HIV Working Group

Bryan E. Shepherd, Ph.D.
Professor, Department of Biostatistics, Vanderbilt University School of Medicine

“Analyzing Continuous Response Data with Ordinal Cumulative Probability Models”

ABSTRACT: The popular ordinal cumulative link model (which we refer to as the cumulative probability model because probabilities – not links – are cumulative) can be used to directly model continuous response data – no categorizing of the continuous outcome needed. Why would anyone want to do that? For several reasons: Continuous data often require a transformation before fitting a multiple linear regression model – fitting the ordinal cumulative probability model is actually fitting a semi-parametric linear transformation model. These models assume that after some unspecified transformation, to be estimated by the data, the response variable follows a linear model. Hence, these models are quite flexible. As they are rank-based, they are also fairly robust. They are also an excellent analysis option for handling data with detection limits, where the data can be thought of as a mixture of discrete and continuous data. And interpretable quantities can be easily extracted from cumulative probability models including odds ratios, conditional expectations, conditional quantiles, conditional probabilities, and probability indexes. I will present properties of cumulative probability models and demonstrate their use with a wide variety of HIV-related datasets.