What are the general approaches to analyzing survival data?

• A. Non-parametric models only
• B. Semi-parametric models only
• C. Parametric models only
• D. Non-parametric, semi-parametric, and parametric models

Answer: (D)

Survival analysis can be approached with three broad modeling frameworks, each fitting different assumptions about time-to-event data and how covariates affect risk. Non-parametric methods let the data speak without committing to a particular distribution for survival times. The Kaplan-Meier estimator for the survival function is a core example, and log-rank tests are used to compare groups when you don’t want to assume a specific time pattern. This approach is ideal for describing what happens in the data and for simple group comparisons when there’s little prior knowledge about the underlying distribution.

Semi-parametric methods strike a balance by allowing you to adjust for covariates while not specifying the baseline hazard’s shape. The Cox proportional hazards model is the primary tool here. It estimates how covariates multiply the hazard over time, yielding hazard ratios, while keeping the baseline hazard form unspecified. This flexibility makes it robust and widely applicable when you want covariate effects without imposing a time-dependent hazard form.

Parametric methods, on the other hand, require specifying a full distribution for survival times, such as exponential, Weibull, log-normal, or others. If the assumed distribution fits well, these models can be more efficient and also enable extrapolation beyond the observed follow-up. The trade-off is the risk of misspecifying the distribution, which can bias results if the chosen form doesn’t reflect the true survival pattern.

You choose among these based on the data and goals: non-parametric for description and simple comparisons, semi-parametric for covariate effects with flexible baseline risk, and parametric when you have a good reason to assume a particular time-to-event distribution and may need extrapolation. That’s why all three broad approaches are used in survival analysis.