了从缺失统计,缺失机制识别到缺失处理的标准化流程。结果 将归纳的标准化流程分步骤开发为缺失统计、缺失识别、缺失处理等功能模块并进行了集成化,构建了缺失机制识别及处理集成系统。结论 标准化操作流程及集成系统实现了缺失机制识别加缺失数据处理全过程,操作方式简单便捷,结果展示直观易懂,为缺失数据的处理提供了更为简便可行的选择,便于医学工作者实际应用。     

Recovery of information from multiple imputation: a simulation study

ABSTRACT: BACKGROUND: Multiple imputation is becoming increasingly popular for handling missing data. However, it is often implemented without adequate consideration of whether it offers any advantage over complete case analysis for the research question of interest, or whether potential gains may be offset by bias from a poorly fitting imputation model, particularly as the amount of missing data increases. METHODS: Simulated datasets (n = 1000) drawn from a synthetic population were used to explore information recovery from multiple imputation in estimating the coefficient of a binary exposure variable when various proportions of data (10-90%) were set missing at random in a highly-skewed continuous covariate or in the binary exposure. Imputation was performed using multivariate normal imputation (MVNI), with a simple or zero-skewness log transformation to manage non-normality. Bias, precision, mean-squared error and coverage for a set of regression parameter estimates were compared between multiple imputation and complete case analyses. RESULTS: For missingness in the continuous covariate, multiple imputation produced less bias and greater precision for the effect of the binary exposure variable, compared with complete case analysis, with larger gains in precision with more missing data. However, even with only moderate missingness, large bias and substantial under-coverage were apparent in estimating the continuous covariate's effect when skewness was not adequately addressed. For missingness in the binary covariate, all estimates had negligible bias but gains in precision from multiple imputation were minimal, particularly for the coefficient of the binary exposure. CONCLUSIONS: Although multiple imputation can be useful if covariates required for confounding adjustment are missing, benefits are likely to be minimal when data are missing in the exposure variable of interest. Furthermore, when there are large amounts of missingness, multiple imputation can become unreliable and introduce bias not present in a complete case analysis if the imputation model is not appropriate. Epidemiologists dealing with missing data should keep in mind the potential limitations as well as the potential benefits of multiple imputation. Further work is needed to provide clearer guidelines on effective application of this method.     

Multiple imputation methods for bivariate outcomes in cluster randomised trials

Missing observations are common in cluster randomised trials. The problem is exacerbated when modelling bivariate outcomes jointly, as the proportion of complete cases is often considerably smaller than the proportion having either of the outcomes fully observed. Approaches taken to handling such missing data include the following: complete case analysis, single‐level multiple imputation that ignores the clustering, multiple imputation with a fixed effect for each cluster and multilevel multiple imputation. We contrasted the alternative approaches to handling missing data in a cost‐effectiveness analysis that uses data from a cluster randomised trial to evaluate an exercise intervention for care home residents. We then conducted a simulation study to assess the performance of these approaches on bivariate continuous outcomes, in terms of confidence interval coverage and empirical bias in the estimated treatment effects. Missing‐at‐random clustered data scenarios were simulated following a full‐factorial design. Across all the missing data mechanisms considered, the multiple imputation methods provided estimators with negligible bias, while complete case analysis resulted in biased treatment effect estimates in scenarios where the randomised treatment arm was associated with missingness. Confidence interval coverage was generally in excess of nominal levels (up to 99.8%) following fixed‐effects multiple imputation and too low following single‐level multiple imputation. Multilevel multiple imputation led to coverage levels of approximately 95% throughout. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.     

Missing data strategies for time-varying confounders in comparative effectiveness studies of non-missing time-varying exposures and right-censored outcomes

The treatment of missing data in comparative effectiveness studies with right-censored outcomes and time-varying covariates is challenging because of the multilevel structure of the data. In particular, the performance of an accessible method like multiple imputation (MI) under an imputation model that ignores the multilevel structure is unknown and has not been compared to complete-case (CC) and single imputation methods that are most commonly applied in this context. Through an extensive simulation study, we compared statistical properties among CC analysis, last value carried forward, mean imputation, the use of missing indicators, and MI-based approaches with and without auxiliary variables under an extended Cox model when the interest lies in characterizing relationships between non-missing time-varying exposures and right-censored outcomes. MI demonstrated favorable properties under a moderate missing-at-random condition (absolute bias <0.1) and outperformed CC and single imputation methods, even when the MI method did not account for correlated observations in the imputation model. The performance of MI decreased with increasing complexity such as when the missing data mechanism involved the exposure of interest, but was still preferred over other methods considered and performed well in the presence of strong auxiliary variables. We recommend considering MI that ignores the multilevel structure in the imputation model when data are missing in a time-varying confounder, incorporating variables associated with missingness in the MI models as well as conducting sensitivity analyses across plausible assumptions.     

Attrition in longitudinal studies. How to deal with missing data

The purpose of this paper was to illustrate the influence of missing data on the results of longitudinal statistical analyses [i.e., MANOVA for repeated measurements and Generalised Estimating Equations (GEE)] and to illustrate the influence of using different imputation methods to replace missing data. Besides a complete dataset, four incomplete datasets were considered: two datasets with 10% missing data and two datasets with 25% missing data. In both situations missingness was considered independent and dependent on observed data. Imputation methods were divided into cross-sectional methods (i.e., mean of series, hot deck, and cross-sectional regression) and longitudinal methods (i.e., last value carried forward, longitudinal interpolation, and longitudinal regression). Besides these, also the multiple imputation method was applied and discussed. The analyses were performed on a particular (observational) longitudinal dataset, with particular missing data patterns and imputation methods. The results of this illustration shows that when MANOVA for repeated measurements is used, imputation methods are highly recommendable (because MANOVA as implemented in the software used, uses listwise deletion of cases with a missing value). Applying GEE analysis, imputation methods were not necessary. When imputation methods were used, longitudinal imputation methods were often preferable above cross-sectional imputation methods, in a way that the point estimates and standard errors were closer to the estimates derived from the complete dataset. Furthermore, this study showed that the theoretically more valid multiple imputation method did not lead to different point estimates than the more simple (longitudinal) imputation methods. However, the estimated standard errors appeared to be theoretically more adequate, because they reflect the uncertainty in estimation caused by missing values.     

多种缺失机制共存的定量纵向缺失数据处理方法的模拟比较研究

目的 比较在处理多种缺失机制共存的定量纵向缺失数据时,基于对照的模式混合模型（PMM）、重复测量的混合效应模型（MMRM）以及多重填补法(MI)的统计性能。方法 采用Monte Carlo技术模拟产生包含完全随机缺失、随机缺失和非随机缺失中两种或三种缺失机制的定量纵向缺失数据集,评价三类处理方法的统计性能。结果 基于对照的PMM控制Ⅰ类错误率在较低水平,检验效能最低。MMRM和MI的Ⅰ类错误率可控,检验效能高于基于对照的PMM。两组疗效无差异的情况下,所有方法的估计误差相当,基于对照的PMM方法的95%置信区间覆盖率最高;有差异的情况下,各方法受符合其缺失机制假设的缺失比例大小影响。含有非随机缺失数据时,基于对照的PMM基本不高估疗效差异,95%置信区间覆盖率最高,MMRM和MI高估疗效差异,95%置信区间覆盖率较低。所有方法的95%置信区间宽度相当。结论 分析多种缺失机制共存,特别是含有非随机缺失的纵向缺失数据时,MMRM和MI的统计性能有所降低,可采用基于对照的PMM进行敏感性分析,但需要注意其具体假设,防止估计过于保守。     

Multiple imputation of cognitive performance as a repeatedly measured outcome

Longitudinal studies of cognitive performance are sensitive to dropout, as participants experiencing cognitive deficits are less likely to attend study visits, which may bias estimated associations between exposures of interest and cognitive decline. Multiple imputation is a powerful tool for handling missing data, however its use for missing cognitive outcome measures in longitudinal analyses remains limited. We use multiple imputation by chained equations (MICE) to impute cognitive performance scores of participants who did not attend the 2011–2013 exam of the Atherosclerosis Risk in Communities Study. We examined the validity of imputed scores using observed and simulated data under varying assumptions. We examined differences in the estimated association between diabetes at baseline and 20-year cognitive decline with and without imputed values. Lastly, we discuss how different analytic methods (mixed models and models fit using generalized estimate equations) and choice of for whom to impute result in different estimands. Validation using observed data showed MICE produced unbiased imputations. Simulations showed a substantial reduction in the bias of the 20-year association between diabetes and cognitive decline comparing MICE (3–4 % bias) to analyses of available data only (16–23 % bias) in a construct where missingness was strongly informative but realistic. Associations between diabetes and 20-year cognitive decline were substantially stronger with MICE than in available-case analyses. Our study suggests when informative data are available for non-examined participants, MICE can be an effective tool for imputing cognitive performance and improving assessment of cognitive decline, though careful thought should be given to target imputation population and analytic model chosen, as they may yield different estimands.     

Propensity score estimation with missing values using a multiple imputation missingness pattern (MIMP) approach

Propensity scores have been used widely as a bias reduction method to estimate the treatment effect in nonrandomized studies. Since many covariates are generally included in the model for estimating the propensity scores, the proportion of subjects with at least one missing covariate could be large. While many methods have been proposed for propensity score‐based estimation in the presence of missing covariates, little has been published comparing the performance of these methods. In this article we propose a novel method called multiple imputation missingness pattern (MIMP) and compare it with the naive estimator (ignoring propensity score) and three commonly used methods of handling missing covariates in propensity score‐based estimation (separate estimation of propensity scores within each pattern of missing data, multiple imputation and discarding missing data) under different mechanisms of missing data and degree of correlation among covariates. Simulation shows that all adjusted estimators are much less biased than the naive estimator. Under certain conditions MIMP provides benefits (smaller bias and mean‐squared error) compared with existing alternatives. Copyright © 2009 John Wiley & Sons, Ltd.     

Missing data in longitudinal studies: cross-sectional multiple imputation provides similar estimates to full-information maximum likelihood

PurposeThe aim of this research was to examine, in an exploratory manner, whether cross-sectional multiple imputation generates valid parameter estimates for a latent growth curve model in a longitudinal data set with nonmonotone missingness.MethodsA simulated longitudinal data set of N = 5000 was generated and consisted of a continuous dependent variable, assessed at three measurement occasions and a categorical time-invariant independent variable. Missing data had a nonmonotone pattern and the proportion of missingness increased from the initial to the final measurement occasion (5%–20%). Three methods were considered to deal with missing data: listwise deletion, full-information maximum likelihood, and multiple imputation. A latent growth curve model was specified and analysis of variance was used to compare parameter estimates between the full data set and missing data approaches.ResultsMultiple imputation resulted in significantly lower slope variance compared with the full data set. There were no differences in any parameter estimates between the multiple imputation and full-information maximum likelihood approaches.ConclusionsThis study suggested that in longitudinal studies with nonmonotone missingness, cross-sectional imputation at each time point may be viable and produces estimates comparable with those obtained with full-information maximum likelihood. Future research pursuing the validity of this method is warranted.     

Dealing with missing outcome data in randomized trials and observational studies

Although missing outcome data are an important problem in randomized trials and observational studies, methods to address this issue can be difficult to apply. Using simulated data, the authors compared 3 methods to handle missing outcome data: 1) complete case analysis; 2) single imputation; and 3) multiple imputation (all 3 with and without covariate adjustment). Simulated scenarios focused on continuous or dichotomous missing outcome data from randomized trials or observational studies. When outcomes were missing at random, single and multiple imputations yielded unbiased estimates after covariate adjustment. Estimates obtained by complete case analysis with covariate adjustment were unbiased as well, with coverage close to 95%. When outcome data were missing not at random, all methods gave biased estimates, but handling missing outcome data by means of 1 of the 3 methods reduced bias compared with a complete case analysis without covariate adjustment. Complete case analysis with covariate adjustment and multiple imputation yield similar estimates in the event of missing outcome data, as long as the same predictors of missingness are included. Hence, complete case analysis with covariate adjustment can and should be used as the analysis of choice more often. Multiple imputation, in addition, can accommodate the missing-not-at-random scenario more flexibly, making it especially suited for sensitivity analyses.     

Joint Longitudinal Models for Dealing With Missing at Random Data in Trial-Based Economic Evaluations

ObjectivesIn trial-based economic evaluation, some individuals are typically associated with missing data at some time point, so that their corresponding aggregated outcomes (eg, quality-adjusted life-years) cannot be evaluated. Restricting the analysis to the complete cases is inefficient and can result in biased estimates, while imputation methods are often implemented under a missing at random (MAR) assumption. We propose the use of joint longitudinal models to extend standard approaches by taking into account the longitudinal structure to improve the estimation of the targeted quantities under MAR.MethodsWe compare the results from methods that handle missingness at an aggregated (case deletion, baseline imputation, and joint aggregated models) and disaggregated (joint longitudinal models) level under MAR. The methods are compared using a simulation study and applied to data from 2 real case studies.ResultsSimulations show that, according to which data affect the missingness process, aggregated methods may lead to biased results, while joint longitudinal models lead to valid inferences under MAR. The analysis of the 2 case studies support these results as both parameter estimates and cost-effectiveness results vary based on the amount of data incorporated into the model.ConclusionsOur analyses suggest that methods implemented at the aggregated level are potentially biased under MAR as they ignore the information from the partially observed follow-up data. This limitation can be overcome by extending the analysis to a longitudinal framework using joint models, which can incorporate all the available evidence.     

Bias due to missing exposure data using complete-case analysis in the proportional hazards regression model

We studied bias due to missing exposure data in the proportional hazards regression model when using complete-case analysis (CCA). Eleven missing data scenarios were considered: one with missing completely at random (MCAR), four missing at random (MAR), and six non-ignorable missingness scenarios, with a variety of hazard ratios, censoring fractions, missingness fractions and sample sizes. When missingness was MCAR or dependent only on the exposure, there was negligible bias (2-3 per cent) that was similar to the difference between the estimate in the full data set with no missing data and the true parameter. In contrast, substantial bias occurred when missingness was dependent on outcome or both outcome and exposure. For models with hazard ratio of 3.5, a sample size of 400, 20 per cent censoring and 40 per cent missing data, the relative bias for the hazard ratio ranged between 7 per cent and 64 per cent. We observed important differences in the direction and magnitude of biases under the various missing data mechanisms. For example, in scenarios where missingness was associated with longer or shorter follow-up, the biases were notably different, although both mechanisms are MAR. The hazard ratio was underestimated (with larger bias) when missingness was associated with longer follow-up and overestimated (with smaller bias) when associated with shorter follow-up. If it is known that missingness is associated with a less frequently observed outcome or with both the outcome and exposure, CCA may result in an invalid inference and other methods for handling missing data should be considered.     

Addressing missing data in confounders when estimating propensity scores for continuous exposures

Propensity score models are frequently used to estimate causal effects in observational studies. One unresolved issue in fitting these models is handling missing values in the propensity score model covariates. As these models usually contain a large set of covariates, using only individuals with complete data significantly decreases the sample size and statistical power. Several missing data imputation approaches have been proposed, including multiple imputation (MI), MI with missingness pattern (MIMP), and treatment mean imputation. Generalized boosted modeling (GBM), which is a nonparametric approach to estimate propensity scores, can automatically handle missingness in the covariates. Although the performance of MI, MIMP, and treatment mean imputation have previously been compared for binary treatments, they have not been compared for continuous exposures or with single imputation and GBM. We compared these approaches in estimating the generalized propensity score (GPS) for a continuous exposure in both a simulation study and in empirical data. Using GBM with the incomplete data to estimate the GPS did not perform well in the simulation. Missing values should be imputed before estimating propensity scores using GBM or any other approach for estimating the GPS.     

THE ANALYSIS OF INCOMPLETE DATA IN THE THREE-PERIOD TWO-TREATMENT CROSS-OVER DESIGN FOR CLINICAL TRIALS

The additional time to complete a three-period two-treatment (3P2T) cross-over trial may cause a greater number of patient dropouts than with a two-period trial. This paper develops maximum likelihood (ML), single imputation and multiple imputation missing data analysis methods for the 3P2T cross-over designs. We use a simulation study to compare and contrast these methods with one another and with the benchmark method of missing data analysis for cross-over trials, the complete case (CC) method. Data patterns examined include those where the missingness differs between the drug types and depends on the unobserved data. Depending on the missing data mechanism and the rate of missingness of the data, one can realize substantial improvements in information recovery by using data from the partially completed patients. We recommend these approaches for the 3P2T cross-over designs.     

Binary variable multiple‐model multiple imputation to address missing data mechanism uncertainty: application to a smoking cessation trial

The true missing data mechanism is never known in practice. We present a method for generating multiple imputations for binary variables, which formally incorporates missing data mechanism uncertainty. Imputations are generated from a distribution of imputation models rather than a single model, with the distribution reflecting subjective notions of missing data mechanism uncertainty. Parameter estimates and standard errors are obtained using rules for nested multiple imputation. Using simulation, we investigate the impact of missing data mechanism uncertainty on post‐imputation inferences and show that incorporating this uncertainty can increase the coverage of parameter estimates. We apply our method to a longitudinal smoking cessation trial where nonignorably missing data were a concern. Our method provides a simple approach for formalizing subjective notions regarding nonresponse and can be implemented using existing imputation software. Copyright © 2014 John Wiley & Sons, Ltd.     

Multiple imputation of missing dual-energy X-ray absorptiometry data in the National Health and Nutrition Examination Survey

In 1999, dual-energy x-ray absorptiometry (DXA) scans were added to the National Health and Nutrition Examination Survey (NHANES) to provide information on soft tissue composition and bone mineral content. However, in 1999-2004, DXA data were missing in whole or in part for about 21 per cent of the NHANES participants eligible for the DXA examination; and the missingness is associated with important characteristics such as body mass index and age. To handle this missing-data problem, multiple imputation of the missing DXA data was performed. Several features made the project interesting and challenging statistically, including the relationship between missingness on the DXA measures and the values of other variables; the highly multivariate nature of the variables being imputed; the need to transform the DXA variables during the imputation process; the desire to use a large number of non-DXA predictors, many of which had small amounts of missing data themselves, in the imputation models; the use of lower bounds in the imputation procedure; and relationships between the DXA variables and other variables, which helped both in creating and evaluating the imputations. This paper describes the imputation models, methods, and evaluations for this publicly available data resource and demonstrates properties of the imputations via examples of analyses of the data. The analyses suggest that imputation helps to correct biases that occur in estimates based on the data without imputation, and that it helps to increase the precision of estimates as well. Moreover, multiple imputation usually yields larger estimated standard errors than those obtained with single imputation.     

A functional multiple imputation approach to incomplete longitudinal data

In designed longitudinal studies, information from the same set of subjects are collected repeatedly over time. The longitudinal measurements are often subject to missing data which impose an analytic challenge. We propose a functional multiple imputation approach modeling longitudinal response profiles as smooth curves of time under a functional mixed effects model. We develop a Gibbs sampling algorithm to draw model parameters and imputations for missing values, using a blocking technique for an increased computational efficiency. In an illustrative example, we apply a multiple imputation analysis to data from the Panel Study of Income Dynamics and the Child Development Supplement to investigate the gradient effect of family income on children's health status. Our simulation study demonstrates that this approach performs well under varying modeling assumptions on the time trajectory functions and missingness patterns.     

The use of missingness screens in clinical epidemiologic research has implications for regression modeling

OBJECTIVE: Properly handling missing data is a challenge, especially when working with older populations that have high levels of morbidity and mortality. We illustrate methods for understanding whether missing values are ignorable and describe implications of their use in regression modeling. STUDY DESIGN AND SETTING: The use of missingness screens such as Little's missing completely at random "MCAR test" (1988) and the "Index of Sensitivity to Nonignorability (ISNI)" by Troxel and colleagues (2004)introduces complications for regression modeling, and, particularly, for risk factor selection. In a case study of older patients with simulated missing values for a delirium outcome set in a 14-bed medical intensive care unit, we outline a model fitting process that incorporates the use of missingness screens, controls for collinearity, and selects variables based on model fit. RESULTS: The proposed model fitting process identifies more actual risk factors for ICU delirium than does a complete case analysis. CONCLUSION: Use of imputation and other methods for handling missing data assist in the identification of risk factors. They do so accurately only when correct assumptions are made about the nature of missing data. Missingness screens enable researchers to investigate these assumptions.     

Bias arising from missing data in predictive models

OBJECTIVE: The purpose of this study is to determine the effect of three common approaches to handling missing data on the results of a predictive model. STUDY DESIGN AND SETTING: Monte Carlo simulation study using simulated data was used. A baseline logistic regression using complete data was performed to predict hospital admission, based on the white blood cell count (WBC) (dichotomized as normal or high), presence of fever, or procedures performed (PROC). A series of simulations was then performed in which WBC data were deleted for varying proportions (15-85%) of patients under various patterns of missingness. Three analytic approaches were used: analysis restricted to cases with complete data, missing data assumed to be normal (MAN), and use of imputed values. RESULTS: In the baseline analysis, all three predictors were all significantly associated with admission. Using either the MAN approach or imputation, the odds ratio (OR) for WBC was substantially over- or underestimated depending on the missingness pattern, and there was considerable bias toward the null in the OR estimates for fever. In the CC analyses, OR for WBC was consistently biased toward the null, OR for PROC was biased away from the null, and the OR for fever was biased toward or away from the null. Estimates for overall model discrimination were substantially biased using all analytic approaches. CONCLUSIONS: All three methods of handling large amounts of missing data can lead to biased estimates of the OR and of model performance in predictive models. Predictor variables that are measured inconsistently can affect the validity of such models.     

A comparison of two methods for the estimation of precision with incomplete longitudinal data, jointly modelled with a time-to-event outcome

Several methods for the estimation and comparison of rates of change in longitudinal studies with staggered entry and informative drop-outs have been recently proposed. For multivariate normal linear models, REML estimation is used. There are various approaches to maximizing the corresponding log-likelihood; in this paper we use a restricted iterative generalized least squares method (RIGLS) combined with a nested EM algorithm. An important statistical problem in such approaches is the estimation of the standard errors adjusted for the missing data (observed data information matrix). Louis has provided a general technique for computing the observed data information in terms of completed data quantities within the EM framework. The multiple imputation (MI) method for obtaining variances can be regarded as an alternative to this. The aim of this paper is to develop, apply and compare the Louis and a modified MI method in the setting of longitudinal studies where the source of missing data is either death or disease progression (informative) or end of the study (assumed non-informative). Longitudinal data are simultaneously modelled with the missingness process. The methods are illustrated by modelling CD4 count data from an HIV-1 clinical trial and evaluated through simulation studies. Both methods, Louis and MI, are used with Monte Carlo simulations of the missing data using the appropriate conditional distributions, the former with 100 simulations, the latter with 5 and 10. It is seen that naive SEs based on the completed data likelihood can be seriously biased. This bias was largely corrected by Louis and modified MI methods, which gave broadly similar estimates. Given the relative simplicity of the modified MI method, it may be preferable.