Choosing the Right Regression Model: A Visual Guide for Outcome Types in Clinical Research

In clinical epidemiology and biostatistics, choosing the correct regression model hinges on the characteristics of the outcome variable YY. The table below aligns outcome types with the appropriate regression model, the mathematical behavior of the model, the assumed statistical distribution, and an intuitive memory aid to support learning:

Table: Mapping Outcome Types to Regression Models

Model	Nature of Y	Mathematical Shape	Distribution	Memory Aid
Linear (regress)	Continuous	Straight Line	Normal	Floating mean values
Logistic (logistic)	Binary	Sigmoid Curve	Binomial	Curves between 0–1
Poisson (poisson)	Count/Event	Log-linear (exponential)	Poisson	More count → steeper rise
Cox (stcox)	Time-to-event	Survival Step-curve	Time-to-event	Survival in steps

---

Narrative Summary

Each model corresponds not only to a different statistical function but also to a fundamentally distinct mathematical and visual interpretation:

1. Linear Regression (regress)

   • Y: Continuous variable (e.g., blood pressure)

   • Graph: A straight line through data points; models mean change

   • Distribution: Assumes normally distributed errors

   • Use Case: Estimating the change in means across groups or continuous predictors
     

2. Logistic Regression (logistic)

   • Y: Binary outcome (e.g., alive vs. dead)

   • Graph: S-shaped sigmoid curve; models probability

   • Distribution: Binomial distribution with a logit link

   • Use Case: Estimating odds ratios; constrained between 0–1
     

3. Poisson Regression (poisson)

   • Y: Count outcome (e.g., number of infections)

   • Graph: Exponential curve (linear in log scale)

   • Distribution: Poisson

   • Use Case: Modeling incidence rates or event frequencies
     

4. Cox Proportional Hazards Model (stcox)

   • Y: Time until an event (e.g., time to death)

   • Graph: Stepwise survival function or cumulative hazard curve

   • Distribution: Semi-parametric (no baseline hazard assumption)

   • Use Case: Estimating hazard ratios for time-to-event data
     

This framework simplifies the learning process for graduate students and researchers in clinical statistics, providing a clear link between outcome type, appropriate model, and its visual-mathematical rationale.

Let me know if you'd like this converted to a formatted PDF or Word document for inclusion in your coursework.