Biostatistics Weekly Seminar

Extensions of Ordinal Cumulative Probability Models

Yuqi Tian
Vanderbilt University Medical Center

Continuous response variables can be analyzed with ordinal cumulative probability models (CPMs), also known as “cumulative link models”. Continuous outcomes often need to be transformed to meet modeling assumptions. CPMs semi-parametrically estimate the transformation and they directly model the cumulative distribution function, from which conditional expectations, quantiles, probability indices, and other interpretable parameters can be easily derived. In this talk, we present some extensions of CPMs. First, we compare CPMs with most likely transformation models (MLTs), which parametrically estimate the transformation using flexible basis functions. Second, we extend CPMs to deal with multiple detection limits. Detection limits are common in biomedical research, but most analysis approaches either explicitly assign a value to the undetectable measures or implicitly make parametric assumptions about the distribution of data outside the detection limits. Third, we extend CPMs to model clustered/longitudinal continuous response variables; our approach is equivalent to fitting an ordinal GEE model with an independence working correlation structure. We illustrate the proposed approaches through simulations and applications to HIV studies.

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09 September 2020

Topic revision: r1 - 02 Sep 2020, AndrewSpieker

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