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Semiparametric linear transformation models: Effect measures, estimators, and applications.

Jan De Neve1, Olivier Thas2,3, Thomas A Gerds4

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Summary

Semiparametric transformation models offer a flexible approach for analyzing uncensored continuous outcomes. A novel probabilistic index measure and a new estimator demonstrate superior performance, particularly when the working model is misspecified.

Keywords:
probabilistic indexproportional hazard modelproportional odds modelsemiparametric regression

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Semiparametric linear transformation models are versatile regression tools, with the Cox proportional hazards model being a key example.
  • These models are extensively studied for right-censored data in survival analysis.
  • Linear regression is often unsuitable for certain continuous outcomes.

Purpose of the Study:

  • To adapt transformation models for uncensored continuous outcomes where linear regression is inappropriate.
  • To introduce the probabilistic index as a unified effect measure for transformation models.
  • To compare the performance of different estimators for these models.

Main Methods:

  • The study considers transformation models for uncensored continuous outcomes.
  • A probabilistic index is introduced as a uniform effect measure.
  • Three estimators are discussed and compared: partial likelihood, binary generalized linear models, and probabilistic index model estimating equations, all using a working Cox regression model.

Main Results:

  • The probabilistic index model estimating equations estimator shows superior performance regarding bias and variance.
  • This improved performance is especially notable when the working Cox regression model is misspecified.
  • The methods are illustrated using data from an urban alcohol and drug detoxification unit.

Conclusions:

  • Transformation models can be effectively applied to uncensored continuous outcomes.
  • The probabilistic index provides a valuable and uniform measure of effect for these models.
  • The proposed probabilistic index model estimator offers a robust alternative, outperforming others under model misspecification.