Using cumulative sums of martingale residuals for model checking in nested case-control studies

Area of Science:

• Biostatistics
• Epidemiology
• Survival Analysis

Background:

• Cox regression is standard for cohort studies but requires extensive covariate data, which is costly and wasteful for large cohorts, especially in biomarker research.
• Nested case-control designs reduce data collection needs by focusing on cases and sampled controls, but lack established methods for checking Cox model fit.
• Martingale residuals are effective for assessing Cox model fit in cohort data, but analogous methods for nested case-control data are underdeveloped.

Purpose of the Study:

• To introduce and validate martingale residual-based methods for checking Cox regression model fit in nested case-control studies.
• To provide practical tools for assessing model adequacy in this specific study design.
• To enable more efficient and cost-effective analysis of large cohort and biomarker studies.

Main Methods:

• Definition of martingale residuals tailored for nested case-control data.
• Development of cumulative sum plots and tests utilizing these residuals.
• Demonstration of how to implement these methods using existing statistical software.

Main Results:

• Successfully defined martingale residuals applicable to nested case-control data.
• Established the utility of cumulative sum plots and tests for evaluating Cox model fit in this design.
• Confirmed that these methods can be implemented with readily available software.

Conclusions:

• The proposed martingale residual methods provide a valuable tool for model checking in nested case-control studies.
• These methods address a critical gap in the analysis of nested case-control data, enhancing the reliability of Cox regression.
• The approach facilitates efficient analysis, reducing the burden of data collection and preserving biological resources.