Hazard function modeling

A wide variety of outcomes can be characterized by their time of occurrence. The hazard function describes how the instantaneous risk of the event occurring changes over time. Hazard function modeling aids in interpreting this temporal evolution, allows for extrapolations to future time points, and quantifies the impact of covariates. Estimates of survival over time may also be obtained from the hazard function. Formal definitions of the hazard and survival functions are provided, along with details of models that are traditionally used: the exponential, Weibull, Gompertz, gamma, lognormal, and log‐logistic. Limitations of these models are discussed, which motivate the use of models with increased flexibility. These include fractional polynomials, spline‐based models, and dynamic survival models. These models make the assumption that the hazard function is smooth over time. This is a less‐restrictive assumption than those employed by traditional models. Formal definitions are provided for these flexible models, along with a discussion of their strengths and limitations.