simultaneous analysis of mixed discrete and continuous outcomes using nonlinear threshold models

• Published in: Journal of agricultural, biological, and environmental statistics Vol. 12; no. 1; pp. 55 - 77
• Main Authors: Coffey, T, Gennings, C
• Format: Journal Article
• Language: English
• Published: Washington, DC American Statistical Association and the International Biometric Society 01.03.2007; American Statistical Association; International Biometric Society
• Subjects: Agronomy. Soil science and plant productions; algorithms; Analytical estimating; Biological and medical sciences; Biometrics; Biometrics, statistics, experimental designs, modeling, agricultural computer applications; Confidence interval; correlation; Correlations; dose response; Dose response relationship; equations; estimation; Estimation methods; Estimators; Fundamental and applied biological sciences. Psychology; Generalities. Biometrics, experimentation. Remote sensing; generalized estimating equations; methodology; Modeling; multiple outcomes; neurotoxicity; nonlinear models; Parametric models; Standard error; Generalized estimating equations (GEE); Multiple outcomes; Continuous; Correlated responses; Non linear model; Dose threshold; Estimating equation; Threshold dose
• ISSN: 1085-7117; 1537-2693
• DOI: 10.1198/108571107X177690

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.