Robust estimation of the effect of an exposure on the change in a continuous outcome
Abstract Background The change in two measurements of a continuous outcome can be modelled directly with a linear regression model, or indirectly with a random effects model (REM) of the individual measurements. These methods are susceptible to model misspecifications, which are commonly addressed b...
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doaj-922a6a4d775a4a0a908cabff79db968f2020-11-25T03:26:19ZengBMCBMC Medical Research Methodology1471-22882020-06-0120111110.1186/s12874-020-01027-6Robust estimation of the effect of an exposure on the change in a continuous outcomeYilin Ning0Nathalie C. Støer1Peh Joo Ho2Shih Ling Kao3Kee Yuan Ngiam4Eric Yin Hao Khoo5Soo Chin Lee6E-Shyong Tai7Mikael Hartman8Marie Reilly9Chuen Seng Tan10NUS Graduate School for Integrative Sciences and Engineering, National University of SingaporeNorwegian National Advisory Unit on Women’s Health, Oslo University HospitalSaw Swee Hock School of Public Health, National University of Singapore and National University Health SystemYong Loo Lin School of Medicine, Department of Medicine, National University of Singapore and National University Health SystemYong Loo Lin School of Medicine, Department of Surgery, National University of Singapore and National University Health SystemYong Loo Lin School of Medicine, Department of Medicine, National University of Singapore and National University Health SystemCancer Science Institute of Singapore, National University of SingaporeYong Loo Lin School of Medicine, Department of Medicine, National University of Singapore and National University Health SystemNUS Graduate School for Integrative Sciences and Engineering, National University of SingaporeDepartment of Medical Epidemiology and Biostatistics, Karolinska InstitutetSaw Swee Hock School of Public Health, National University of Singapore and National University Health SystemAbstract Background The change in two measurements of a continuous outcome can be modelled directly with a linear regression model, or indirectly with a random effects model (REM) of the individual measurements. These methods are susceptible to model misspecifications, which are commonly addressed by applying monotonic transformations (e.g., Box-Cox transformation) to the outcomes. However, transforming the outcomes complicates the data analysis, especially when variable selection is involved. We propose a robust alternative through a novel application of the conditional probit (cprobit) model. Methods The cprobit model analyzes the ordered outcomes within each subject, making the estimate invariant to monotonic transformation on the outcome. By scaling the estimate from the cprobit model, we obtain the exposure effect on the change in the observed or Box-Cox transformed outcome, pending the adequacy of the normality assumption on the raw or transformed scale. Results Using simulated data, we demonstrated a similar good performance of the cprobit model and REM with and without transformation, except for some bias from both methods when the Box-Cox transformation was applied to scenarios with small sample size and strong effects. Only the cprobit model was robust to skewed subject-specific intercept terms when a Box-Cox transformation was used. Using two real datasets from the breast cancer and inpatient glycemic variability studies which utilize electronic medical records, we illustrated the application of our proposed robust approach as a seamless three-step workflow that facilitates the use of Box-Cox transformation to address non-normality with a common underlying model. Conclusions The cprobit model provides a seamless and robust inference on the change in continuous outcomes, and its three-step workflow is implemented in an R package for easy accessibility.http://link.springer.com/article/10.1186/s12874-020-01027-6Box-Cox transformationConditional probit modelNormal errorsRandom effects model |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Yilin Ning Nathalie C. Støer Peh Joo Ho Shih Ling Kao Kee Yuan Ngiam Eric Yin Hao Khoo Soo Chin Lee E-Shyong Tai Mikael Hartman Marie Reilly Chuen Seng Tan |
spellingShingle |
Yilin Ning Nathalie C. Støer Peh Joo Ho Shih Ling Kao Kee Yuan Ngiam Eric Yin Hao Khoo Soo Chin Lee E-Shyong Tai Mikael Hartman Marie Reilly Chuen Seng Tan Robust estimation of the effect of an exposure on the change in a continuous outcome BMC Medical Research Methodology Box-Cox transformation Conditional probit model Normal errors Random effects model |
author_facet |
Yilin Ning Nathalie C. Støer Peh Joo Ho Shih Ling Kao Kee Yuan Ngiam Eric Yin Hao Khoo Soo Chin Lee E-Shyong Tai Mikael Hartman Marie Reilly Chuen Seng Tan |
author_sort |
Yilin Ning |
title |
Robust estimation of the effect of an exposure on the change in a continuous outcome |
title_short |
Robust estimation of the effect of an exposure on the change in a continuous outcome |
title_full |
Robust estimation of the effect of an exposure on the change in a continuous outcome |
title_fullStr |
Robust estimation of the effect of an exposure on the change in a continuous outcome |
title_full_unstemmed |
Robust estimation of the effect of an exposure on the change in a continuous outcome |
title_sort |
robust estimation of the effect of an exposure on the change in a continuous outcome |
publisher |
BMC |
series |
BMC Medical Research Methodology |
issn |
1471-2288 |
publishDate |
2020-06-01 |
description |
Abstract Background The change in two measurements of a continuous outcome can be modelled directly with a linear regression model, or indirectly with a random effects model (REM) of the individual measurements. These methods are susceptible to model misspecifications, which are commonly addressed by applying monotonic transformations (e.g., Box-Cox transformation) to the outcomes. However, transforming the outcomes complicates the data analysis, especially when variable selection is involved. We propose a robust alternative through a novel application of the conditional probit (cprobit) model. Methods The cprobit model analyzes the ordered outcomes within each subject, making the estimate invariant to monotonic transformation on the outcome. By scaling the estimate from the cprobit model, we obtain the exposure effect on the change in the observed or Box-Cox transformed outcome, pending the adequacy of the normality assumption on the raw or transformed scale. Results Using simulated data, we demonstrated a similar good performance of the cprobit model and REM with and without transformation, except for some bias from both methods when the Box-Cox transformation was applied to scenarios with small sample size and strong effects. Only the cprobit model was robust to skewed subject-specific intercept terms when a Box-Cox transformation was used. Using two real datasets from the breast cancer and inpatient glycemic variability studies which utilize electronic medical records, we illustrated the application of our proposed robust approach as a seamless three-step workflow that facilitates the use of Box-Cox transformation to address non-normality with a common underlying model. Conclusions The cprobit model provides a seamless and robust inference on the change in continuous outcomes, and its three-step workflow is implemented in an R package for easy accessibility. |
topic |
Box-Cox transformation Conditional probit model Normal errors Random effects model |
url |
http://link.springer.com/article/10.1186/s12874-020-01027-6 |
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