Missing data: Discussion points from the PSI missing data expert group

The Points to Consider Document on Missing Data was adopted by the Committee of Health and Medicinal Products (CHMP) in December 2001. In September 2007 the CHMP issued a recommendation to review the document, with particular emphasis on summarizing and critically appraising the pattern of drop‐outs, explaining the role and limitations of the ‘last observation carried forward’ method and describing the CHMP's cautionary stance on the use of mixed models. In preparation for the release of the updated guidance document, statisticians in the Pharmaceutical Industry held a one‐day expert group meeting in September 2008. Topics that were debated included minimizing the extent of missing data and understanding the missing data mechanism, defining the principles for handling missing data and understanding the assumptions underlying different analysis methods. A clear message from the meeting was that at present, biostatisticians tend only to react to missing data. Limited pro‐active planning is undertaken when designing clinical trials. Missing data mechanisms for a trial need to be considered during the planning phase and the impact on the objectives assessed. Another area for improvement is in the understanding of the pattern of missing data observed during a trial and thus the missing data mechanism via the plotting of data; for example, use of Kaplan–Meier curves looking at time to withdrawal. Copyright © 2009 John Wiley & Sons, Ltd.     

论信息空间责任人的追踪机制

实名制是一种简单化的责任人追踪办法,其机理是事先将信息空间主体一对一地映射到现实空间,再借用现实空间已经建立起的责任人追踪制度来解决信息空间的责任人追踪问题。然而,信息空间的魅力在于,主体在自我感觉隐身的前提下可以获得自由感,如果要求信息空间主体在行为之前就将身份映射到现实空间,其隐身自由感则荡然无存。所以,让信息主体脱掉隐身衣、“警惕且谨慎”地生存于信息空间的办法,在解决信息责任人追踪问题的同时,也从根本上消灭了信息空间的隐身快感。建立信息空间与现实空间之间的主体映射数据库是方便、快捷、低成本地追踪信息空间责任人的有效手段,其既将信息责任人追踪成本降低到可容忍限度内,又不至于过分伤害信息空间的隐身自由感。映射数据库属于国家秘密,非经合法授权不可使用。     

论侵权归责原则的内涵与外延

对作为侵权法核心内容的归责原则学界理解不一,但归责原则的发展史就是归责原则内涵的体现史,究其历史可以发现,归责原则的实质是立法者追究行为人法律责任所依据的理由。无过错责任原则并非单个归责原则而是多个归责原则的概括,其中最为重要是危险责任原则。当前私法中,主要存在过错责任原则与危险责任原则,而这两原则之间是重叠交叉同时适用的关系。     

Estimating the population mean in the case of missing data using simple random sampling

In this paper, we suggest three new ratio estimators of the population mean using quartiles of the auxiliary variable when there are missing data from the sample units. The suggested estimators are investigated under the simple random sampling method. We obtain the mean square errors equations for these estimators. The suggested estimators are compared with the sample mean and ratio estimators in the case of missing data. Also, they are compared with estimators in Singh and Horn [Compromised imputation in survey sampling, Metrika 51 (2000), pp. 267–276], Singh and Deo [Imputation by power transformation, Statist. Papers 45 (2003), pp. 555–579], and Kadilar and Cingi [Estimators for the population mean in the case of missing data, Commun. Stat.-Theory Methods, 37 (2008), pp. 2226–2236] and present under which conditions the proposed estimators are more efficient than other estimators. In terms of accuracy and of the coverage of the bootstrap confidence intervals, the suggested estimators performed better than other estimators.     

Effect of Violation of the Normal Assumption on MI and ML Estimators in the Analysis of Incomplete Data

Asymptotic distributions of normal-theory-based ML/MI estimators are studied in a simple regression model under general distributions with MAR missing data. The asymptotic variance of the ML/MI estimator of residuals’ variance is explicitly derived, from which it follows that the kurtosis of the error distribution primarily affects the asymptotic variance. Results of numerical simulations conducted to study finite sample properties of the estimators, conformed largely to the asymptotic results, and they also indicated interesting findings particularly for small samples, which do not follow from the asymptotic property. It is concluded that the ML estimators perform best in the situation studied here.     

Practical Advice on How to Impute Continuous Data When the Ultimate Interest Centers on Dichotomized Outcomes Through Pre-Specified Thresholds

Multiple imputation under the multivariate normality assumption has often been regarded as a viable model-based approach in dealing with incomplete continuous data in the last two decades. A situation where the measurements are taken on a continuous scale with an ultimate interest in dichotomized versions through discipline-specific thresholds is not uncommon in applied research, especially in medical and social sciences. In practice, researchers generally tend to impute missing values for continuous outcomes under a Gaussian imputation model, and then dichotomize them via commonly-accepted cut-off points. An alternative strategy is creating multiply imputed data sets after dichotomization under a log-linear imputation model that uses a saturated multinomial structure. In this work, the performances of the two imputation methods were examined on a fairly wide range of simulated incomplete data sets that exhibit varying distributional characteristics such as skewness and multimodality. Behavior of efficiency and accuracy measures was explored to determine the extent to which the procedures work properly. The conclusion drawn is that dichotomization before carrying out a log-linear imputation should be the preferred approach except for a few special cases. I recommend that researchers use the atypical second strategy whenever the interest centers on binary quantities that are obtained through underlying continuous measurements. A possible explanation is that erratic/idiosyncratic aspects that are not accommodated by a Gaussian model are probably transformed into better-behaving discrete trends in this particular missing-data setting. This premise outweighs the assertion that continuous variables inherently carry more information, leading to a counter-intuitive, but potentially useful result for practitioners.     

对侵权法归责原则的思考

侵权法的归责问题是侵权法的核心问题,理论界对此争论较多。文章对我国现有侵权归责原则理论进行分析,认为有关理论存在法理和认识上的缺陷,作者提出了自己一些观点,并建议将我国侵权法归责原则确立为过错责任和严格责任的统一。     

General purpose multiply robust data integration procedures for handling nonprobability samples

In recent years, there has been an increased interest in combining probability and nonprobability samples. Nonprobability sample are cheaper and quicker to conduct but the resulting estimators are vulnerable to bias as the participation probabilities are unknown. To adjust for the potential bias, estimation procedures based on parametric or nonparametric models have been discussed in the literature. However, the validity of the resulting estimators relies heavily on the validity of the underlying models. Also, nonparametric approaches may suffer from the curse of dimensionality and poor efficiency. We propose a data integration approach by combining multiple outcome regression models and propensity score models. The proposed approach can be used for estimating general parameters including totals, means, distribution functions, and percentiles. The resulting estimators are multiply robust in the sense that they remain consistent if all but one model are misspecified. The asymptotic properties of point and variance estimators are established. The results from a simulation study show the benefits of the proposed method in terms of bias and efficiency. Finally, we apply the proposed method using data from the Korea National Health and Nutrition Examination Survey and data from the National Health Insurance Sharing Services.