-- KathrynStoltzfus - 22 Dec 2017

We study the application of a widely used ordinal regression model, the cumulative probability model (CPM), sometimes referred to as the 'cumulative link model', for continuous outcomes. Such models are attractive for the analysis of continuous response variables because they are invariant to any monotonic transformation of the outcome and because they directly model the cumulative distribution function from which summaries such as expectations and quantiles can easily be derived. Such models can also readily handle mixed type distributions. We describe the motivation, estimation, inference, model assumptions, and diagnostics. We demonstrate that CPMs applied to continuous outcomes are semiparametric transformation models. Extensive simulations are performed to investigate the finite sample performance of these models. We illustrate their application, with model diagnostics, in a study of the treatment of HIV. CD4 cell count and viral load 6 months after the initiation of antiretroviral therapy are modeled using CPMs; both variables typically require transformations, and viral load has a large proportion of measurements below a detection limit. This work is joint work with Qi Liu, Chun Li, and Frank Harrell.
Topic revision: r1 - 22 Dec 2017, KathrynStoltzfus

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