# Biostatistics, Dept. of

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Biostatistics creates and applies methods for quantitative research in the health sciences. Our faculty conduct research across the spectrum of statistical science from foundations of inference to the discovery of new methodology to health applications. Our designs and analytic methods enable health scientists and professionals in academia, government, pharmaceutical companies, medical research organizations and elsewhere to efficiently acquire knowledge and draw valid conclusions from their ever-expanding sources of information.

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Item Relationship of somatosensory evoked potentials and cerebral oxygen consumption during hypoxic hypoxia in dogs(American Heart Association, 1986) Traystman, R. J.; Zeger, Scott L.; McPherson, R. W.The effects of hypoxic hypoxia on cerebral hemodynamics and somatosensory evoked potential (SEP) were studied in 10 pentobarbital anestheteized dogs. Cerebral blood flow (CBF) was measured using the venous outflow technique and cerebral oxygen consumption (CMRO2) was calculated from the arterio-cerebro-venous oxygen difference times CBF. SEP was evaluated by percutaneous stimulation of an upper extremity nerve and was recorded over the contralateral somatosensory cortex. The latencies of the initial negative wave (N1), second positive wave (P2) and the amplitude of the primary complex (P1N1) were measured. Animals were breathed sequentially with oxygen concentrations of 21, 10, 6, 5, and 4.5% for five minutes each. Animals were returned to room air breathing when the amplitude of the SEP decreased to less than 20% of control and were observed for 30 minutes following reoxygenation. Severe hypoxia (4.5% O2) increased CBF to 200% of control, decreased CMRO2 to 45% of control, decreased amplitude and increased latency of SEP. Following reoxygenation, as CMRO2 increased toward control, latency of SEP decreased and amplitude increased and CBF returned to baseline within 30 min. During hypoxia and reoxygenation, the latencies of N1 and P2 and the amplitude of P1N1 were correlated with CMRO2 in individual animals. We conclude that changes in SEP amplitude and latency reflect changes in CMRO2 despite high CBF during rapidly progressive hypoxic hypoxia and following reoxygenation.Item Feedback Models for Discrete and Continuous Time Series(Statistica Sinica, 1991) Liang, Kung-Yee; Zeger, Scott L.In public health research, it is common to follow a cohort of subjects over time, observing a vector of health indicators and a set of covariates at each of many visits. An objective of analysis is to characterize the inter-dependencies, in particular, the feedback of one response upon another while accounting for the covariates. With Gaussian responses, multivariate autoregressive models that incorporate feedback are commonly used. This paper discusses analogous Markov models for multivariate discrete and mixed discrete/continuous response variables. One special case is an extension of seemingly unrelated regressions to discrete and continuous outcomes. A generalized estimating equations approach that requires correct specification of only conditional means and variances is discussed. The methods are illustrated by a study of infectious diseases and vitamin A deficiency in Indonesian children.Item The effects on survival of early treatment of human immunodeficiency virus infection.(New England Journal of Medicine, 1992-04-16) Graham, Neil M. H.; Detels, Roger; Zeger, Scott L.; Park, Lawrence P.; Vermund, Sten H.; Phair, John P.; Rinaldo, Charles R.BACKGROUND. Zidovudine has been shown to prolong survival in patients with the acquired immunodeficiency syndrome (AIDS) and, in persons with human immunodeficiency virus (HIV) infection but not AIDS, to delay the progression to AIDS. However, it is still uncertain whether treatment before the development of AIDS prolongs survival. METHODS. We analyzed data from a cohort of 2162 high-risk men who were already seropositive for HIV type 1 (HIV-1) and 406 men who seroconverted from October 1986 through April 1991. There were 306 deaths. The probabilities of death were compared among men at similar stages of disease who began zidovudine therapy before the diagnosis of AIDS and among those who did not. Relative risks of death were calculated for each of five initial disease states on the basis of CD4+ cell counts and clinical symptoms and signs appearing over follow-up periods of 6, 12, 18, and 24 months. Adjustments were also made for the use of prophylaxis against Pneumocystis carinii pneumonia (PCP). RESULTS. After we controlled for CD4+ cell count and symptoms, the use of zidovudine with or without PCP prophylaxis before the development of AIDS significantly reduced mortality in all follow-up periods. The relative risks of death were 0.43 (95 percent confidence interval, 0.23 to 0.78) at 6 months, 0.54 (95 percent confidence interval, 0.38 to 0.78) at 12 months, 0.59 (95 percent confidence interval, 0.44 to 0.79) at 18 months, and 0.67 (95 percent confidence interval, 0.52 to 0.86) at 24 months. After we adjusted for the effects of PCP prophylaxis, zidovudine alone significantly reduced mortality at 6, 12, and 18 months (relative risks, 0.45, 0.59, and 0.70, respectively), but not at 24 months (relative risk, 0.81). Among zidovudine users, those who also used PCP prophylaxis before the development of AIDS had significantly lower mortality at 18 and 24 months than those who did not (relative risks, 0.62 and 0.60, respectively). CONCLUSIONS. The results of this study support the hypothesis that in HIV-1 infection, early treatment with zidovudine and PCP prophylaxis improves survival in addition to slowing the progression to AIDS.Item Inference Based on Estimating Functions in the Presence of Nuisance Parameters(Institute of Mathematical Statistics, 1995) Zeger, Scott L.; Liang, Kung-YeeIn many studies, the scientific objective can be formulated in terms of a statistical model indexed by parameters, only some of which are of scientific interest. The other "nuisance parameters" are required to complete the specification of the probability mechanism but are not of intrinsic value in themselves. It is well known that nuisance parameters can have a profound impact on inference. Many approaches have been proposed to eliminate or reduce their impact. In this paper, we consider two situations: where the likelihood is completely specified; and where only a part of the random mechanism can be reasonably assumed. In either case, we examine methods for dealing with nuisance parameters from the vantage point of parameter estimating functions. To establish a context, we begin with a review of the basic concepts and limitations of optimal estimating functions. We introduce a hierarchy of orthogonality conditions for estimating functions that helps to characterize the sensitivity of inferences to nuisance parameters. It applies to both the fully and partly parametric cases. Throughout the paper, we rely on examples to illustrate the main ideas.Item Marginalized Multilevel Models and Likelihood Inference(Institute of Mathematical Statistics, 2000) Zeger, Scott L.; Heagerty, Patrick J.Hierarchical or "multilevel" regression models typically parameterize the mean response conditional on unobserved latent variables or "random" effects and then make simple assumptions regarding their distribution. The interpretation of a regression parameter in such a model is the change in possibly transformed mean response per unit change in a particular predictor having controlled for all conditioning variables including the random effects. An often overlooked limitation of the conditional formulation for nonlinear models is that the interpretation of regression coefficients and their estimates can be highly sensitive to difficult-to-verify assumptions about the distribution of random effects, particularly the dependence of the latent variable distribution on covariates. In this article, we present an alternative parameterization for the multilevel model in which the marginal mean, rather than the conditional mean given random effects, is regressed on covariates. The impact of random effects model violations on the marginal and more traditional conditional parameters is compared through calculation of asymptotic relative biases. A simple two-level example from a study of teratogenicity is presented where the binomial overdispersion depends on the binary treatment assignment and greatly influences likelihood-based estimates of the treatment effect in the conditional model. A second example considers a three-level structure where attitudes toward abortion over time are correlated with person and district level covariates. We observe that regression parameters in conditionally specified models are more sensitive to random effects assumptions than their counterparts in the marginal formulation.Item FINE PARTICULATE AIR POLLUTION AND MORTALITY IN 20 U.S. CITIES, 1987 - 1994(New England Journal of Medicine, 2000-12-14) Zeger, Scott L.; Coursac, Ivan; Curriero, Frank C.; Dominici, Francesca; Samet, Jonathan M.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.Item Spatial and Temporal Variation in PM2.5 Chemical Composition in the United States for Health Effects Studies(Environmental Health Perspectives, 2007-07) Samet, Jonathan M.; Zeger, Scott L.; Ebisu, Keita; Dominici, Francesca; Bell, Michelle L.