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.
Browsing Biostatistics, Dept. of by Subject "Logistic regression"
(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.
(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.