A bias-corrected covariance estimate for improved inference with quadratic inference functions

Area of Science:

• Statistics
• Biostatistics
• Correlated Data Analysis

Background:

• Quadratic inference functions (QIF) are increasingly used for correlated data analysis.
• QIF offers advantages over generalized estimating equations (GEE), particularly in parameter estimation efficiency when covariance structures are misspecified.

Purpose of the Study:

• To investigate the finite-sample bias in standard error estimates derived from the asymptotic covariance formula in QIF.
• To propose and validate adjustments to the QIF covariance formula to correct for small-sample biases.

Main Methods:

• The study analyzes the asymptotic covariance formula used in QIF for standard error estimation.
• Simulations are conducted to evaluate the performance of the proposed adjustments in small to moderately sized samples.
• The proposed method is applied to real-world data from a cluster randomized trial and a longitudinal study.

Main Results:

• Standard error estimates from the asymptotic QIF covariance formula exhibit significant downward bias in small to moderate samples.
• This bias leads to inflated test sizes and reduced coverage probabilities.
• The proposed adjustments effectively eliminate finite-sample biases, substantially improving standard error estimates, inference, and coverage.

Conclusions:

• The asymptotic covariance formula in QIF can yield biased standard errors in smaller samples.
• Adjustments to the QIF covariance formula are necessary for accurate inference in finite samples.
• The proposed method enhances the reliability of QIF for analyzing correlated data in practical applications.