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Modeling continuous covariates with a "spike" at zero: Bivariate approaches.

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|April 14, 2016
PubMed
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This study introduces novel methods for analyzing variables with a spike at zero, common in health research like smoking or alcohol intake. These techniques improve modeling of complex relationships for better epidemiological insights.

Keywords:
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Area of Science:

  • Epidemiology
  • Biostatistics
  • Statistical Modeling

Background:

  • Many epidemiological and clinical research predictors have zero values for a large proportion of observations, termed variables with a spike at zero (SAZ).
  • Examples of SAZ variables include smoking and alcohol consumption, which exhibit a continuous distribution for non-zero values.
  • Existing fractional polynomial (FP) procedures have been extended to handle SAZ variables by incorporating a binary indicator for zero values, forming the FP-spike procedure.

Purpose of the Study:

  • To introduce and evaluate four new bivariate approaches for modeling two variables with a spike at zero (SAZ).
  • To assess the performance of these methods in accounting for the bivariate distribution of zero and non-zero values, including correlated variables.
  • To illustrate the application and comparison of these methods using a case-control study on laryngeal cancer.

Main Methods:

  • The paper presents four bivariate approaches: Bi-Sep, Bi-D3, Bi-D1, and Bi-Sub.
  • Bi-Sep applies the univariate FP-spike procedure independently to each SAZ variable.
  • Bi-D3, Bi-D1, and Bi-Sub simultaneously consider the proportions of zeros in both variables within binary indicators, enabling the analysis of correlated SAZ variables.
  • The methods are applicable to covariates with arbitrary distributions and can be extended to three or more SAZ variables, potentially combined with log-linear models for correlation analysis.

Main Results:

  • The univariate FP-spike procedure generally yields interpretable functional relationships.
  • The bivariate approaches offer different strategies for handling the zero-inflated nature of SAZ variables.
  • The case-control study on laryngeal cancer serves as an illustration for comparing the results of the proposed methods.

Conclusions:

  • The developed bivariate methods provide robust strategies for analyzing two variables with a spike at zero in epidemiological and clinical research.
  • These approaches enhance the modeling of complex relationships involving zero-inflated predictors.
  • The study outlines a pathway for extending these methods to scenarios with multiple SAZ variables, offering comprehensive tools for statistical analysis.