Algorithm Overview

This page provides a short description of each model implemented in gen_surv. For mathematical details see 📘 Mathematical Foundations of gen_surv.

Cox Proportional Hazards Model (CPHM)

The hazard at time $t$ is proportional to a baseline hazard multiplied by the exponential of covariate effects. It is widely used for modelling relative risks under the proportional hazards assumption. See Cox (1972) in the References for the seminal paper.

Accelerated Failure Time Models (AFT)

These parametric models directly relate covariates to survival time. gen_surv includes log-normal, log-logistic and Weibull variants allowing different baseline distributions. They are convenient when the effect of covariates accelerates or decelerates event times.

Continuous-Time Multi-State Markov Model (CMM)

Transitions between states are governed by a generator matrix. This model is suited for illness-death and other multi-state processes where state occupancy changes continuously over time. The mathematical formulation follows the counting-process approach of Andersen et al. Andersen et al. (1993).

Time-Dependent Covariate Model (TDCM)

Extends the Cox model to covariates that vary during follow-up. Covariates are simulated in a piecewise fashion with optional correlation across segments.

Time-Homogeneous Hidden Markov Model (THMM)

Handles processes with unobserved states that emit observable values. The latent transitions follow a homogeneous Markov chain while emissions are Gaussian. For background on these models see Zucchini et al. Zucchini et al. (2017).

Competing Risks

Allows multiple failure types with cause-specific hazards. gen_surv supports constant and Weibull hazards for each cause. The subdistribution approach of Fine and Gray Fine and Gray (1999) is commonly used for analysis.

Mixture Cure Model

Assumes a proportion of individuals will never experience the event. A logistic component determines who is cured, while uncured subjects follow an exponential failure distribution. Mixture cure models were introduced by Farewell Farewell (1982).

Piecewise Exponential Model

Approximates complex hazard shapes by dividing follow-up time into intervals with constant hazard within each interval. This yields a flexible baseline hazard while remaining computationally simple.

For additional reading on these methods please see the References.