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Semiparametric linear transformation models: Effect measures, estimators, and applications
Author(s) -
De Neve Jan,
Thas Olivier,
Gerds Thomas A.
Publication year - 2019
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.8078
Subject(s) - estimator , semiparametric regression , generalized linear model , estimating equations , linear model , transformation (genetics) , linear regression , mathematics , econometrics , regression analysis , probabilistic logic , proportional hazards model , statistics , semiparametric model , variance (accounting) , computer science , economics , biochemistry , chemistry , accounting , gene
Semiparametric linear transformation models form a versatile class of regression models with the Cox proportional hazards model being the most well‐known member. These models are well studied for right censored outcomes and are typically used in survival analysis. We consider transformation models as a tool for situations with uncensored continuous outcomes where linear regression is not appropriate. We introduce the probabilistic index as a uniform effect measure for the class of transformation models. We discuss and compare three estimators using a working Cox regression model: the partial likelihood estimator, an estimator based on binary generalized linear models and one based on probabilistic index model estimating equations. The latter has a superior performance in terms of bias and variance when the working model is misspecified. For the purpose of illustration, we analyze data that were collected at an urban alcohol and drug detoxification unit.