What are common hazard function families in survival analysis?

• A. Exponential and normal.
• B. Gamma and Gompertz.
• C. Log-normal and log-logistic.
• D. Constant and Weibull.

Answer: (D)

In survival analysis, the hazard function describes the instantaneous risk of an event at time t, given survival to that time. The two most commonly used hazard shapes in simple parametric modeling are the constant hazard and the Weibull hazard. A constant hazard means the risk does not change over time, which corresponds to the exponential model. The Weibull hazard is more flexible: h(t) = (k/λ)(t/λ)^{k-1}, so it can model increasing risk over time (k>1) or decreasing risk (k<1), with k=1 reducing to the constant hazard case. This combination—constant (exponential) and Weibull—covers the staple, widely used hazard forms in teaching and practice because they span a simple, flexible range of time-varying risks. Other options mix distributions with hazards that aren’t standard, or include shapes that aren’t typically described as the basic hazard-function families used for straightforward parametric survival modeling.