Combining the complete-data and nonresponse models for drawing imputations under MAR

In multiple imputation (MI), the resulting estimates are consistent if the imputation model is correct. To specify the imputation model, it is recommended to combine two sets of variables: those that are related to the incomplete variable and those that are related to the missingness mechanism. Several possibilities exist, but it is not clear how they perform in practice. The method that simply groups all variables together into the imputation model and four other methods that are based on the propensity scores are presented. Two of them are new and have not been used in the context of MI. The performance of the methods is investigated by a simulation study under different missing at random mechanisms for different types of variables. We conclude that all methods, except for one method based on the propensity scores, perform well. It turns out that as long as the relevant variables are taken into the imputation model, the form of the imputation model has only a minor effect in the quality of the imputations.     

A joint model of binary and longitudinal data with non-ignorable missingness,with application to marital stress and late-life major depression in women

Understanding how long-term marital stress affects major depressive disorder (MDD) in older women has clinical implications for the treatment of women at risk. In this paper, we consider the problem of predicting MDD in older women (mean age 60) from a marital stress scale administered four times during the preceding 20-year period, with a greater dropout by women experiencing marital stress or MDD. To analyze these data, we propose a Bayesian joint model consisting of: (1) a linear mixed effects model for the longitudinal measurements, (2) a generalized linear model for the binary primary endpoint, and (3) a shared parameter model for the missing data mechanism. Our analysis indicates that MDD in older women is significantly associated with higher levels of prior marital stress and increasing marital stress over time, although there is a generally decreasing trend in marital stress. This is the first study to propose a joint model for incompletely observed longitudinal measurements, a binary primary endpoint, and non-ignorable missing data; a comparison shows that the joint model yields better predictive accuracy than a two-stage model. These findings suggest that women who experience marital stress in mid-life need treatment to help prevent late-life MDD, which has serious consequences for older persons.     

A flexible marginal modelling strategy for non-monotone missing data

Summary.  Much research has been devoted to modelling strategies for longitudinal data with missingness, recently especially within the missingness not at random context. In this paper, the relatively unexplored but practically highly relevant domain of non-monotone missingness with multivariate ordinal responses is broached. For this, a dedicated version of the multivariate Dale model is formulated. Furthermore, we also assess the sensitivity of these models to their assumptions, by using the technique of global influence.     

Pattern-mixture models for categorical outcomes with non-monotone missingness

Although most models for incomplete longitudinal data are formulated within the selection model framework, pattern-mixture models have gained considerable interest in recent years [R.J.A. Little, Pattern-mixture models for multivariate incomplete data, J. Am. Stat. Assoc. 88 (1993), pp. 125–134; R.J.A. Lrittle, A class of pattern-mixture models for normal incomplete data, Biometrika 81 (1994), pp. 471–483], since it is often argued that selection models, although many are identifiable, should be approached with caution, especially in the context of MNAR models [R.J. Glynn, N.M. Laird, and D.B. Rubin, Selection modeling versus mixture modeling with nonignorable nonresponse, in Drawing Inferences from Self-selected Samples, H. Wainer, ed., Springer-Verlag, New York, 1986, pp. 115–142]. In this paper, the focus is on several strategies to fit pattern-mixture models for non-monotone categorical outcomes. The issue of under-identification in pattern-mixture models is addressed through identifying restrictions. Attention will be given to the derivation of the marginal covariate effect in pattern-mixture models for non-monotone categorical data, which is less straightforward than in the case of linear models for continuous data. The techniques developed will be used to analyse data from a clinical study in psychiatry.     

Multiple imputation using multivariate gh transformations

Multiple imputation has emerged as a popular approach to handling data sets with missing values. For incomplete continuous variables, imputations are usually produced using multivariate normal models. However, this approach might be problematic for variables with a strong non-normal shape, as it would generate imputations incoherent with actual distributions and thus lead to incorrect inferences. For non-normal data, we consider a multivariate extension of Tukey's gh distribution/transformation [38] to accommodate skewness and/or kurtosis and capture the correlation among the variables. We propose an algorithm to fit the incomplete data with the model and generate imputations. We apply the method to a national data set for hospital performance on several standard quality measures, which are highly skewed to the left and substantially correlated with each other. We use Monte Carlo studies to assess the performance of the proposed approach. We discuss possible generalizations and give some advices to practitioners on how to handle non-normal incomplete data.     

Analysis of ordinal outcomes with longitudinal covariates subject to missingness

We propose a mixture model for data with an ordinal outcome and a longitudinal covariate that is subject to missingness. Data from a tailored telephone delivered, smoking cessation intervention for construction laborers are used to illustrate the method, which considers as an outcome a categorical measure of smoking cessation, and evaluates the effectiveness of the motivational telephone interviews on this outcome. We propose two model structures for the longitudinal covariate, for the case when the missing data are missing at random, and when the missing data mechanism is non-ignorable. A generalized EM algorithm is used to obtain maximum likelihood estimates.     

Effect of heteroscedasticity between treatment groups on mixed‐effects models for repeated measures

Mixed‐effects models for repeated measures (MMRM) analyses using the Kenward‐Roger method for adjusting standard errors and degrees of freedom in an “unstructured” (UN) covariance structure are increasingly becoming common in primary analyses for group comparisons in longitudinal clinical trials. We evaluate the performance of an MMRM‐UN analysis using the Kenward‐Roger method when the variance of outcome between treatment groups is unequal. In addition, we provide alternative approaches for valid inferences in the MMRM analysis framework. Two simulations are conducted in cases with (1) unequal variance but equal correlation between the treatment groups and (2) unequal variance and unequal correlation between the groups. Our results in the first simulation indicate that MMRM‐UN analysis using the Kenward‐Roger method based on a common covariance matrix for the groups yields notably poor coverage probability (CP) with confidence intervals for the treatment effect when both the variance and the sample size between the groups are disparate. In addition, even when the randomization ratio is 1:1, the CP will fall seriously below the nominal confidence level if a treatment group with a large dropout proportion has a larger variance. Mixed‐effects models for repeated measures analysis with the Mancl and DeRouen covariance estimator shows relatively better performance than the traditional MMRM‐UN analysis method. In the second simulation, the traditional MMRM‐UN analysis leads to bias of the treatment effect and yields notably poor CP. Mixed‐effects models for repeated measures analysis fitting separate UN covariance structures for each group provides an unbiased estimate of the treatment effect and an acceptable CP. We do not recommend MMRM‐UN analysis using the Kenward‐Roger method based on a common covariance matrix for treatment groups, although it is frequently seen in applications, when heteroscedasticity between the groups is apparent in incomplete longitudinal data.     

An application of nonparametric regression to missing data in large market surveys

Non-response (or missing data) is often encountered in large-scale surveys. To enable the behavioural analysis of these data sets, statistical treatments are commonly applied to complete or remove these data. However, the correctness of such procedures critically depends on the nature of the underlying missingness generation process. Clearly, the efficacy of applying either case deletion or imputation procedures rests on the unknown missingness generation mechanism. The contribution of this paper is twofold. The study is the first to propose a simple sequential method to attempt to identify the form of missingness. Second, the effectiveness of the tests is assessed by generating (experimentally) nine missing data sets by imposed MCAR, MAR and NMAR processes, with data removed.     

A unified empirical likelihood approach for testing MCAR and subsequent estimation

For an estimation with missing data, a crucial step is to determine if the data are missing completely at random (MCAR), in which case a complete‐case analysis would suffice. Most existing tests for MCAR do not provide a method for a subsequent estimation once the MCAR is rejected. In the setting of estimating means, we propose a unified approach for testing MCAR and the subsequent estimation. Upon rejecting MCAR, the same set of weights used for testing can then be used for estimation. The resulting estimators are consistent if the missingness of each response variable depends only on a set of fully observed auxiliary variables and the true outcome regression model is among the user‐specified functions for deriving the weights. The proposed method is based on the calibration idea from survey sampling literature and the empirical likelihood theory.     

间歇低氧对大鼠血管内皮细胞生长因子表达的影响

目的观察慢性间歇低氧对大鼠血管内皮细胞生长因子（VEGF）表达的影响。方法72只雄性Wistar大鼠随机均分为间歇低氧组（IH组）、实验对照组（SC组）和空白对照组（UC组）。IH组大鼠循环给予充入氮气和压缩空气（每一次循环60秒,使舱内最低氧浓度达4%～6%,然后恢复至21%,8h/d）;向SC组舱内循环充入压缩空气,UC组不予任何干预。应用免疫组化法（ELASA）检测各组大鼠分别在3,6,9周末血清VEGF的表达水平。结果IH组大鼠3、6、9周VEGF表达均增加,并且随间歇低氧时间的延长而VEGF水平逐渐升高,从第3周[（193.16±102.13）pg/ml]开始高于SC组[（154.08±89.79）pg/ml]和UC组[（118.13±64.26）pg/ml]水平（P〈0.05,P〈0.01）,第9周末IH组[（256.15±113.58）pg/ml]显著高于SC组[（154.36±90.32）pg/ml]（P〈0.01）,两组均明显高于UC组（P〈0.05）,IH组大鼠VEGF水平与间歇低氧时间呈正相关（P〈0.05）。结论慢性间歇低氧可以诱导大鼠VEGF表达增强,血清VEGF表达增强与血管内皮功能受损有关,提示VEGF对慢性间歇低氧有内皮保护作用。