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Relative Risk

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Relative risk (RR) is a statistical measure commonly used in epidemiology to compare the likelihood of a particular event occurring between two groups. This metric is important for evaluating the relationship between exposure to a specific risk factor and the probability of a particular outcome. It plays a crucial role in medical research, public health studies, and risk assessment. Relative risk quantifies how much more (or less) likely an event is to occur in an exposed group compared to an...

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Related Experiment Video

Updated: Jun 26, 2026

An R-Based Landscape Validation of a Competing Risk Model

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Laplace's approximation for relative risk frailty models.

Shibao Feng¹, Lei Nie, Robert A Wolfe

¹Genentech, Inc., South San Francisco, CA 94080, USA. shibaof@gene.com

Lifetime Data Analysis

|February 3, 2009

Summary

Laplace

Area of Science:

Biostatistics
Survival Analysis
Statistical Modeling

Background:

Relative risk frailty models are crucial for analyzing clustered and recurrent time-to-event data.
Accurate estimation is vital for reliable insights in such complex datasets.

Purpose of the Study:

To apply Laplace's approximation to marginal distributions within parametric relative risk frailty models.
To evaluate the consistency and convergence rates of approximate maximum likelihood estimators (MLE).

Main Methods:

Utilized Laplace's approximation for integral calculations in parametric relative risk frailty models.
Investigated the asymptotic properties of the approximate maximum likelihood estimators (MLE).
Conducted comparative analysis against alternative estimators via simulation.

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Main Results:

Approximate maximum likelihood estimators (MLE) demonstrate consistency under regularity conditions.
The convergence rate of approximate MLE depends on both the number of subjects and members per subject.
Laplace's approximation provides a viable method for analyzing complex survival data.

Conclusions:

Laplace's approximation offers a computationally efficient and statistically sound approach for parametric relative risk frailty models.
The method is validated through simulation and application to real-world kidney transplant data.
This technique enhances the analysis of clustered and recurrent event data in biostatistics.