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A note on obtaining correct marginal predictions from a random intercepts model for binary outcomes.

Menelaos Pavlou1, Gareth Ambler2, Shaun Seaman3

  • 1Department of Statistical Science, University College London, Gower St., London, WC1E 6BT, UK. m.pavlou@ucl.ac.uk.

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Accurate marginal risk predictions from random intercepts models require integrating over random effects. Incorrectly omitting random effects leads to poor calibration in clustered binary outcome data.

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Area of Science:

  • Statistics
  • Biostatistics

Background:

  • Clustered data with binary outcomes are commonly analyzed using random intercepts models or generalized estimating equations (GEE).
  • These methods yield either cluster-specific or population-average inferences.

Purpose of the Study:

  • To compare the calibration of two approaches for marginal risk calculation from random effects models.
  • To identify and explain the incorrect method often used for marginal risk calculation.

Main Methods:

  • Focus on marginal risk calculation for a member of a new cluster using random effects models.
  • Marginal risk calculation involves integrating over the distribution of random effects.
  • Comparison of correct integration versus incorrect calculation (setting random effects to zero).

Main Results:

  • Incorrect marginal risk calculation leads to poorly calibrated predictions, with mis-calibration worsening with increased clustering.
  • Simulation studies demonstrate that the correct method, integrating over random effects, yields excellent calibration.
  • Clarification of why the incorrect approach results in poor model calibration.

Conclusions:

  • The logistic random intercepts model can produce valid marginal predictions.
  • Correct marginal predictions are achieved by integrating over the distribution of random effects.