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Summary A procedure is derived for extracting the observed information matrix when the EM algorithm is used to find maximum likelihood estimates in incomplete data problems. The technique requires computation of a complete‐data gradient vector or second derivative matrix, but not those associated with the incomplete data likelihood. In addition, a method useful in speeding up the convergence of the EM algorithm is developed. Two examples are presented.

Background Obesity and its cardiovascular complications are extremely common medical problems, but evidence on how to accomplish weight loss in clinical practice is sparse. Methods We conducted a randomized, controlled trial to examine the effects of two behavioral weight-loss interventions in 415 obese patients with at least one cardiovascular risk factor. Participants were recruited from six primary care practices; 63.6% were women, 41.0% were black, and the mean age was 54.0 years. One intervention provided patients with weight-loss support remotely — through the telephone, a study-specific Web site, and e-mail. The other intervention provided in-person support during group and individual sessions, along with the three remote means of support. There was also a control group in which weight loss was self-directed. Outcomes were compared between each intervention group and the control group and between the two intervention groups. For both interventions, primary care providers reinforced participation at routinely scheduled visits. The trial duration was 24 months. Results At baseline, the mean body-mass index (the weight in kilograms divided by the square of the height in meters) for all participants was 36.6, and the mean weight was 103.8 kg. At 24 months, the mean change in weight from baseline was −0.8 kg in the control group, −4.6 kg in the group receiving remote support only (P<0.001 for the comparison with the control group), and −5.1 kg in the group receiving in-person support (P<0.001 for the comparison with the control group). The percentage of participants who lost 5% or more of their initial weight was 18.8% in the control group, 38.2% in the group receiving remote support only, and 41.4% in the group receiving in-person support. The change in weight from baseline did not differ significantly between the two intervention groups. Conclusions In two behavioral interventions, one delivered with in-person support and the other delivered remotely, without face-to-face contact between participants and weight-loss coaches, obese patients achieved and sustained clinically significant weight loss over a period of 24 months. (Funded by the National Heart, Lung, and Blood Institute and others; ClinicalTrials.gov number, NCT00783315.)

We investigate two-stage parametric and two-stage semi-parametric estimation procedures for the association parameter in copula models for bivariate survival data where censoring in either or both components is allowed. We derive asymptotic properties of the estimators and compare their performance by simulations. Both parametric and semi-parametric estimators of the association parameter are efficient at independence, and the parameter estimates in the margins have high efficiency and are robust to misspecification of dependency structures. In addition, we propose a consistent variance estimator for the semi-parametric estimator of the association parameter. We apply the proposed methods to an AIDS data set for illustration.

Use of newer therapies for HIV was associated with a large benefit in terms of mortality that was not diminished by any increase in the rate of cardiovascular or cerebrovascular events or related mortality. Fear of accelerated vascular disease need not compromise antiretroviral therapy over the short term. However, prolonged survival among HIV infected patients means that longer-term observation and analysis are required.

The use of complex value-added models that attempt to isolate the contributions of teachers or schools to student development is increasing. Several variations on these models are being applied in the research literature, and policy makers have expressed interest in using these models for evaluating teachers and schools. In this article, we present a general multivariate, longitudinal mixed-model that incorporates the complex grouping structures inherent to longitudinal student data linked to teachers. We summarize the principal existing modeling approaches, show how these approaches are special cases of the proposed model, and discuss possible extensions to model more complex data structures. We present simulation and analytical results that clarify the interplay between estimated teacher effects and repeated outcomes on students over time. We also explore the potential impact of model misspecifications, including missing student covariates and assumptions about the accumulation of teacher effects over time, on key inferences made from the models. We conclude that mixed models that account for student correlation over time are reasonably robust to such misspecifications when all the schools in the sample serve similar student populations. However, student characteristics are likely to confound estimated teacher effects when schools serve distinctly different populations.

Summary.Multicity time series studies of particulate matter and mortality and morbidity have provided evidence that daily variation in air pollution levels is associated with daily variation in mortality counts. These findings served as key epidemiological evidence for the recent review of the US national ambient air quality standards for particulate matter. As a result, methodological issues concerning time series analysis of the relationship between air pollution and health have attracted the attention of the scientific community and critics have raised concerns about the adequacy of current model formulations. Time series data on pollution and mortality are generally analysed by using log-linear, Poisson regression models for overdispersed counts with the daily number of deaths as outcome, the (possibly lagged) daily level of pollution as a linear predictor and smooth functions of weather variables and calendar time used to adjust for timevarying confounders. Investigators around the world have used different approaches to adjust for confounding, making it difficult to compare results across studies. To date, the statistical properties of these different approaches have not been comprehensively compared. To address these issues, we quantify and characterize model uncertainty and model choice in adjusting for seasonal and long-term trends in time series models of air pollution and mortality. First, we conduct a simulation study to compare and describe the properties of statistical methods that are commonly used for confounding adjustment. We generate data under several confounding scenarios and systematically compare the performance of the various methods with respect to the mean-squared error of the estimated air pollution coefficient. We find that the bias in the estimates generally decreases with more aggressive smoothing and that model selection methods which optimize prediction may not be suitable for obtaining an estimate with small bias. Second, we apply and compare the modelling approaches with the National Morbidity, Mortality, and Air Pollution Study database which comprises daily time series of several pollutants, weather variables and mortality counts covering the period 1987-2000 for the largest 100 cities in the USA. When applying these approaches to adjusting for seasonal and long-term trends we find that the Study's estimates for the national average effect of PM 10 at lag 1 on mortality vary over approximately a twofold range, with 95% posterior intervals always excluding zero risk.

The literature on exposure to lipophilic agents such as polychlorinated biphenyls (PCBs) is conflicting, posing challenges for the interpretation of potential human health risks. Laboratory variation in quantifying PCBs may account for some of the conflicting study results. For example, for quantification purposes, blood is often used as a proxy for adipose tissue, which makes it necessary to model serum lipids when assessing health risks of PCBs. Using a simulation study, we evaluated four statistical models (unadjusted, standardized, adjusted, and two-stage) for the analysis of PCB exposure, serum lipids, and health outcome risk (breast cancer). We applied eight candidate true causal scenarios, depicted by directed acyclic graphs, to illustrate the ramifications of misspecification of underlying assumptions when interpreting results. Statistical models that deviated from underlying causal assumptions generated biased results. Lipid standardization, or the division of serum concentrations by serum lipids, was observed to be highly prone to bias. We conclude that investigators must consider biology, biologic medium (e.g., nonfasting blood samples), laboratory measurement, and other underlying modeling assumptions when devising a statistical plan for assessing health outcomes in relation to environmental exposures.