The simultaneous analysis of mixed discrete and continuous outcomes using nonlinear threshold models |
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Authors: | Todd Coffey Chris Gennings |
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Institution: | (1) Centre for Applied Pharmacokinetic Research, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK;(2) School of Pharmacy and Pharmaceutical Sciences, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK |
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Abstract: | Mixed discrete and continuous outcomes are commonly measured on each experimental unit in dose-response studies in toxicology.
The dose-response relationships for these outcomes often have dose thresholds and nonlinear patterns. In addition, the endpoints
are typically correlated, and a statistical analysis that incorporates the association may result in improved precision. We
propose an extension of the generalized estimating equation (GEE) methodology to simultaneously analyze binary, count, and
continuous outcomes with nonlinear threshold models that incorporates the intra-subject correlation. The methodology uses
a quasi-likelihood framework and a working correlation matrix, and is appropriate when the marginal expectation of each outcome
is of primary interest and the correlation between endpoints is a nuisance parameter. Because the derivatives of threshold
models are not continuous at each point of the parameter space, we describe the necessary modifications that result in asymptotically
normal and consistent estimators. Using dose-response data from a neurotoxicity experiment, the methodology is illustrated
by analyzing five outcomes of mixed type with nonlinear threshold models. In this example, the incorporation of the intra-subject
correlation resulted in decreased standard errors for the threshold parameters. |
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