Spurious interaction as a result of categorization

• Core Argument: Categorizing continuous exposure variables in regression models, a common practice in epidemiology, can introduce spurious interaction effects that do not exist in the original continuous scale.
• Mechanism: This phenomenon is demonstrated analytically and is interpreted as a form of differential measurement error or residual confounding caused by the categorization process.
• Conclusion: Spurious interaction is induced unless the correlated variables are dichotomized at the median or are uncorrelated. The paper strongly recommends avoiding categorization to ensure valid results, suggesting non-parametric models as a preferred alternative.

PubMed: 30732587 DOI: 10.1186/s12874-019-0667-2 Overview generated by: Gemini 2.5 Flash, 26/11/2025

Key Findings: The Generation of Spurious Interaction

This paper presents an additional argument against the common practice in epidemiological and clinical research of converting continuous exposure variables into categorical variables. It demonstrates that such categorization can lead to spurious interaction effects in multiple regression models, even when no true interaction exists between the continuous variables.

The spurious interaction problem is fundamentally linked to other well-known issues caused by categorization, including loss of information and statistical power and an increased risk of Type I error if continuous confounder variables are also categorized.

Study Design and Methods

The investigation used a combination of analytical and simulation-based methods:

Analytical Development

The authors derived precise analytical expressions for the linear regression model with two bivariate normally distributed exposure variables (\(X_1\) and \(X_2\)) and a continuous outcome (\(Y\)). Crucially, the true model assumed no interaction between the continuous exposure variables. The analysis then examined the conditions under which an interaction term would appear in a model using the categorized versions (\(\tilde{X}_1\) and \(\tilde{X}_2\)).

Interpretation

The authors interpret the spurious interaction in two related ways: 1. Measurement Error: Categorization is viewed as an extreme form of differential measurement error. Because the reliability (as measured by the point-biserial correlation) of the categorized variable \(\tilde{X}_i\) varies with the level of the other variable \(X_j\), the measurement error is differential, which is known to induce interaction. 2. Residual Confounding: Categorization of a continuous variable leaves residual confounding. Differences in this residual confounding across strata defined by the other exposure variable may lead to the observed spurious interaction.

Results

Analytical Result

For two correlated, normally distributed exposure variables, both categorized at the same cut point (\(c\)), a spurious interaction term (\(\tilde{\beta}_3\)) will be induced unless one of two conditions is met: * The two variables are uncorrelated (\(\rho=0\)). * The variables are categorized precisely at the median (\(c=0\) in the standardized case).

Empirical Illustrations and Simulation Findings

• Real Data Examples: The paper provides two practical examples (one linear model for lung function and one logistic model for myocardial infarction mortality) showing that categorization can change the interpretation of data by generating a statistically significant interaction where the original continuous model showed a non-significant or practically insignificant effect.
• Magnitude: Simulations demonstrated that the magnitude of the induced interaction term (relative to the main effects) increases substantially as the chosen cut point becomes more extreme (further from the median) and as the correlation (\(\rho\)) between the variables increases.
• Generalizability: Simulations using different distributions (Normal, Uniform, and Chi-square) confirmed that the general effect of spurious interaction due to categorization is present across various distributional shapes.

Conclusions and Recommendations

The primary conclusion is a strong recommendation that the categorization of continuous variables in regression modeling should be avoided.

The practice introduces a number of problems, including biased estimates, loss of power, and inflated Type-I error rates, with the generation of spurious interaction being another critical drawback.

If an interaction effect is found in an analysis using categorized explanatory variables, the researcher must consider the categorization method itself as a potential and likely explanation for the finding.

As alternatives, the authors suggest: * Using non-parametric regression methods if the relationship cannot be easily modeled by classical parametric models. * If one chooses to categorize despite the warnings, it is preferable to categorize into more than two groups to minimize the resulting information loss.