Which method should I use?

Recommendations for: analyze the time until an event occurs with censored observations

1. Weibull RegressionSurvival

   Weibull regression is a fully parametric survival model, formalised by Kalbfleisch and Prentice, that assumes survival times follow a Weibull distribution. A shape parameter controls whether the hazard increases, decreases, or remains constant over time, while covariates shift the scale of the distribution to express how predictors affect survival.

2. Kaplan-Meier EstimatorStatistics

   The Kaplan-Meier estimator is a nonparametric method for estimating the survival function S(t) — the probability that an individual survives beyond time t — from data that include censored observations. Introduced by Edward L. Kaplan and Paul Meier in their landmark 1958 JASA paper, it is the standard first step in any survival analysis and is among the most-cited statistical methods in biomedical research.

3. Royston-Parmar ModelSurvival

   The Royston-Parmar model, introduced by Royston and Parmar in 2002, is a modern parametric approach to survival analysis that replaces the rigid distributional assumptions of classical models with a restricted cubic spline fitted to the log-cumulative-hazard scale. It combines the interpretability of a fully parametric model with the flexibility to capture non-standard hazard shapes, and it supports proportional-hazards, accelerated failure-time, and proportional-odds link functions.

4. Kaplan-MeierSurvival

   The Kaplan-Meier estimator, introduced by Kaplan and Meier in 1958, is a non-parametric method that estimates the survival curve — the probability of remaining event-free over time — from right-censored time-to-event data. The log-rank test is the companion procedure used to compare survival curves between groups.

5. Accelerated Failure Time ModelSurvival

   The Accelerated Failure Time model is a parametric regression approach to survival analysis — formally reviewed and advocated by L. J. Wei in 1992 — in which covariates act as multiplicative factors that directly stretch or compress the time-to-event scale. Unlike the Cox proportional-hazards model, which models how covariates shift the hazard rate, AFT models express the covariate effect as an acceleration or deceleration of the time axis itself.

6. Cox RegressionSurvival

   Cox proportional hazards regression, introduced by D. R. Cox in 1972, is a semi-parametric model that estimates how one or more covariates affect the hazard — the instantaneous rate of experiencing an event — while leaving the baseline hazard function unspecified. It is the standard multivariable method in survival analysis and produces hazard ratios that quantify the relative risk associated with each predictor.