Modeling unobserved heterogeneity in multistate event history data using frailty and weighted survival approaches

Abstract

Abstract Conventional survival analysis models typically assume that the hazard function depends solely on the baseline hazard and covariate values, overlooking unobserved factors that influence survival outcomes. In practice, however, unmeasured variables often contribute to heterogeneity among seemingly similar individuals. Frailty models offer an effective approach to account for such unobserved heterogeneity, providing a robust framework for analyzing naturally clustered survival data. This study applies frailty models to multistate event history data, emphasizing their ability to handle unobserved heterogeneity. We introduce individual-specific survival weights to adjust survival times, better reflecting the impact of unmeasured factors. These weighted survival times are critical when data exhibit bias or when standard models fail to fully capture the influence of investigated variables. Through a simulation study, we evaluate the effectiveness and performance of frailty models in a multistate framework, comparing mean, mean squared error (MSE), and bias of regression coefficients with and without frailty. For example, in the simulated dataset for age bias has reduced from -0.01 in unweighted survival time to -0.03 in weighted survival time for transition $$\tau _{12}$$ , similarly for $$\tau _{23}$$ bias has reduced from 0.01 to -0.05. Our findings underscore the importance of addressing unobserved heterogeneity in survival analysis, particularly in multistate models with weighted survival times.

Affiliated Institutions

• University of Dundee GB
• Indian Institute of Technology Dhanbad IN
• Genomics (United Kingdom) GB

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