Flexible Parametric Inference for Cause-Specific Hazard-Competing Risk Models Under Interval Censoring
Author(s)
Michael Crowther, PhD.
Red Door Analytics, Stockholm, Sweden.
Red Door Analytics, Stockholm, Sweden.
OBJECTIVES: Interval censoring is a common, yet often overlooked, issue in survival analysis, whereby we only know an event occurred within a particular time interval, rather than its exact event time. In the context of competing risks, the methodological challenges increase dramatically. In this paper, we develop a general approach to fit cause-specific hazard competing risk models allowing for interval censoring in a continuous time framework.
METHODS: We derive and implement a general joint likelihood for parametric and complex spline-based cause-specific hazard models. We then extend to a Bayesian version of the framework to allow prior information to be incorporated, before deriving a range of useful predictions, such as cumulative incidence functions and time lost due to specific causes of death. We evaluate the proposed methods through simulation and application to a prostate cancer trial dataset with competing causes of death.
RESULTS: Based on simulation results, we find 1) the method provides unbiased estimates of cause-specific hazard ratios and cumulative incidence functions, in scenarios where the model is well specified, and 2) if interval censoring is not accounted for in the analysis, we find substantial bias and poor coverage of both treatment effects and measures of absolute risk. In the illustrative example, the treatment effect on the risk of death due to prostate cancer was successfully isolated from effects on death due to cardiovascular disease and other causes. Further measures such as restricted mean survival time, and time lost due to specific causes of death are also quantified and contrasted between groups, with appropriate uncertainty.
CONCLUSIONS: Failure to account for interval censoring can cause bias in both cause-specific hazard ratios and survival/event probabilities, especially as the width of the intervals grow, relative to follow-up time. Methods and software to account for interval censoring in a continuous time, competing risks setting should therefore be employed.
METHODS: We derive and implement a general joint likelihood for parametric and complex spline-based cause-specific hazard models. We then extend to a Bayesian version of the framework to allow prior information to be incorporated, before deriving a range of useful predictions, such as cumulative incidence functions and time lost due to specific causes of death. We evaluate the proposed methods through simulation and application to a prostate cancer trial dataset with competing causes of death.
RESULTS: Based on simulation results, we find 1) the method provides unbiased estimates of cause-specific hazard ratios and cumulative incidence functions, in scenarios where the model is well specified, and 2) if interval censoring is not accounted for in the analysis, we find substantial bias and poor coverage of both treatment effects and measures of absolute risk. In the illustrative example, the treatment effect on the risk of death due to prostate cancer was successfully isolated from effects on death due to cardiovascular disease and other causes. Further measures such as restricted mean survival time, and time lost due to specific causes of death are also quantified and contrasted between groups, with appropriate uncertainty.
CONCLUSIONS: Failure to account for interval censoring can cause bias in both cause-specific hazard ratios and survival/event probabilities, especially as the width of the intervals grow, relative to follow-up time. Methods and software to account for interval censoring in a continuous time, competing risks setting should therefore be employed.
Conference/Value in Health Info
2025-11, ISPOR Europe 2025, Glasgow, Scotland
Value in Health, Volume 28, Issue S2
Code
MSR110
Topic
Epidemiology & Public Health, Health Technology Assessment, Methodological & Statistical Research
Topic Subcategory
Confounding, Selection Bias Correction, Causal Inference
Disease
Oncology