Archetypical models

In medical research, regression models can be used to quantify relationships between predictors (e.g. age, treatment, comorbidities) and outcomes. Four archetypical models  and their extensions are often applied:

 Linear Regression

 This model is used when the outcome is continuous, such as e.g. blood pressure or lab values. The model assumes that the outcome has a straight-line relationship with the predictors, that data points are independent with consisten spread, and that the differences between actual and predicted values are normally distributed.

Results for are given trough coefficients that estimates how much the outcome increases or decreases per unit change in the predictor. 

 Logistic Regression

 Applied when the outcome is binary (e.g. disease vs. no disease). It assumes that the predictors have a linear relationship with the log-odds of the outcome and that the data points are independent.

It estimates the odds of the event occurring, with results typically presented as odds ratios (ORs). For instance, an OR of 1.8 for group 1 when compared to group 2 means the odds of disease are 80% higher in group 1 when compared to group 2.

Cox Regression (Proportional Hazards Model)

Cox is used for time-to-event data, such as survival or time to recurrence. It assumes that the effect of predictors on the risk of events is consistent over time, that observations are independent, and that hazard ratios between groups stay constant throughout the study period.

It assesses the effect of predictors on the hazard, or risk per time unit. Results are usually reported as hazard ratios (HRs), which represent the relative likelihood of the event at any time.

 Poisson Regression

Poisson is used for count data, particularly when the counts are over a period of time or/or space (e.g. number of infections per patient-year). It estimates rate ratios (e.g. incidence rate ratio, IRR), allowing comparison of event rates between groups.

References:

Harrell, F. E. (2015). Regression modeling strategies: With applications to linear models, logistic and ordinal regression, and survival analysis (2nd ed.). Springer.