Quantile regression and restricted cubic splines are useful for exploring relationships between continuous variables

Abstract Objective Ordinary least squares (OLS) regression, commonly called linear regression, is often used to assess, or adjust for, the relationship between a continuous independent variable and the mean of a continuous dependent variable, implicitly assuming a linear relationship between them. L...

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Bibliographic Details
Published in:Journal of clinical epidemiology 2009-05, Vol.62 (5), p.511-517.e1
Main Authors: Marrie, Ruth Ann, MD, PhD, Dawson, Neal V., MD, Garland, Allan, MD, MA
Format: Article
Language:English
Subjects:
Algorithms
Biological and medical sciences
Cognition
Cognition Disorders - epidemiology
Computerized, statistical medical data processing and models in biomedicine
Data Interpretation, Statistical
Economic models
Epidemiology
General aspects. Methods
Humans
Intensive Care Units
Internal Medicine
Length of Stay - statistics & numerical data
Linear Models
Linear regression
Medical research
Medical sciences
Models, Statistical
Multiple Sclerosis - epidemiology
Multivariate analysis
Quantile regression
Regression Analysis
Research Design - statistics & numerical data
Restricted cubic splines
Severity of Illness Index
Statistical analysis
Statistical models
Studies
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Summary:Abstract Objective Ordinary least squares (OLS) regression, commonly called linear regression, is often used to assess, or adjust for, the relationship between a continuous independent variable and the mean of a continuous dependent variable, implicitly assuming a linear relationship between them. Linearity may not hold, however, and analyzing the mean of the dependent variable may not capture the full nature of such relationships. Our goal is to demonstrate how combined use of quantile regression and restricted cubic splines (RCS) can reveal the true nature and complexity of relationships between continuous variables. Study Design and Setting We provide a review of methodologic concepts, followed by two examples using real data sets. In the first example, we analyzed the relationship between cognition and disease duration in multiple sclerosis. In the second example, we analyzed the relationship between length of stay (LOS) and severity of illness in the intensive care unit (ICU). Results In both examples, quantile regression showed that the relationship between the variables of interest was heterogeneous. In the second example, RCS uncovered nonlinearity of the relationship between severity of illness and length of stay. Conclusion Together, quantile regression and RCS are a powerful combination for exploring relationships between continuous variables.
ISSN:0895-4356
1878-5921
DOI:10.1016/j.jclinepi.2008.05.015