Optimal weight in estimating and comparing areas under the receiver operating characteristic curve using longitudinal...

Area of Science:

• Biostatistics
• Longitudinal Data Analysis
• Medical Statistics

Background:

• Longitudinal studies often involve repeated marker measurements alongside a dichotomous outcome.
• Non-parametric methods exist for estimating the area under the ROC curve (AUC) for repeated markers, with existing schemes for low or high within-patient correlation.
• Current methods lack clarity on optimal weighting for modest within-patient correlation.

Purpose of the Study:

• To determine optimal weights that minimize the variance of AUC estimates for repeated markers in longitudinal studies.
• To identify optimal weights for minimizing the variance of the AUC difference between two repeated markers.
• To evaluate the efficiency of existing weighting schemes compared to newly derived optimal weights.

Main Methods:

• Investigated optimal weighting schemes for non-parametric estimation of AUC in longitudinal studies.
• Derived weights that minimize variance for single and multiple repeated markers.
• Analyzed the impact of within-patient correlation and case proportion on optimal weights.

Main Results:

• Optimal weights are dependent on within-patient control-case correlation and the proportion of cases.
• Existing weighting schemes (Emir et al.) can result in substantial efficiency loss.
• Efficiency loss is particularly severe with high within-subject correlation and a small proportion of cases.

Conclusions:

• The proposed optimal weights offer improved variance reduction for AUC estimation in longitudinal studies.
• Careful consideration of weighting is crucial, especially in scenarios with high within-subject correlation and low case prevalence.
• The findings highlight limitations of existing non-parametric methods and suggest a more robust approach for analyzing repeated markers.