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Updated: Jan 28, 2026

Establishing a Competing Risk Regression Nomogram Model for Survival Data

Establishing a Competing Risk Regression Nomogram Model for Survival Data

Published on: October 23, 2020

Additive-multiplicative hazards regression models for interval-censored semi-competing risks data with missing

Jinheum Kim¹, Jayoun Kim², Seong W Kim³

¹Department of Applied Statistics, University of Suwon, Suwon, 18323, South Korea.

BMC Medical Research Methodology

|March 8, 2019

Summary

This study introduces a multi-state model to analyze semi-competing risks data when participants are lost to follow-up (LTF). The model treats LTF as a non-fatal event, improving analysis of both fatal and non-fatal outcomes in clinical trials.

Keywords:

Additive and multiplicative hazards model Interval censoring Missing intermediate event Multi-state model Semi-competing risks data log-normal frailty

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Area of Science:

Biostatistics
Survival Analysis
Clinical Trials Methodology

Background:

Participant withdrawal, known as lost-to-follow-up (LTF), is common in clinical trials and survival analysis.
Lost-to-follow-up complicates the interpretation of disease censoring, as it's uncertain if the disease process has truly ended.
The illness process itself can be censored by lost-to-follow-up, necessitating models that account for this uncertainty.

Purpose of the Study:

To propose a novel multi-state model for analyzing semi-competing risks data.
To specifically address situations where intermediate non-fatal events may be missing due to lost-to-follow-up.
To treat lost-to-follow-up as a distinct non-fatal event rather than censoring.

Main Methods:

Utilized an additive and multiplicative hazards model with log-normal frailty.
Constructed a conditional likelihood to estimate transition intensities among states in the multi-state model.
Employed adaptive importance sampling for marginalization and the iterative quasi-Newton algorithm for parameter estimation.

Main Results:

Simulation studies demonstrated the robustness of the proposed estimation method to frailty distribution misspecifications.
The estimators showed good finite-sample performance regarding relative bias and coverage probability.
Analysis of PAQUID data yielded significant findings, highlighting the model's applicability to real-world datasets.

Conclusions:

The proposed multi-state model effectively handles semi-competing risks data with potential missing non-fatal event information.
Simulation results confirmed that regression parameter coverage probabilities closely approximate the nominal 0.95 level.
Real-world data analysis indicated sex-based differences in dementia transition and mortality risks.