What is the purpose of a proportional hazards (Cox) model in cohort data?

• A. To estimate the risk difference over time.
• B. To estimate the relative risk at a single time point.
• C. To estimate the odds ratio.
• D. To estimate the hazard ratio between groups.

Answer: (D)

In time-to-event analysis, the proportional hazards (Cox) model is used to compare how quickly events occur between groups while handling censored data and adjusting for other factors. It expresses the hazard, the instantaneous risk of the event at time t, as h(t|X) = h0(t) exp(betaX). The key quantity is the hazard ratio, exp(beta), which tells you how much the instantaneous risk differs between groups at any given time, assuming this ratio stays constant over time (the proportional hazards assumption).

This makes the Cox model best for estimating the hazard ratio between groups. It directly describes relative instantaneous risk across time and can incorporate multiple covariates to adjust for confounding. It does not directly provide the risk difference over time, which is an absolute measure of event probability, nor does it give an odds ratio (that comes from logistic regression). It also isn’t designed to report a relative risk at a single time point; instead, it focuses on the ratio of hazards throughout the follow-up period.