Explained variation in shared frailty models

Area of Science:

• Biostatistics
• Medical Informatics
• Epidemiology

Background:

• Explained variation quantifies the improvement in predictive accuracy from prognostic factors over unconditional prediction.
• Existing methods for explained variation accommodate various factor types but struggle with random effects, limiting their application in complex study designs.

Purpose of the Study:

• To extend the explained variation measure to incorporate random factors, such as center effects in multicenter studies.
• To enable direct comparison of the importance of random factors (e.g., study centers) against other prognostic factors.

Main Methods:

• Extension of the Schemper and Henderson (2000) explained variation measure for shared frailty Cox models.
• Development of an SAS macro and an R function for practical implementation.
• Monte Carlo simulation to explore empirical properties of variation explained by random factors.

Main Results:

• The extended explained variation measure successfully accommodates random factors, allowing for their importance to be quantified and compared.
• The Monte Carlo study provided insights into the behavior of explained variation attributed to random factors.
• Application to an Austrian colon cancer multicenter study demonstrated the practical utility of the approach.

Conclusions:

• The extended explained variation measure provides a robust method for ranking the importance of both fixed and random prognostic factors in complex studies.
• This approach enhances the interpretability of multicenter studies by allowing direct comparison of center effects with other predictors.
• The developed SAS macro and R function facilitate the application of this advanced statistical technique in research.