Year: 2023
Type: article
Abstract: Regression models for continuous outcomes frequently require a transformation of the outcome, which is often specified a priori or estimated from a parametric family. Cumulative probability models (CPMs) nonparametrically estimate the transformation by treating the continuous outcome as if it is ordered categorically. They thus represent a flexible analysis approach for continuous outcomes. However, it is difficult to establish asymptotic properties for CPMs due to the potentially unbounded range of the transformation. Here we show asymptotic properties for CPMs when applied to slightly modified data where bounds, one lower and one upper, are chosen and the outcomes outside the bounds are set as two ordinal categories. We prove the uniform consistency of the estimated regression coefficients and of the estimated transformation function between the bounds. We also describe their joint asymptotic distribution, and show that the estimated regression coefficients attain the semiparametric efficiency bound. We show with simulations that results from this approach and those from using the CPM on the original data are very similar when a small fraction of the data are modified. We reanalyze a dataset of HIV-positive patients with CPMs to illustrate and compare the approaches.
Source: Mathematics
DOI: 10.3390/math11244896
Authors: Chun Li, Yuqi Tian, Donglin Zeng, Bryan E. Shepherd
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,336
Awards: G4800624620, The dynamics of HIV, aging, and T lymphocyte exhaustion, Tennessee Center for AIDS Research (TN-CFAR), Semiparametric Regression Analysis of Interval-Censored Data in Current Cohort Studies, Statistical Methods for Ordinal Variables in HIV/AIDS Studies, Statistical and Machine Learning Methods to Improve Dynamic Treatment Regimens Estimation Using Real World Data.
OpenAlex ID: W4389440431