Header

UZH-Logo

Maintenance Infos

An empirical comparison of two novel transformation models


Tian, Yuqi; Hothorn, Torsten; Li, Chun; Harrell, Frank E; Shepherd, Bryan E (2020). An empirical comparison of two novel transformation models. Statistics in Medicine, 39(5):562-576.

Abstract

Continuous response variables are often transformed to meet modeling assumptions, but the choice of the transformation can be challenging. Two transformation models have recently been proposed: semiparametric cumulative probability models (CPMs) and parametric most likely transformation models (MLTs). Both approaches model the cumulative distribution function and require specifying a link function, which implicitly assumes that the responses follow a known distribution after some monotonic transformation. However, the two approaches estimate the transformation differently. With CPMs, an ordinal regression model is fit, which essentially treats each continuous response as a unique category and therefore nonparametrically estimates the transformation; CPMs are semiparametric linear transformation models. In contrast, with MLTs, the transformation is parameterized using flexible basis functions. Conditional expectations and quantiles are readily derived from both methods on the response variable's original scale. We compare the two methods with extensive simulations. We find that both methods generally have good performance with moderate and large sample sizes. MLTs slightly outperformed CPMs in small sample sizes under correct models. CPMs tended to be somewhat more robust to model misspecification and outcome rounding. Except in the simplest situations, both methods outperform basic transformation approaches commonly used in practice. We apply both methods to an HIV biomarker study.

Abstract

Continuous response variables are often transformed to meet modeling assumptions, but the choice of the transformation can be challenging. Two transformation models have recently been proposed: semiparametric cumulative probability models (CPMs) and parametric most likely transformation models (MLTs). Both approaches model the cumulative distribution function and require specifying a link function, which implicitly assumes that the responses follow a known distribution after some monotonic transformation. However, the two approaches estimate the transformation differently. With CPMs, an ordinal regression model is fit, which essentially treats each continuous response as a unique category and therefore nonparametrically estimates the transformation; CPMs are semiparametric linear transformation models. In contrast, with MLTs, the transformation is parameterized using flexible basis functions. Conditional expectations and quantiles are readily derived from both methods on the response variable's original scale. We compare the two methods with extensive simulations. We find that both methods generally have good performance with moderate and large sample sizes. MLTs slightly outperformed CPMs in small sample sizes under correct models. CPMs tended to be somewhat more robust to model misspecification and outcome rounding. Except in the simplest situations, both methods outperform basic transformation approaches commonly used in practice. We apply both methods to an HIV biomarker study.

Statistics

Citations

Dimensions.ai Metrics
1 citation in Web of Science®
1 citation in Scopus®
Google Scholar™

Altmetrics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:04 Faculty of Medicine > Epidemiology, Biostatistics and Prevention Institute (EBPI)
Dewey Decimal Classification:610 Medicine & health
Scopus Subject Areas:Health Sciences > Epidemiology
Physical Sciences > Statistics and Probability
Uncontrolled Keywords:Statistics and Probability, Epidemiology
Language:English
Date:28 February 2020
Deposited On:25 Jan 2021 15:43
Last Modified:26 Jan 2021 21:01
Publisher:Wiley-Blackwell Publishing, Inc.
ISSN:0277-6715
OA Status:Closed
Publisher DOI:https://doi.org/10.1002/sim.8425
PubMed ID:31808976
Project Information:
  • : FunderSNSF
  • : Grant ID200021_184603
  • : Project TitleA Lego System for Transformation Inference

Download

Full text not available from this repository.
View at publisher

Get full-text in a library