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Estimating predicted probabilities from logistic regression: different methods correspond to different target

Clemma J Muller1, Richard F MacLehose2

  • 1Division of Epidemiology, University of Minnesota, Minneapolis, MN, USA jaco0484@umn.edu.

International Journal of Epidemiology
|March 8, 2014
PubMed
Summary

Marginal standardization is the correct method for estimating predicted probabilities in the overall population after logistic regression. Prediction at the means should be avoided with binary confounders due to nonsensical results.

Keywords:
Biaslogistic regressionpredicted probabilitiesriskstandardizationtarget population

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Area of Science:

  • Biostatistics
  • Epidemiology
  • Statistical Modeling

Background:

  • Three common methods for estimating predicted probabilities after confounder-adjusted logistic regression are marginal standardization, prediction at the modes, and prediction at the means.
  • A critical, often overlooked, aspect is that each method targets a different population.
  • Prediction at the means is frequently misinterpreted and can produce invalid estimates, especially with dichotomous confounders.

Purpose of the Study:

  • To clarify the target populations associated with different methods of estimating predicted probabilities.
  • To highlight the practical implications and potential misinterpretations of these methods in statistical analysis.
  • To provide guidance on appropriate methods for inference to specific populations.

Main Methods:

  • Review and comparison of marginal standardization, prediction at the modes, and prediction at the means.
  • Demonstration of discrepancies using an applied example.
  • Provision of statistical software syntax (SAS and Stata) for implementation.

Main Results:

  • Marginal standardization enables inference to the entire study population.
  • Prediction at the modes or means restricts inference to specific strata of observations.
  • Prediction at the means yields nonsensical results for strata not represented in the data, particularly with binary confounders.

Conclusions:

  • Marginal standardization is the recommended method for population-level inference.
  • Prediction at the modes and means require cautious application and interpretation.
  • Prediction at the means is inappropriate for binary confounders; Stata offers simpler marginal standardization methods compared to SAS.