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Multisample adjusted U-statistics that account for confounding covariates.

Glen A Satten1, Maiying Kong2, Somnath Datta3

  • 1Division of Reproductive Health, Centers for Disease Control and Prevention, Atlanta, Georgia, USA.

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Summary

We developed adjusted U-statistics to compare distributions across groups, accounting for confounding covariates. This method effectively tests for differences in data, even with complex relationships, improving statistical analysis.

Keywords:
adjusted U-statisticsmultiple group comparisonpropensity score

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Area of Science:

  • Statistics
  • Biostatistics
  • Genetics

Background:

  • Multisample U-statistics compare distributions but can be confounded by covariates.
  • Confounding variables may distort observed differences in group distributions.
  • Existing methods struggle to adjust for confounding in U-statistic applications.

Purpose of the Study:

  • To propose adjusted U-statistics for comparing distributions across multiple groups while controlling for confounding covariates.
  • To establish the asymptotic properties and variance of these adjusted U-statistics.
  • To demonstrate the practical utility of the adjusted U-statistics in simulations and real-world data.

Main Methods:

  • Individually reweighted data using stratification or propensity scores to construct adjusted U-statistics.
  • Theoretical establishment of asymptotic normality for the adjusted U-statistics.
  • Derivation of a closed-form expression for the asymptotic variance.

Main Results:

  • The proposed adjusted U-statistics effectively control for confounding covariates.
  • Asymptotic normality and a closed-form variance were established for the adjusted statistics.
  • Simulations and a case-control study confirmed the method's utility in detecting distribution differences.

Conclusions:

  • Adjusted U-statistics provide a robust method for comparing distributions in the presence of confounding.
  • The approach is applicable to both prospective and retrospective study designs.
  • The method was successfully applied to analyze haplotype similarity in a case-control genetic study.