Assess predictive values of a binary diagnostic test under a nested case-control design.

Area of Science:

• Biostatistics
• Epidemiology
• Diagnostic Test Evaluation

Background:

• Diagnostic test predictive values are typically assessed using random sampling.
• Rare diseases necessitate more efficient designs like nested case-control studies, which oversample cases.
• Direct estimators for predictive values in nested case-control designs are biased due to case oversampling.

Purpose of the Study:

• To derive asymptotic variance formulas for inverse probability weighting (IPW) estimators of predictive values.
• To quantify the efficiency gains of nested case-control designs over simple random sampling for rare diseases.
• To address the lack of variance expressions for IPW estimators in this context.

Main Methods:

• Developed asymptotic variance formulas for IPW estimators of predictive values.
• Incorporated the variance of estimated weights into the variance formulas.
• Compared efficiency gains between nested case-control and random sampling designs.
• Validated formulas via simulation and a real-world D-dimer test accuracy example.

Main Results:

• The proposed variance formulas accurately estimate the precision of IPW estimators.
• Nested case-control designs demonstrate substantial variance reduction for rare diseases compared to random sampling.
• The variance formulas account for the uncertainty introduced by estimated weights.

Conclusions:

• The derived variance formulas are crucial for accurate assessment of predictive values using IPW in nested case-control studies.
• Nested case-control designs are highly efficient for evaluating diagnostic tests in rare disease populations.
• This work provides essential tools for biostatisticians and epidemiologists studying diagnostic accuracy.