Chapter 7: Modeling Outcomes and Applied Measures

Multivariable regression

Builds on simple linear regression

• two or more explanatory variables

• includes two or more explanatory variables

• helps control for confounding

• estimates the independent effect of each variable

hazard rate ratio

• used in survival analysis

• compares the rate at which events occur in two groups

• based on time-t-event data

• accounts for varying follow-up times (person-time)'

A Hazard Ratio (HR) compares event rates between two groups, telling you if an event (like death, disease, or failure) happens more or less often in one group over time, with HR=1 meaning no difference, HR > 1 meaning higher risk in the first group (e.g., twice as fast), and HR < 1 meaning lower risk (e.g., half the rate), often used in survival analysis to see treatment effects. 

Key Interpretations

• HR = 1: The event occurs at the same rate in both groups (no difference).

• HR > 1: The event is more likely or happens faster in the first (or experimental) group compared to the second (control) group.

  • Example: HR of 2.0 means the event rate is twice as high.

• HR < 1: The event is less likely or happens slower in the first group.

  • Example: HR of 0.5 means the event rate is half as high, suggesting a protective effect or better outcome. 

Number needed to treat (NNT)

Ex) Clinical Trial

20% of people in the control group had a heart attack

10% of people in the treatment group had a heart attack

Formula : NNT = 1 / Absolute Risk reduction

ARR= 20 % - 10 % = 10% or 0.10

NNT = 1/.10 = 10

Interpretation: We would need to treat 10 people with the new therapy to prevent one additional heart attack

Absolute Risk Reducition

Ex) Clinical Trial

20% of people in the control group had a heart attack

10% of people in the treatment group had a heart attack

Absolute risk reduction (ARR) refers to the actual difference in risk between the treated and the control group.