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Approximate median regression for complex survey data with skewed response.

Raphael André Fraser1, Stuart R Lipsitz2, Debajyoti Sinha3

  • 1Division of Biostatistics, Medical College of Wisconsin, Milwaukee, Wisconsin, U.S.A.

Biometrics
|April 11, 2016
PubMed
Summary

This study introduces a new statistical method, double-transform-both-sides (DTBS) estimating equations, to analyze skewed data from complex national surveys. This approach accurately identifies disease risk factors, like those for cancer, in population health research.

Keywords:
Complex surveyMedian regressionQuantile regressionSandwich estimatorTransform-both-sides

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Area of Science:

  • Statistics
  • Public Health
  • Biostatistics

Background:

  • Large national surveys provide valuable data for population health research.
  • Complex survey designs (stratification, multistage sampling, weighting) pose challenges for standard statistical methods.
  • Identifying disease risk factors using regression models requires appropriate analytical techniques for complex survey data.

Purpose of the Study:

  • To develop a statistical method that accommodates complex survey design features for analyzing highly skewed response variables.
  • To estimate median regression parameters for skewed data from large national surveys.
  • To address limitations of existing methods when applied to complex survey data.

Main Methods:

  • Proposed a double-transform-both-sides (DTBS) estimating equations approach.
  • Applied Box-Cox type transformations twice to both the outcome and regression function.
  • Utilized standard sandwich variance estimates, avoiding resampling methods needed for minimizing absolute deviations (MAD) approaches.

Main Results:

  • The DTBS approach effectively accommodates complex survey design features.
  • The method provides robust estimation for highly skewed response variables.
  • DTBS demonstrated a smaller mean square error compared to the minimizing absolute deviations (MAD) approach.

Conclusions:

  • The DTBS estimating equations approach is a valid and robust method for analyzing highly skewed data from complex national surveys.
  • This method enhances the assessment of population characteristics and identification of disease risk factors.
  • The approach is motivated by and applicable to real-world health data, such as urinary iodine concentration from national surveys.