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Age-dependent U-shaped risk functions and Aalen's additive risk model
1Department of Biostatistics, University of Copenhagen, Denmark. torbenm@dina.kvl.dk
Biometrics
|September 29, 1998
Summary
This study introduces a method to find the optimal body mass index (BMI) for lowest failure risk over time. The research helps understand how BMI affects mortality risk, offering insights into health and longevity.
Area of Science:
- Epidemiology
- Biostatistics
- Survival Analysis
Background:
- Epidemiologic studies frequently observe a quadratic relationship between failure risk and covariates.
- Aalen's additive risk model is suitable for time-varying covariate effects.
Purpose of the Study:
- To investigate the nadir (lowest risk point) of a covariate within Aalen's additive risk model.
- To develop a statistical test for time-independent nadirs and estimate the nadir when it is constant.
- To apply these methods to analyze the relationship between body mass index and time to death.
Main Methods:
- Utilizing Aalen's additive risk model to accommodate time-varying covariate effects.
- Proposing a hypothesis test to determine if the covariate's nadir is constant over time.
- Developing an estimator for the nadir when it is time-independent.
- Deriving large sample properties for the proposed test statistic and estimator.
Main Results:
- The study provides a framework for identifying the covariate value associated with minimum risk.
- Methods are demonstrated using real-world data on body mass index and mortality.
- Statistical properties of the proposed methods are theoretically established.
Conclusions:
- The developed methods allow for the estimation and testing of time-independent nadirs in survival data.
- Understanding the nadir's time-dependency is crucial for accurate risk assessment.
- The findings have implications for public health research, particularly concerning factors like body mass index and mortality.