A generalized linear mixed model for longitudinal binary data with a marginal logit link function

Longitudinal studies of a binary outcome are common in the health, social, and behavioral sciences. In general, a feature of random effects logistic regression models for longitudinal binary data is that the marginal functional form, when integrated over the distribution of the random effects, is no longer of logistic form. Recently, Wang and Louis [Biometrika 90 (2003) 765--775] proposed a random intercept model in the clustered binary data setting where the marginal model has a logistic form. An acknowledged limitation of their model is that it allows only a single random effect that varies from cluster to cluster. In this paper we propose a modification of their model to handle longitudinal data, allowing separate, but correlated, random intercepts at each measurement occasion. The proposed model allows for a flexible correlation structure among the random intercepts, where the correlations can be interpreted in terms of Kendall's $\tau$. For example, the marginal correlations among the repeated binary outcomes can decline with increasing time separation, while the model retains the property of having matching conditional and marginal logit link functions. Finally, the proposed method is used to analyze data from a longitudinal study designed to monitor cardiac abnormalities in children born to HIV-infected women.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS390 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Interpretation and the Constraints on International Courts

This paper argues that methodologies of interpretation do not do what they promise – they do not constrain interpretation by providing neutral steps that one can follow in finding out a meaning of a text – but nevertheless do their constraining work by being part of what can be described as the legal practice

The Values of Tangible User Interfaces: How to discover, assess and evaluate them?

Since the introduction of Tangible User Interfaces, in the beginning of the 90s, a generation grew up interacting with computers. At the same time the context of computing changed dramatically: from a device used almost exclusively by specialists, it evolved to a general device that plays a dominant role in our societies. But where does this leave TUI? In many respects, the idea of tangibility plays a marginal role in Human Computer Interaction. It makes sense to re-evaluate the intrinsic values of TUI design. This paper proposes to research the appropriate metrics to do so

The practices of apartheid as a war crime: a critical analysis

The human suffering caused by the political ideology of apartheid in South Africa during the Apartheid era (1948-1994) prompted worldwide condemnation and a variety of diplomatic and legal responses. Amongst these responses was the attempt to have apartheid recognised both as a crime against humanity in the 1973 Apartheid Convention as well as a war crime in Article 85(4)(c) of Additional Protocol I. This article examines the origins, nature and current status of the practices of apartheid as a war crime and its possible application to the Israeli-Palestinian conflict

Joint generalized estimating equations for multivariate longitudinal binary outcomes with missing data: an application to acquired immune deficiency syndrome data

In a large, prospective longitudinal study designed to monitor cardiac abnormalities in children born to HIV-infected women, instead of a single outcome variable, there are multiple binary outcomes (e.g., abnormal heart rate, abnormal blood pressure, abnormal heart wall thickness) considered as joint measures of heart function over time. In the presence of missing responses at some time points, longitudinal marginal models for these multiple outcomes can be estimated using generalized estimating equations (GEE) (Liang and Zeger, 1986), and consistent estimates can be obtained under the assumption of a missing completely at random (MCAR) mechanism. When the missing data mechanism is missing at random (MAR), that is the probability of missing a particular outcome at a time-point depends on observed values of that outcome and the remaining outcomes at other time points, we propose joint estimation of the marginal models using a single modified GEE based on an EM-type algorithm. The proposed method is motivated by the longitudinal study of cardiac abnormalities in children born to HIV-infected women and analyses of these data are presented to illustrate the application of the method. Further, in an asymptotic study of bias, we show that under an MAR mechanism in which missingness depends on all observed outcome variables, our joint estimation via the modified GEE produces almost unbiased estimates, provided the correlation model has been correctly specified, whereas estimates from standard GEE can lead to substantial bias

A weighted combination of pseudo-likelihood estimators for longitudinal binary data subject to non-ignorable non-monotone missingness

For longitudinal binary data with non-monotone non-ignorably missing outcomes over time, a full likelihood approach is complicated algebraically, and with many follow-up times, maximum likelihood estimation can be computationally prohibitive. As alternatives, two pseudo-likelihood approaches have been proposed that use minimal parametric assumptions. One formulation requires specification of the marginal distributions of the outcome and missing data mechanism at each time point, but uses an “independence working assumption,” i.e., an assumption that observations are independent over time. Another method avoids having to estimate the missing data mechanism by formulating a “protective estimator.” In simulations, these two estimators can be very inefficient, both for estimating time trends in the first case and for estimating both time-varying and time-stationary effects in the second. In this paper, we propose use of the optimal weighted combination of these two estimators, and in simulations we show that the optimal weighted combination can be much more efficient than either estimator alone. Finally, the proposed method is used to analyze data from two longitudinal clinical trials of HIV-infected patients

An extension of the Wilcoxon rank sum test for complex sample survey data: Extension of Wilcoxon Rank Sum Test

In complex survey sampling, a fraction of a finite population is sampled. Often, the survey is conducted so that each subject in the population has a different probability of being selected into the sample. Further, many complex surveys involve stratification and clustering. For generalizability of the sample to the finite population, these features of the design are usually incorporated in the analysis. While the Wilcoxon rank sum test is commonly used to compare an ordinal variable in bivariate analyses, no simple extension of the Wilcoxon rank sum test has been proposed for complex survey data. With multinomial sampling of independent subjects, the Wilcoxon rank-sum test statistic equals the score test statistic for the group effect from a proportional odds cumulative logistic regression model for an ordinal outcome. Using this regression framework, for complex survey data, we formulate a similar proportional odds cumulative logistic regression model for the ordinal variable, and use an estimating equations score statistic for no group effect as an extension of the Wilcoxon test. The proposed method is applied to a complex survey designed to produce national estimates of the health care use, expenditures, sources of payment, and insurance coverage

PainDroid: An android-based virtual reality application for pain assessment

Earlier studies in the field of pain research suggest that little efficient intervention currently exists in response to the exponential increase in the prevalence of pain. In this paper, we present an Android application (PainDroid) with multimodal functionality that could be enhanced with Virtual Reality (VR) technology, which has been designed for the purpose of improving the assessment of this notoriously difficult medical concern. Pain- Droid has been evaluated for its usability and acceptability with a pilot group of potential users and clinicians, with initial results suggesting that it can be an effective and usable tool for improving the assessment of pain. Participant experiences indicated that the application was easy to use and the potential of the application was similarly appreciated by the clinicians involved in the evaluation. Our findings may be of considerable interest to healthcare providers, policy makers, and other parties that might be actively involved in the area of pain and VR research