A win ratio approach to comparing continuous non‐normal outcomes in clinical trials

Clinical trials are often designed to compare continuous non‐normal outcomes. The conventional statistical method for such a comparison is a non‐parametric Mann–Whitney test, which provides a P‐value for testing the hypothesis that the distributions of both treatment groups are identical, but does not provide a simple and straightforward estimate of treatment effect. For that, Hodges and Lehmann proposed estimating the shift parameter between two populations and its confidence interval (CI). However, such a shift parameter does not have a straightforward interpretation, and its CI contains zero in some cases when Mann–Whitney test produces a significant result. To overcome the aforementioned problems, we introduce the use of the win ratio for analysing such data. Patients in the new and control treatment are formed into all possible pairs. For each pair, the new treatment patient is labelled a ‘winner’ or a ‘loser’ if it is known who had the more favourable outcome. The win ratio is the total number of winners divided by the total numbers of losers. A 95% CI for the win ratio can be obtained using the bootstrap method. Statistical properties of the win ratio statistic are investigated using two real trial data sets and six simulation studies. Results show that the win ratio method has about the same power as the Mann–Whitney method. We recommend the use of the win ratio method for estimating the treatment effect (and CI) and the Mann–Whitney method for calculating the P‐value for comparing continuous non‐Normal outcomes when the amount of tied pairs is small. Copyright © 2016 John Wiley & Sons, Ltd.     

A generalized analytic solution to the win ratio to analyze a composite endpoint considering the clinical importance order among components

A composite endpoint consists of multiple endpoints combined in one outcome. It is frequently used as the primary endpoint in randomized clinical trials. There are two main disadvantages associated with the use of composite endpoints: a) in conventional analyses, all components are treated equally important; and b) in time‐to‐event analyses, the first event considered may not be the most important component. Recently Pocock et al. (2012) introduced the win ratio method to address these disadvantages. This method has two alternative approaches: the matched pair approach and the unmatched pair approach. In the unmatched pair approach, the confidence interval is constructed based on bootstrap resampling, and the hypothesis testing is based on the non‐parametric method by Finkelstein and Schoenfeld (1999). Luo et al. (2015) developed a close‐form variance estimator of the win ratio for the unmatched pair approach, based on a composite endpoint with two components and a specific algorithm determining winners, losers and ties. We extend the unmatched pair approach to provide a generalized analytical solution to both hypothesis testing and confidence interval construction for the win ratio, based on its logarithmic asymptotic distribution. This asymptotic distribution is derived via U‐statistics following Wei and Johnson (1985). We perform simulations assessing the confidence intervals constructed based on our approach versus those per the bootstrap resampling and per Luo et al. We have also applied our approach to a liver transplant Phase III study. This application and the simulation studies show that the win ratio can be a better statistical measure than the odds ratio when the importance order among components matters; and the method per our approach and that by Luo et al., although derived based on large sample theory, are not limited to a large sample, but are also good for relatively small sample sizes. Different from Pocock et al. and Luo et al., our approach is a generalized analytical method, which is valid for any algorithm determining winners, losers and ties. Copyright © 2016 John Wiley & Sons, Ltd.     

Polling opinions in the 2005 election

The winners of the General Election in May were not the political parties but the opinion pollsters, says Paul Baines . After 1992, when most pollsters predicted a hung parliament rather than a Conservative win, and 2001, when they overestimated the Labour lead, the 2005 election result was awaited by many pollsters with trepidation. Would their final eve-of-poll results be accurate or not?     

数字经济的统计界定和产业分类研究

当前,数字经济已经成为引领科技革命和产业变革的核心力量,然而国内外尚无统一的数字经济定义和产业分类标准,亟需明确数字经济统计界定,统一产业分类标准,为进一步研究分析提供支撑。首先,本文在系统梳理数字经济狭义和广义定义基础上对数字经济进行了广义界定。其次,将其生产活动归纳为核心活动和应用活动两部分。最后,进一步构建中国数字经济产业分类体系,将数字经济核心活动识别为数字设备制造业、数字产品贸易业、数字技术服务业和数字驱动产业4个大类、19个中类,将数字经济应用活动识别为电子商务产业、数字内容产业、数字金融产业、数字政府产业和 其他数字产业5个大类、24个中类,共计9个大类、43个中类。本文研究成果有望为完善中国数字经济产业分类标准、制定产业政策和定量测算产业规模提供参考。     

Modeling the Distribution of Price Sensitivity and Implications for Optimal Retail Pricing

This article focuses on the distribution of price sensitivity across consumers. We employ a random-coefficient logit model in which brand-specific intercepts and price-slope coefficients are allowed to vary across households. The model is estimated with panel data for two product categories. The implications of the estimated model are deduced through an optimal retail pricing analysis that combines the panel data with chain-level cost figures. We test parametric distributional assumptions using semiparametric density estimates based on series expansions.     

Bayesian hierarchical models for the prediction of volleyball results

Statistical modelling of sports data has become more and more popular in the recent years and different types of models have been proposed to achieve a variety of objectives: from identifying the key characteristics which lead a team to win or lose to predicting the outcome of a game or the team rankings in national leagues. Although not as popular as football or basketball, volleyball is a team sport with both national and international level competitions in almost every country. However, there is almost no study investigating the prediction of volleyball game outcomes and team rankings in national leagues. We propose a Bayesian hierarchical model for the prediction of the rankings of volleyball national teams, which also allows to estimate the results of each match in the league. We consider two alternative model specifications of different complexity which are validated using data from the women''s volleyball Italian Serie A1 2017–2018 season.     

The SLA DBIO 100 Poll: 100 Journals Voted by SLA’s BioMedical and Life Sciences Division as the Most Influential over the Last 100 Years

Abstract

An expert opinion poll of the members of the BioMedical and Life Sciences Division (DBIO) of the Special Libraries Association (SLA), conducted on the occasion of the SLA's Centennial (Washington, DC, June 14–17, 2009), identified 100 journals across three major categories (Clinical Medicine and Allied Health Sciences, Journals Primarily Reporting Molecular and Cellular Biology, and Journals of Natural History) as the most influential over the last 100 years. The Top Ten, containing winners from all three of these groups, were also named, as were a “Journal” and a “Publisher” of the Centennial.”     

A transformation for estimating the trinomial logit model with grouped data

For logit models where the outcome variables are the proportions of individuals falling into each of three categories, this paper develops a data transformation through which GLS estimates can be obtained by running OLS on the transformed data.     

The SLA DBIO 100 Poll: 100 Journals Voted by SLA’s BioMedical and Life Sciences Division as the Most Influential over the Last 100 Years

An expert opinion poll of the members of the BioMedical and Life Sciences Division (DBIO) of the Special Libraries Association (SLA), conducted on the occasion of the SLA's Centennial (Washington, DC, June 14–17, 2009), identified 100 journals across three major categories (Clinical Medicine and Allied Health Sciences, Journals Primarily Reporting Molecular and Cellular Biology, and Journals of Natural History) as the most influential over the last 100 years. The Top Ten, containing winners from all three of these groups, were also named, as were a “Journal” and a “Publisher” of the Centennial.”     

ESTIMATING A LOGIT MODEL WITH RANDOMIZED DATA: THE CASE OF COCAINE USE

In his influential book, Maddala (1983) suggests combining randomized response survey data with other personal information to estimate logit models predicting immoral, unpopular, or unlawful behaviour. This study is one of the first to implement this technique using real data. Models of college students' recent cocaine use are estimated with academic performance and socio-economic characteristics as determinants. Parameter estimates obtained from randomized response surveys are compared to those obtained using conventional, direct question surveys. The results indicate that randomized response estimates provide useful information on the degree to which inferences regarding the determinants of cocaine use are sensitive to survey type.     

Win statistics (win ratio,win odds,and net benefit) can complement one another to show the strength of the treatment effect on time-to-event outcomes

Conventional analyses of a composite of multiple time-to-event outcomes use the time to the first event. However, the first event may not be the most important outcome. To address this limitation, generalized pairwise comparisons and win statistics (win ratio, win odds, and net benefit) have become popular and have been applied to clinical trial practice. However, win ratio, win odds, and net benefit have typically been used separately. In this article, we examine the use of these three win statistics jointly for time-to-event outcomes. First, we explain the relation of point estimates and variances among the three win statistics, and the relation between the net benefit and the Mann–Whitney U statistic. Then we explain that the three win statistics are based on the same win proportions, and they test the same null hypothesis of equal win probabilities in two groups. We show theoretically that the Z-values of the corresponding statistical tests are approximately equal; therefore, the three win statistics provide very similar p-values and statistical powers. Finally, using simulation studies and data from a clinical trial, we demonstrate that, when there is no (or little) censoring, the three win statistics can complement one another to show the strength of the treatment effect. However, when the amount of censoring is not small, and without adjustment for censoring, the win odds and the net benefit may have an advantage for interpreting the treatment effect; with adjustment (e.g., IPCW adjustment) for censoring, the three win statistics can complement one another to show the strength of the treatment effect. For calculations we use the R package WINS, available on the CRAN (Comprehensive R Archive Network).     

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.     

陕西省城镇化健康发展研究及政策建议

促进城镇化健康发展是当前国内学术界比较关注的问题。以城镇化适宜度指标、城镇化初始动力指标、城镇化后续动力指标、城镇竞争力水平指标、城镇现代化水平指标五个方面的评价指标体系对城镇化健康发展进行评价，根据陕西省的有关统计资料，通过因子分析和聚类分析，将2005年陕西省城镇化健康发展的水平划分为四类，指出其发展的特点，并就存在的问题提出应分别采取低成本领先战略、差异化战略、突出重点战略等政策建议。     

Retrospective change detection in categorical time series

The aim of this paper is to propose methods of detecting change in the coefficients of a multinomial logistic regression model for categorical time series offline. The alternatives to the null hypothesis of stationarity can be either the hypothesis that it is not true, or that there is a temporary change in the sequence. We use the efficient score vector of the partial likelihood function. This has several advantages. First, the alternative value of the parameter does not have to be estimated; hence, we have a procedure that has a simple structure with only one parameter estimation using all available observations. This is in contrast with the generalized likelihood ratio-based change point tests. The efficient score vector is used in various ways. As a vector, its components correspond to the different components of the multinomial logistic regression model’s parameter vector. Using its quadratic form a test can be defined, where the presence of a change in any or all parameters is tested for. If there are too many parameters one can test for any subset while treating the rest as nuisance parameters. Our motivating example is a DNA sequence of four categories, and our test result shows that in the published data the distribution of the four categories is not stationary.     

Multiplicative-interaction logit models for i×j×2 three-way tables

Multiplicative-interaction (M-I) logit models are proposed for three-way IxJx2 contingency tables where the third variable constitutes a binary response. Models are derived by assigning unknown scores to the categories and forming product interactions from them. Asymptotic results under special sampling constraints are derived for maximum likelihood estimates and the goodness-of-fit statistics. The class of models proposed in this paper are found to be useful when no obvious scores are available. An example is included.     

Likelihood-Based comparison of stable paretian and competing models: Evidence from daily exchange rates

Considering alternative models for exchange rates has always been a central issue in applied research. Despite this fact, formal likelihood-based comparisons of competing models are extremely rare. In this paper, we apply the Bayesian marginal likelihood concept to compare GARCH, stable, stable GARCH, stochastic volatility, and a new stable Paretian stochastic volatility model for seven major currencies. Inference is based on combining Monte Carlo methods with Laplace integration. The empirical results show that neither GARCH nor stable models are clear winners, and a GARCH model with stable innovations is the model best supported by the data.     

Sibling death clustering in India: state dependence versus unobserved heterogeneity

Summary.  Data from a range of environments indicate that the incidence of death is not randomly distributed across families but, rather, that there is a clustering of death among siblings. A natural explanation of this would be that there are (observed or unobserved) differences across families, e.g. in genetic frailty, education or living standards. Another hypothesis that is of considerable interest for both theory and policy is that there is a causal process whereby the death of a child influences the risk of death of the succeeding child in the family. Drawing language from the literature on the economics of unemployment, the causal effect is referred to here as state dependence (or scarring). The paper investigates the extent of state dependence in India, distinguishing this from family level risk factors that are common to siblings. It offers some methodological innovations on previous research. Estimates are obtained for each of three Indian states, which exhibit dramatic differences in socio-economic and demographic variables. The results suggest a significant degree of state dependence in each of the three regions. Eliminating scarring, it is estimated, would reduce the incidence of infant mortality (among children who are born after the first child) by 9.8% in the state of Uttar Pradesh, 6.0% in West Bengal and 5.9% in Kerala.     

Modelling the probability distribution of prize winnings in the UK National Lottery: consequences of conscious selection

Summary.  In the statistical and economics literature on lotteries, the problem of designing attractive games has been studied by using models in which sales are a function of the structure of prizes. Recently the prize structure has been proxied by using the moments of the prize distribution. Such modelling is a vital input into the process of designing appealing new lottery games that can generate large revenues for good causes. We show how conscious selection, the process by which lottery players choose numbers non-randomly, complicates the multivariate distribution of prize winners by introducing massive overdispersion of numbers of winners, and large correlations between the numbers of different types of prize winner. Although it is possible intuitively to reach a qualitative understanding of the data, an a priori model does not fit well. We therefore construct an empirical model of the joint distribution of prize winners and use it to calculate the moments of ticket value as a function of sales. The new model gives much higher estimates of ticket value moments, particularly skewness, than previously obtained. Our results will have consequences for policy decisions regarding game design. A spin-off result is that, on the basis of the results of model fitting, lottery players may increase the expected value of their ticket by strategically choosing numbers which are less popular with other lottery players.     

The stratified win statistics (win ratio,win odds,and net benefit)

The win odds and the net benefit are related directly to each other and indirectly, through ties, to the win ratio. These three win statistics test the same null hypothesis of equal win probabilities between two groups. They provide similar p-values and powers, because the Z-values of their statistical tests are approximately equal. Thus, they can complement one another to show the strength of a treatment effect. In this article, we show that the estimated variances of the win statistics are also directly related regardless of ties or indirectly related through ties. Since its introduction in 2018, the stratified win ratio has been applied in designs and analyses of clinical trials, including Phase III and Phase IV studies. This article generalizes the stratified method to the win odds and the net benefit. As a result, the relations of the three win statistics and the approximate equivalence of their statistical tests also hold for the stratified win statistics.     

Point-symmetry models and decomposition for collapsed square contingency tables

For square contingency tables with ordered categories, there may be some cases that one wants to analyze them by considering collapsed tables with some adjacent categories combined in the original table. This paper proposes three kinds of new models which have the structure of point-symmetry (PS), quasi point-symmetry and marginal point-symmetry for collapsed square tables. This paper also gives a decomposition of the PS model for collapsed square tables. The father's and his daughter's occupational mobility data are analyzed using new models.