Assessing Balance of Baseline Time-Dependent Covariates via the Fréchet Distance

Area of Science:

• Statistics
• Biostatistics
• Data Science

Background:

• Assessing covariate balance is crucial for group comparisons, especially with real-world data.
• Traditional methods often focus on baseline covariates, neglecting longitudinal ones.
• Existing methods for longitudinal covariates (pointwise differences, slopes, weights) have limitations.

Purpose of the Study:

• To introduce and evaluate the Fréchet distance as a method for assessing covariate balance in time-dependent data.
• To establish a threshold for the Fréchet distance equivalent to a 10% standardized difference in functional parameters.
• To demonstrate the application of Fréchet distance using real-world longitudinal data.

Main Methods:

• Developed a method using Fréchet distance to quantify the balance of time-dependent covariates.
• Defined a 10% threshold for standardized differences in linear and nonlinear curves.
• Applied the Fréchet distance to longitudinal hemoglobin A1c data from diabetic patients.

Main Results:

• The Fréchet distance provides a viable alternative for assessing longitudinal covariate balance.
• A 10% threshold for functional parameter differences was related to a specific Fréchet distance, dependent on noise levels.
• Analysis of hemoglobin A1c trajectories revealed an imbalance between patient groups at the 10% mark.
• A Beta distribution approximated the Fréchet distance distribution in most scenarios.

Conclusions:

• The Fréchet distance offers advantages in assessing covariate balance, including handling curves of varying lengths, shapes, and time points.
• This method is more flexible than pointwise differences or slope comparisons for complex longitudinal data.
• Future research will explore its utility with missing data and within-group heterogeneity.