Bayesian methods for dealing with missing data problems

Missing data, a common but challenging issue in most studies, may lead to biased and inefficient inferences if handled inappropriately. As a natural and powerful way for dealing with missing data, Bayesian approach has received much attention in the literature. This paper reviews the recent developments and applications of Bayesian methods for dealing with ignorable and non-ignorable missing data. We firstly introduce missing data mechanisms and Bayesian framework for dealing with missing data, and then introduce missing data models under ignorable and non-ignorable missing data circumstances based on the literature. After that, important issues of Bayesian inference, including prior construction, posterior computation, model comparison and sensitivity analysis, are discussed. Finally, several future issues that deserve further research are summarized and concluded.     

Semiparametric inference for estimating equations with nonignorably missing covariates

We consider statistical inference of unknown parameters in estimating equations (EEs) when some covariates have nonignorably missing values, which is quite common in practice but has rarely been discussed in the literature. When an instrument, a fully observed covariate vector that helps identifying parameters under nonignorable missingness, is available, the conditional distribution of the missing covariates given other covariates can be estimated by the pseudolikelihood method of Zhao and Shao [(2015), ‘Semiparametric pseudo likelihoods in generalised linear models with nonignorable missing data’, Journal of the American Statistical Association, 110, 1577–1590)] and be used to construct unbiased EEs. These modified EEs then constitute a basis for valid inference by empirical likelihood. Our method is applicable to a wide range of EEs used in practice. It is semiparametric since no parametric model for the propensity of missing covariate data is assumed. Asymptotic properties of the proposed estimator and the empirical likelihood ratio test statistic are derived. Some simulation results and a real data analysis are presented for illustration.     

Estimation of Stratified Mark‐Specific Proportional Hazards Models with Missing Marks

Abstract. An objective of randomized placebo‐controlled preventive HIV vaccine efficacy trials is to assess the relationship between the vaccine effect to prevent infection and the genetic distance of the exposing HIV to the HIV strain represented in the vaccine construct. Motivated by this objective, recently a mark‐specific proportional hazards (PH) model with a continuum of competing risks has been studied, where the genetic distance of the transmitting strain is the continuous ‘mark’ defined and observable only in failures. A high percentage of genetic marks of interest may be missing for a variety of reasons, predominantly because rapid evolution of HIV sequences after transmission before a blood sample is drawn from which HIV sequences are measured. This research investigates the stratified mark‐specific PH model with missing marks where the baseline functions may vary with strata. We develop two consistent estimation approaches, the first based on the inverse probability weighted complete‐case (IPW) technique, and the second based on augmenting the IPW estimator by incorporating auxiliary information predictive of the mark. We investigate the asymptotic properties and finite‐sample performance of the two estimators, and show that the augmented IPW estimator, which satisfies a double robustness property, is more efficient.     

Handling of missing data in long‐term clinical trials: a case study

Missing data in clinical trials is a well‐known problem, and the classical statistical methods used can be overly simple. This case study shows how well‐established missing data theory can be applied to efficacy data collected in a long‐term open‐label trial with a discontinuation rate of almost 50%. Satisfaction with treatment in chronically constipated patients was the efficacy measure assessed at baseline and every 3 months postbaseline. The improvement in treatment satisfaction from baseline was originally analyzed with a paired t‐test ignoring missing data and discarding the correlation structure of the longitudinal data. As the original analysis started from missing completely at random assumptions regarding the missing data process, the satisfaction data were re‐examined, and several missing at random (MAR) and missing not at random (MNAR) techniques resulted in adjusted estimate for the improvement in satisfaction over 12 months. Throughout the different sensitivity analyses, the effect sizes remained significant and clinically relevant. Thus, even for an open‐label trial design, sensitivity analysis, with different assumptions for the nature of dropouts (MAR or MNAR) and with different classes of models (selection, pattern‐mixture, or multiple imputation models), has been found useful and provides evidence towards the robustness of the original analyses; additional sensitivity analyses could be undertaken to further qualify robustness. Copyright © 2012 John Wiley & Sons, Ltd.     

追寻“真苏轼”——从《一本书读懂中国美术史》说起

研究探讨"真苏轼",应严守学术规范,作正确解读。以《一本书读懂中国美术史》为例,可见误读频仍。该文用不足两千字的篇幅介绍苏轼生平及其文人画理论,竟有十来处违背学术规范,甚至出现令人啼笑皆非的漏误。此类所谓论著歪曲了苏轼本真,因此需呼吁:"真苏轼"不要离去,"真学者"与你同在。     

Motherhood status and union formation in Moshi,Tanzania 2002–2003

Age at first union is increasing throughout much of sub-Saharan Africa at the same time that not all couples are waiting for marriage before their first sexual intercourse. We assessed the effect of a premarital first birth on entrance into a first union in an urban area in East Africa—Moshi, Tanzania. The data come from the Moshi Infertility Survey of 2002–2003. Women who spent less than a year in single motherhood were significantly more likely than childless women to enter into a first union, although the magnitude of this relationship was weaker for more recent cohorts. Women who had been single mothers for 5 or more years (about two-thirds of women with a premarital birth) were significantly less likely than women without children to enter into a first union.     

从传统制度到制度缺失——箐口村的垃圾处理问题

1998年之前,箐口村是一个没有现代厕所和垃圾处理场的村寨。此后,旅游和政府介入,该村的垃圾处理便按照村民原来的方式和政府规定的方式进行,即回归自然、填埋、焚烧。2008年世博集团和当地旅游局签订旅游开发协议,聘请专门的卫生保洁员对箐口民俗村的卫生状况进行维护,但处理成效却无法达标。随着旅游的扩大,该村的垃圾开始成灾。...     

Toward Best Practices in Analyzing Datasets with Missing Data: Comparisons and Recommendations

Although several methods have been developed to allow for the analysis of data in the presence of missing values, no clear guide exists to help family researchers in choosing among the many options and procedures available. We delineate these options and examine the sensitivity of the findings in a regression model estimated in three random samples from the National Survey of Families and Households (n = 250–2,000). These results, combined with findings from simulation studies, are used to guide answers to a set of 10 common questions asked by researchers when selecting a missing data approach. Modern missing data techniques were found to perform better than traditional ones, but differences between the types of modern approaches had minor effects on the estimates and substantive conclusions. Our findings suggest that the researcher has considerable flexibility in selecting among modern options for handling missing data.     

基于数据缺失率和缺失模式的多重插补误差研究

文章通过多重插补方法对不同缺失率和缺失模式的多变量缺失样本进行插补,研究了多重插补误差与缺失率和缺失模式的依赖关系。结果表明,当缺失率为0~15%时,多重插补误差与缺失率呈线性关系;当缺失率大于15%时,两者呈偏离线性关系。多重插补误差与缺失模式的方差均值比呈正相关性,当方差均值比越大时,误差也越大。     

Effects of correlation and missing data on sample size estimation in longitudinal clinical trials

In longitudinal clinical trials, a common objective is to compare the rates of changes in an outcome variable between two treatment groups. Generalized estimating equation (GEE) has been widely used to examine if the rates of changes are significantly different between treatment groups due to its robustness to misspecification of the true correlation structure and randomly missing data. The sample size formula for repeated outcomes is based on the assumption of missing completely at random and a large sample approximation. A simulation study is conducted to investigate the performance of GEE sample size formula with small sample sizes, damped exponential family of correlation structure and non‐ignorable missing data. Copyright © 2008 John Wiley & Sons, Ltd.