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Analyzing Clustered Continuous Response Variables with Ordinal Regression Models

Continuous response variables often need to be transformed to meet regression modeling assumptions; however, finding the optimal transformation is challenging and results may vary with the choice of transformation. When a continuous response variable is measured repeatedly for a subject or the continuous responses arise from clusters, it is more challenging to model the continuous response data due to correlation within clusters. We extend a widely used ordinal regression model, the cumulative probability model (CPM), to fit clustered continuous response variables based on generalized estimating equation (GEE) methods for ordinal responses. With our approach, estimates of marginal parameters, cumulative distribution functions (CDFs), expectations, and quantiles conditional on covariates can be obtained without pre-transformation of the potentially skewed continuous response data. Computational challenges arise with large numbers of distinct values of the continuous response variable, and we propose two feasible and computationally efficient approaches to fit CPMs for clustered continuous response variables with different working correlation structures. We study finite sample operating characteristics of the estimators via simulation, and illustrate their implementation with two data examples. One studies predictors of CD4:CD8 ratios in an HIV study. The other uses data from The Lung Health Study to investigate the contribution of a single nucleotide polymorphism to lung function decline.