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Regression models for continuous outcomes often require a transformation ofthe outcome, which the user either specify {\it a priori} or estimate from aparametric family. Cumulative probability models (CPMs) nonparametricallyestimate the transformation and are thus a flexible analysis approach forcontinuous outcomes. However, it is difficult to establish asymptoticproperties for CPMs due to the potentially unbounded range of thetransformation. Here we show asymptotic properties for CPMs when applied toslightly modified data where the outcomes are censored at the ends. We proveuniform consistency of the estimated regression coefficients and the estimatedtransformation function over the non-censored region, and describe their jointasymptotic distribution. We show with simulations that results from thiscensored approach and those from the CPM on the original data are similar whena small fraction of data are censored. We reanalyze a dataset of HIV-positivepatients with CPMs to illustrate and compare the approaches.

Asymptotic Properties for Cumulative Probability Models for Continuous Outcomes