Choosing the Right Regression Model in Clinical Research: A Practical Guide

Introduction

Regression models form the cornerstone of modern clinical and epidemiologic analysis. Whether the aim is to understand risk factors, estimate treatment effects, or build prediction models, regression offers a flexible statistical framework. However, with a variety of outcome types and underlying assumptions, choosing the right model—and using it correctly—requires foundational knowledge. This guide provides an integrated summary of regression methods tailored to clinical researchers, with a focus on aligning model type with outcome nature and ensuring valid application through assumption checking.

The Foundation: Regression Assumptions

Every regression model, regardless of its complexity or type, relies on a set of assumptions. Violation of these can lead to misleading results and poor generalizability.

Key Assumptions Include:

Linearity: The relationship between predictors and the outcome is linear on the appropriate scale. This is especially critical for continuous outcomes.
Normality of Residuals: For linear models, residuals should be normally distributed to ensure valid inference.
No Autocorrelation: Observations must be independent. Serial correlation, often in longitudinal data, violates this assumption.
No Multicollinearity: Predictors should not be highly correlated with each other, as this distorts coefficient estimates.
Homoscedasticity: Constant variance of residuals across all levels of the predictor variables.

Illustrative Example: In a study measuring the effect of BMI on blood pressure, checking the residuals' distribution and ensuring linearity in the BMI-blood pressure relationship is crucial before trusting the regression coefficients.

Choosing the Right Regression Model Based on Outcome Type

1. Continuous Outcomes

Use Gaussian (normal) regression, also known as linear regression.

Ordinary Least Squares (OLS):
- Syntax: regress outcome predictors
Generalized Linear Model (GLM) with identity link and Gaussian family:
- Syntax: glm outcome predictors, link(identity) family(gaussian)

Example: Modeling cholesterol level as a function of age, BMI, and diet quality.

2. Count Outcomes

Use Poisson or Negative Binomial regression depending on data dispersion.

Poisson Regression (if variance ≈ mean):
- Syntax: glm outcome predictors, link(log) family(poisson)
Negative Binomial Regression (if overdispersion is present):
- Syntax: glm outcome predictors, link(log) family(nbinomial)

Example: Analyzing the number of hospital admissions per year in patients with chronic obstructive pulmonary disease.

3. Binary Outcomes

Use binomial family regressions with different link functions to derive different measures.

Risk Difference (RD):
- Syntax: glm outcome predictors, link(identity) family(binomial)
Risk Ratio (RR):
- Syntax: glm outcome predictors, link(log) family(binomial), eform
Odds Ratio (OR) (Logistic Regression):
- Syntax: glm outcome predictors, link(logit) family(binomial), eform
- Alternate: logistic outcome predictors
If the model fails to converge:
- Use Poisson regression with robust variance estimates:
  - Syntax: glm outcome predictors, link(log) family(poisson), robust

Example: Estimating the effect of smoking on the probability of developing stroke within 5 years.

4. Multinomial and Ordinal Outcomes

A. Multinomial Logistic Regression

Use when the outcome has more than two unordered categories.

Syntax: mlogit outcome predictors, base(reference) rrr

Example: Modeling treatment choice (surgery, radiotherapy, observation) based on tumor size and age.

B. Ordinal Logistic Regression

Use when the outcome categories have a natural order.

Proportional Odds Model:
- Syntax: ologit outcome predictors
Generalized Ordinal Logistic Models:
- Syntax: gologit2 outcome predictors, auto
Continuation Ratio Models:
- Syntax: ocratio outcome predictors

Assumption: These models often rely on the proportional odds assumption, which must be tested to ensure validity.

Example: Grading disease severity (mild, moderate, severe) based on clinical indicators.

5. Time-to-Event (Survival) Outcomes

A. Semi-Parametric Cox Regression

Ideal when the hazard function is unknown.

Set survival time and status: stset time, failure(status)
Run model: stcox predictors

B. Fully Parametric Survival Models

Use when the hazard follows a known distribution (e.g., Weibull, exponential).

Set survival data: stset time, failure(status)
Run model with distribution: streg predictors, distribution(weibull|gompertz|gamma|exponential)

C. Flexible Parametric Survival Models

Allow for complex hazard functions using spline techniques.

Syntax (after stset): stpm2 predictors, df(3)

Assumption: Survival models often assume proportional hazards, which must be evaluated.

Example: Estimating time to cardiovascular event post-statin initiation using Cox and Weibull models.

Conclusion

Regression analysis offers a powerful suite of tools for clinical researchers, but each model must be tailored to the specific nature of the outcome variable. Beyond simply fitting a model, researchers must carefully validate assumptions and understand the interpretation of regression parameters in each context. Whether estimating probabilities, rates, or survival times, the thoughtful application of regression models enhances both the scientific rigor and clinical relevance of study findings.

Would you like a Stata command reference sheet based on these models or diagnostic tools for checking assumptions?