TY - JOUR
TI - Modeling continuous response variables using ordinal regression
AU - Liu, Qi
AU - Shepherd, Bryan E.
AU - Li, Chun
AU - Harrell, Frank E.
T2 - Statistics in Medicine
AB - We study the application of a widely used ordinal regression model, the cumulative probability model (CPM), 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 find that properly specified CPMs generally have good finite sample performance with moderate sample sizes, but that bias may occur when the sample size is small. Cumulative probability models are fairly robust to minor or moderate link function misspecification in our simulations. For certain purposes, the CPMs are more efficient than other 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.
DA - 2017/11/30/
PY - 2017
DO - 10.1002/sim.7433
DP - PubMed
VL - 36
IS - 27
SP - 4316
EP - 4335
J2 - Stat Med
LA - eng
SN - 1097-0258
KW - Anti-HIV Agents
KW - CD4 Lymphocyte Count
KW - Data Interpretation, Statistical
KW - HIV Infections
KW - Humans
KW - Likelihood Functions
KW - Models, Statistical
KW - Probability
KW - Regression Analysis
KW - Statistics, Nonparametric
KW - Treatment Outcome
KW - Viral Load
KW - nonparametric maximum likelihood estimation
KW - ordinal regression model
KW - rank-based statistics
KW - semiparametric transformation model
ER -