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A Fast EM Algorithm for Fitting Joint Models of a Binary Response and Multiple Longitudinal Covariates Subject to

Paul W Bernhardt1, Daowen Zhang2, Huixia Judy Wang3

  • 1Department of Mathematics and Statistics, Villanova University, Villanova, PA, USA.

Computational Statistics & Data Analysis
|January 20, 2015
PubMed
Summary
This summary is machine-generated.

This study introduces a joint model to analyze the link between binary outcomes and longitudinal biomarkers, even with detection limits. An efficient approximate EM algorithm provides accurate estimates for survival analysis.

Keywords:
Detection limitEM algorithmJoint modelLogistic regressionMultiple longitudinal covariatesNormal approximation

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Area of Science:

  • Biostatistics
  • Longitudinal Data Analysis
  • Survival Analysis

Background:

  • Joint modeling is popular for analyzing associations between responses and longitudinal covariates.
  • The GenIMS study requires modeling survival events using censored longitudinal biomarkers.
  • Existing methods may struggle with multiple longitudinal covariates subject to detection limits.

Purpose of the Study:

  • To propose a joint model for binary outcomes and multiple longitudinal covariates with detection limits.
  • To develop a fast, approximate Expectation-Maximization (EM) algorithm for this joint model.
  • To apply the developed algorithm to the GenIMS data set.

Main Methods:

  • A joint modeling framework is established for binary outcomes and longitudinal covariates.
  • A novel, approximate EM algorithm is developed to handle integration in the E-step.
  • The algorithm's computational complexity is reduced by limiting integration to one dimension.

Main Results:

  • Numerical studies confirm satisfactory parameter and variance estimates.
  • The algorithm performs well with and without censoring on longitudinal covariates.
  • The approximate EM algorithm was successfully applied to analyze the GenIMS data.

Conclusions:

  • The proposed joint model and approximate EM algorithm are effective for analyzing complex longitudinal data.
  • The method provides reliable estimates even with censored and detection-limited covariates.
  • This approach offers a valuable tool for similar biostatistical and survival analysis studies.