Scott L. Zeger

Biomarkers and surrogate endpoints: Preferred definitions and conceptual framework*

genome are dramatically reshaping the research and development pathways for drugs, vaccines, and diagnostics. The growth in the number of molecular entities entering the drug development pipeline has accelerated as a consequence of powerful discovery and screening technologies such as combinatorial chemistry, mass spectrometry, high throughput screening, celland tissue-based DNA microarrays, and proteomic approaches.1 As a consequence, there is an escalating number of therapeutic candidates, which has caused the need for new technologies and strategies to streamline the process to make safe and effective therapies available to patients. One approach to the achievement of more expeditious and informative therapeutic research is the use of precise clinical measurement tools to determine disease progression and the effects of interventions (drugs, surgery, and vaccines). For example, gene-based approaches such as single nucleotide polymorphism maps are now being developed to distinguish the molecular and cellular basis for variations in clinical response to therapy.2 Another approach is the use of a wide array of analytical tools to assess biological parameters, which are referred to as biomarkers. Biomarker measurements can help explain empirical results of clinical trials by relating the effects of interventions on molecular and cellular pathways to clinical responses. In doing so, biomarkers provide an avenue for researchers to gain a mechanistic understanding of the differences in clinical response that may be influenced by uncontrolled variables (for example, drug metabolism). There are a variety of ways that biomarker measurements can aid in the development and evaluation of COMMENTARY

Models for longitudinal data: a generalized estimating equation approach.

This article discusses extensions of generalized linear models for the analysis of longitudinal data. Two approaches are considered: subject-specific (SS) models in which heterogeneity in regression parameters is explicitly modelled; and population-averaged (PA) models in which the aggregate response for the population is the focus. We use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes. When the subject-specific parameters are assumed to follow a Gaussian distribution, simple relationships between the PA and SS parameters are available. The methods are illustrated with an analysis of data on mothers smoking and childrens respiratory disease.

Fine particulate air pollution and mortality in 20 U.S. Cities, 1987-1994

BACKGROUND Air pollution in cities has been linked to increased rates of mortality and morbidity in developed and developing countries. Although these findings have helped lead to a tightening of air-quality standards, their validity with respect to public health has been questioned. METHODS We assessed the effects of five major outdoor-air pollutants on daily mortality rates in 20 of the largest cities and metropolitan areas in the United States from 1987 to 1994. The pollutants were particulate matter that is less than 10 microm in aerodynamic diameter (PM10), ozone, carbon monoxide, sulfur dioxide, and nitrogen dioxide. We used a two-stage analytic approach that pooled data from multiple locations. RESULTS After taking into account potential confounding by other pollutants, we found consistent evidence that the level of PM10 is associated with the rate of death from all causes and from cardiovascular and respiratory illnesses. The estimated increase in the relative rate of death from all causes was 0.51 percent (95 percent posterior interval, 0.07 to 0.93 percent) for each increase in the PM10 level of 10 microg per cubic meter. The estimated increase in the relative rate of death from cardiovascular and respiratory causes was 0.68 percent (95 percent posterior interval, 0.20 to 1.16 percent) for each increase in the PM10 level of 10 microg per cubic meter. There was weaker evidence that increases in ozone levels increased the relative rates of death during the summer, when ozone levels are highest, but not during the winter. Levels of the other pollutants were not significantly related to the mortality rate. CONCLUSIONS There is consistent evidence that the levels of fine particulate matter in the air are associated with the risk of death from all causes and from cardiovascular and respiratory illnesses. These findings strengthen the rationale for controlling the levels of respirable particles in outdoor air.

Generalized Linear Models with Random Effects; a Gibbs Sampling Approach

Abstract Generalized linear models have unified the approach to regression for a wide variety of discrete, continuous, and censored response variables that can be assumed to be independent across experimental units. In applications such as longitudinal studies, genetic studies of families, and survey sampling, observations may be obtained in clusters. Responses from the same cluster cannot be assumed to be independent. With linear models, correlation has been effectively modeled by assuming there are cluster-specific random effects that derive from an underlying mixing distribution. Extensions of generalized linear models to include random effects has, thus far, been hampered by the need for numerical integration to evaluate likelihoods. In this article, we cast the generalized linear random effects model in a Bayesian framework and use a Monte Carlo method, the Gibbs sampler, to overcome the current computational limitations. The resulting algorithm is flexible to easily accommodate changes in the number...

Semiparametric Models for Longitudinal Data with Application to CD4 Cell Numbers in HIV Seroconverters

The paper describes a semiparametric model for longitudinal data which is illustrated by its application to data on the time evolution of CD4 cell numbers in HIV seroconverters. The essential ingredients of the model are a parametric linear model for covariate adjustment, a nonparametric estimation of a smooth time trend, serial correlation between measurements on an individual subject, and random measurement error. A back-fitting algorithm is used in conjunction with a cross-validation prescription to fit the model. A notable feature in the application is that the onset of HIV infection is associated with a sudden drop in CD4 cells followed by a longer-term slower decay. The model is also used to estimate an individuals curve by combining his data with the population curve. Shrinkage toward the population mean trajectory is controlled in a natural way by the estimated covariance structure of the data.

A Social Model for Health Promotion for an Aging Population: Initial Evidence on the Experience Corps Model

This report evaluates whether a program for older volunteers, designed for both benerativity and health promotion, leads to short-term improvements inmultiple behavioral risk factors and positive effects on intermediary risk factors for disability and other morbidities. The Experience Corps® places older volunteers in public elementary schools in roles designed to meet schools’ needs and increase the social, physical, and cognitive activity of the volunteers. This article reports on a pilot randomized trial in Baltimore, Maryland. The 128 volunteers were 60–86 years old; 95% were African American. At follow-up of 4–8 months, physical activity, strength, people one could turn to for help, and cognitive activity increased significantly, and walking speed decreased significantly less, in participants compared to controls. In this pilot trial, physical, cognitive, and social activity increased, suggesting the potential for the Experience Corps to improve health for an aging population and simultaneously improve educational outcomes for children.

Considerations in the evaluation of surrogate endpoints in clinical trials : Summary of a National Institutes of Health Workshop

We report on recommendations from a National Institutes of Health Workshop on methods for evaluating the use of surrogate endpoints in clinical trials, which was attended by experts in biostatistics and clinical trials from a broad array of disease areas. Recent advances in biosciences and technology have increased the ability to understand, measure, and model biological mechanisms; appropriate application of these advances in clinical research settings requires collaboration of quantitative and laboratory scientists. Biomarkers, new examples of which arise rapidly from new technologies, are used frequently in such areas as early detection of disease and identification of patients most likely to benefit from new therapies. There is also scientific interest in exploring whether, and under what conditions, biomarkers may substitute for clinical endpoints of phase III trials, although workshop participants agreed that these considerations apply primarily to situations where trials using clinical endpoints are not feasible. Evaluating candidate biomarkers in the exploratory phases of drug development and investigating surrogate endpoints in confirmatory trials require the establishment of a statistical and inferential framework. As a first step, participants reviewed methods for investigating the degree to which biomarkers can explain or predict the effect of treatments on clinical endpoints measured in clinical trials. They also suggested new approaches appropriate in settings where biomarkers reflect only indirectly the important processes on the causal path to clinical disease and where biomarker measurement errors are of concern. Participants emphasized the need for further research on development of such models, whether they are empirical in nature or attempt to describe mechanisms in mathematical terms. Of special interest were meta-analytic models for combining information from multiple studies involving interventions for the same condition. Recommendations also included considerations for design and conduct of trials and for assemblage of databases needed for such research. Finally, there was a strong recommendation for increased training of quantitative scientists in biologic research as well as in statistical methods and modeling to ensure that there will be an adequate workforce to meet future research needs.

Latent Variable Regression for Multiple Discrete Outcomes

Abstract Quantifying human health and functioning poses significant challenges in many research areas. Commonly in the social and behavioral sciences and increasingly in epidemiologic research, multiple indicators are utilized as responses in lieu of an obvious single measure for an outcome of interest. In this article we study the concomitant latent class model for analyzing such multivariate categorical outcome data. We develop practical theory for reducing and identifying such models. We detail parameter and standard error fitting that parallels standard latent class methodology, thus supplementing the approach proposed by Dayton and Macready. We propose and study diagnostic strategies, exemplifying our methods using physical disability data from an ongoing gerontologic study. Throughout, the focus of our work is on applications for which a primary goal is to study the association between health or functioning and covariates.

Emergency admissions for cardiovascular and respiratory diseases and the chemical composition of fine particle air pollution.

Background Population-based studies have estimated health risks of short-term exposure to fine particles using mass of PM2.5 (particulate matter ≤ 2.5 μm in aerodynamic diameter) as the indicator. Evidence regarding the toxicity of the chemical components of the PM2.5 mixture is limited. Objective In this study we investigated the association between hospital admission for cardiovascular disease (CVD) and respiratory disease and the chemical components of PM2.5 in the United States. Methods We used a national database comprising daily data for 2000–2006 on emergency hospital admissions for cardiovascular and respiratory outcomes, ambient levels of major PM2.5 chemical components [sulfate, nitrate, silicon, elemental carbon (EC), organic carbon matter (OCM), and sodium and ammonium ions], and weather. Using Bayesian hierarchical statistical models, we estimated the associations between daily levels of PM2.5 components and risk of hospital admissions in 119 U.S. urban communities for 12 million Medicare enrollees (≥ 65 years of age). Results In multiple-pollutant models that adjust for the levels of other pollutants, an interquartile range (IQR) increase in EC was associated with a 0.80% [95% posterior interval (PI), 0.34–1.27%] increase in risk of same-day cardiovascular admissions, and an IQR increase in OCM was associated with a 1.01% (95% PI, 0.04–1.98%) increase in risk of respiratory admissions on the same day. Other components were not associated with cardiovascular or respiratory hospital admissions in multiple-pollutant models. Conclusions Ambient levels of EC and OCM, which are generated primarily from vehicle emissions, diesel, and wood burning, were associated with the largest risks of emergency hospitalization across the major chemical constituents of PM2.5.

Revised Analyses of the National Morbidity, Mortality, and Air Pollution Study: Mortality Among Residents Of 90 Cities

This article presents findings from updated analyses of data from 90 U.S. cities assembled for the National Morbidity, Mortality, and Air Pollution Study (NMMAPS). The data were analyzed with a generalized additive model (GAM) using the gamfunction in S-Plus (with default convergence criteria previously used and with more stringent criteria) and with a generalized linear model (GLM) with natural cubic splines. With the original method, the estimated effect of PM10 (particulate matter 10μm in mass median aerodynamic diameter) on total mortality from nonexternal causes was a 0.41% increase per 10−μg/m3 increase in PM10; with the more stringent criteria, the estimate was 0.27%; and with GLM, the effect was 0.21%. The effect of PM10 on respiratory and cardiovascular mortality combined was greater, but the pattern across models was similar. The findings of the updated analysis with regard to spatial heterogeneity across the 90 cities were unchanged from the original analyses.