GRAPHICAL SENSITIVITY ANALYSIS WITH DIFFERENT METHODS OF IMPUTATION FOR A TRIAL WITH PROBABLE NON‐IGNORABLE MISSING DATA

Graphical sensitivity analyses have recently been recommended for clinical trials with non‐ignorable missing outcome. We demonstrate an adaptation of this methodology for a continuous outcome of a trial of three cognitive‐behavioural therapies for mild depression in primary care, in which one arm had unexpectedly high levels of missing data. Fixed‐value and multiple imputations from a normal distribution (assuming either varying mean and fixed standard deviation, or fixed mean and varying standard deviation) were used to obtain contour plots of the contrast estimates with their P‐values superimposed, their confidence intervals, and the root mean square errors. Imputation was based either on the outcome value alone, or on change from baseline. The plots showed fixed‐value imputation to be more sensitive than imputing from a normal distribution, but the normally distributed imputations were subject to sampling noise. The contours of the sensitivity plots were close to linear in appearance, with the slope approximately equal to the ratio of the proportions of subjects with missing data in each trial arm.     

论个人信息网络侵权责任多元归责原则之确立基础

从侵权责任归责原则的发展历史看,技术社会形态、法哲学理论和正义观念构成其确立基础。网络社会里,由于多种技术社会形态并存发展、行为主体与权利人关系多样化、侵害后果状态和归责事由多样化、价值需求和责任形式多样化发展等要求,要实现网络中个人信息权益保护与行为自由的平衡,应当确立个人信息网络侵权责任的多元归责原则：过错责任原则、过错推定责任原则与无过错责任原则。     

Spatial modelling of the two‐party preferred vote in Australian federal elections: 2001–2016

We examine the relationships between electoral socio‐demographic characteristics and two‐party preferences in the six Australian federal elections held between 2001 and 2016. Socio‐demographic information is derived from the Australian Census which occurs every 5 years. Since a census is not directly available for each election, an imputation method is employed to estimate census data for the electorates at the time of each election. This accounts for both spatial and temporal changes in electoral characteristics between censuses. To capture any spatial heterogeneity, a spatial error model is estimated for each election, which incorporates a spatially structured random effect vector. Over time, the impact of most socio‐demographic characteristics that affect electoral two‐party preference do not vary, with age distribution, industry of work, incomes, household mobility and relationships having strong effects in each of the six elections. Education and unemployment are among those that have varying effects. All data featured in this study have been contributed to the eechidna R package (available on CRAN).     

侵权责任法归责原则体系分析

归责原则是侵权责任法内容和体系建立的基础,全面理解归责原则,才能对侵权责任法有深入的了解。我国侵权责任法包括过错责任、过错推定和严格责任三项归责原则,三原则之间以过错责任为基础建立起内在联系,层次分明,衔接过渡,具有逻辑性。     

产品责任原则的经济分析

作者认为，产品责任立法的基本宗旨是促使生产者和销售者将其强加于用户和消费者的外部成本内在化。从经济学角度分析，我国产品质量责任法同时规定了对生产者的严格责任原则和对销售者的契约原则及过失原则，从而为用户和消费者的选择适用提供了交易便利和自由。     

Inference methods for saturated models in longitudinal clinical trials with incomplete binary data

In the longitudinal studies with binary response, it is often of interest to estimate the percentage of positive responses at each time point and the percentage of having at least one positive response by each time point. When missing data exist, the conventional method based on observed percentages could result in erroneous estimates. This study demonstrates two methods of using expectation-maximization (EM) and data augmentation (DA) algorithms in the estimation of the marginal and cumulative probabilities for incomplete longitudinal binary response data. Both methods provide unbiased estimates when the missingness mechanism is missing at random (MAR) assumption. Sensitivity analyses have been performed for cases when the MAR assumption is in question.     

Handling incomplete Quality-of-Life Data

Incomplete data sets are often encountered in theanalysis of quality-of-life (QOL) data. The incompleteness arisesfrom two major sources, namely, missing responses and artificialquantification of response categories. Shen and Lai (1998a)propose using Optimal Scaling (OS) to tackle the problem. The OSmethod based on numerical iterative approach attempts to restorethe continuous property of the measurements and provide estimatesfor missing responses. However, the OS leads to convergenceproblem when there are many missing values in the data set; andit incorporates no mechanisms to provide the standard errors ofthe mean estimates when missing values are filled. Hot-deckimputation is therefore suggested. This paper presents asimulation study to show that the random hot-deck imputationyields reasonable estimates for the population mean and generallypreserves the distribution of the population. In addition, whenapplying the random hot-deck imputation, valid estimates for thestandard error of the mean estimate can be obtained using thevariance formula due to Lai (1998). With hot-deck imputationtaking care of the missing responses and OS quantifying theresponse categories, it is postulated that the problem of dataincompleteness can be more satisfactorily handled. By applyingthe proposed techniques to real survey data, this paper alsopresents the change of the QOL of Hong Kong residents in the lastdecade leading to the turning point of the metropolis in 1997.     

Treatment and reporting of item-level missing data in social science research

Most quantitative studies in the social sciences suffer from missing data. However, despite the large availability of documents and software to treat such data, it appears that many social scientists do not apply good practices regarding missing data. We analyzed quantitative papers published in 2017 in six top-level social science journals. Item-level missing data was found in at least 69.5% of the papers, but their presence was explicitly reported in only 44.4% of all analyzed papers. Moreover, in the majority of cases, the treatments applied to missing data were incorrect, with many uses of deletion methods that are known to produce biased results and to reduce statistical power. The impact of missing data and of their treatment on results was barely discussed. Results show that social scientists underestimate the impact of missing data on their research and that they should pay more attention to the way such data are treated.     

Efficient estimation in a regression model with missing responses

This article examines methods to efficiently estimate the mean response in a linear model with an unknown error distribution under the assumption that the responses are missing at random. We show how the asymptotic variance is affected by the estimator of the regression parameter, and by the imputation method. To estimate the regression parameter, the ordinary least squares is efficient only if the error distribution happens to be normal. If the errors are not normal, then we propose a one step improvement estimator or a maximum empirical likelihood estimator to efficiently estimate the parameter.To investigate the imputation’s impact on the estimation of the mean response, we compare the listwise deletion method and the propensity score method (which do not use imputation at all), and two imputation methods. We demonstrate that listwise deletion and the propensity score method are inefficient. Partial imputation, where only the missing responses are imputed, is compared to full imputation, where both missing and non-missing responses are imputed. Our results reveal that, in general, full imputation is better than partial imputation. However, when the regression parameter is estimated very poorly, the partial imputation will outperform full imputation. The efficient estimator for the mean response is the full imputation estimator that utilizes an efficient estimator of the parameter.