Introducing Multi-State Models in Survival Analysis and Providing an Applied Example to Investigate Factors Related to Changing Status of Heart Transplant Recipients: A Review Article

Abstract

Background: This study introduces and applies multi-state models in survival analysis to examine factors affecting the changing status of heart transplant recipients. Multi-state models are commonly used to describe the pathway of disease progression, and their analytical complexity depends on the number of defined states and possible transitions between them. These models allow for the investigation of the effect of auxiliary variables on the probability of transition between different disease states. Methods: To illustrate the model's functionality, data from heart transplant recipients, taken from the article by Sharples et al., were used. Based on these data, disease progression was collected across four distinct states: state 1 (healthy), state 2 (mild/moderate heart disease), state 3 (severe heart disease), and state 4 (death), with the aim of tracking disease progression and patient transitions from one state to subsequent states. To achieve the desired results, Cox regression and stratified Cox regression models were used. Findings: In this study, data from 622 heart transplant recipients were used, with disease progression defined across four states. The mean and standard deviation (SD) of recipients’ age at transplant was 48.90 ± 10.90 years, of heart donors was 28.80 ± 11.40 years, and the mean post-transplant examination time was 3.84 ± 3.34 years. The occurrence of heart disease after transplantation was higher for recipients of older age. Specifically, a recipient older than 65 years had a higher risk and lower survival compared to a recipient transplanted at a younger age hazard ratio (HR) = 1.845, 95% confidence interval (CI): 1.224-2.778, P < 0.001. Conclusion: The survival of patients who do not develop post-transplant diseases or who experience initial stages of post-transplant disease is higher than that of patients who develop severe post-transplant diseases and experience critical states. Furthermore, receiving a transplant at a younger age is associated with a higher probability of survival and a lower risk of developing post-transplant heart diseases. Therefore, the timing of the heart transplant is a significant and influential factor on disease progression and clinical outcomes. © 2026, Isfahan University of Medical Sciences(IUMS). All rights reserved.