Marginal regression models for analyzing mixed discrete and continuous responses.

Analysis of mixed discrete and continuous data is challenging due to lack of well-defined class of distribution functions to model such data, and analysis of mixed responses in the presence of clustering is even more difficult due to the correlations within the cluster. Literature on analyzing mixed discrete and continuous responses in the presence of clustering addresses only bivariate mixed responses, and no methods are available for analyzing multivariate mixed responses. In this dissertation I develop methods for marginal analysis of mixed discrete and continuous data. I model the marginal expectation and the pairwise associations of the responses in terms of covariates using known link functions. The method is developed in stages. First I consider only bivariate data without clustering. I analyze these data using likelihood methods. In the second stage I consider multivariate data. Here I utilize Generalized Estimating Equations (GEE) to estimate the parameters. I extend these methods to analyze multivariate mixed discrete and continuous data with clustering in the final stage. The parameters are estimated using GEE in this stage as well. Even though the parameters are estimated using different methods at different stages the overall approach for analysis is the same. This approach is flexible in terms of link functions. It also allows the use of different statistics, depending on the application, to measure the pairwise association. It yields generally consistent estimators. The main advantage of this approach is that each response is modeled marginally and is therefore reproducible, unlike previous methods that have been proposed in the literature. In conclusion, this dissertation provides a statistician with tools for (a) modeling pairwise associations between mixed discrete and continuous responses in terms of covariates, and for (b) analyzing multivariate mixed responses in the presence of clustering.Ph.D.Biological SciencesBiostatisticsPure SciencesStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/132476/2/9963899.pd

Meta-Analysis of Clinical Dose–Response in a Large Drug Development Portfolio

<div><p>This article reports the results of a meta-analysis based on dose–response studies conducted by a large pharmaceutical company between 1998–2009. Data collection targeted efficacy endpoints from all compounds with evidence of clinical efficacy during the time period. Safety data were not extracted. The goal of the meta-analysis was to identify consistent quantitative patterns in dose–response across different compounds and diseases. The article presents summaries of the study designs, including the number of studies conducted for each compound, dosing range, the number of doses evaluated, and the number of patients per dose. The  E_max model, ubiquitous in pharmacology research, was fit for each compound. It described the data well, except for a single compound, which had nonmonotone dose–response. Compound-specific estimates and Bayesian hierarchical modeling showed that dose–response curves for most compounds can be approximated by  E_max models with “Hill” parameters close to 1.0. Summaries of the potency estimates show pharmacometric predictions of potency made before the first dose ranging study within a (1/10, 10) multiple of the final estimates for 90% of compounds. The results of the meta-analysis, when combined with compound-specific information, provide an empirical basis for designing and analyzing new dose finding studies using parametric E_max models and Bayesian estimation with empirically derived prior distributions.</p></div