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Average treatment effects on binary outcomes with stochastic covariates.

Christoph Kiefer1, Marcella L Woud2, Simon E Blackwell2

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When analyzing psychological treatments with binary outcomes in RCTs, accounting for random covariates improves standard error accuracy. Standard methods may underestimate errors, particularly with treatment-effect heterogeneity.

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Area of Science:

  • Psychological research methodology
  • Biostatistics
  • Clinical psychology

Background:

  • Randomized controlled trials (RCTs) often use logistic regression for dichotomous outcomes.
  • Average Marginal Effects (AMEs) offer clearer interpretation than odds ratios for covariate-adjusted RCTs.
  • Standard AME calculations may underestimate standard errors by treating covariates as fixed.

Purpose of the Study:

  • To compare standard (fixed-covariate) and stochastic-covariate approaches for AME calculation in binary outcome models.
  • To evaluate the statistical inference quality of these methods in finite samples via simulation.
  • To provide guidance on selecting appropriate covariate handling methods in psychological RCTs.

Main Methods:

  • A simulation study was conducted to compare fixed-covariate and stochastic-covariate approaches.
  • The study focused on statistical inference, particularly standard error estimation for AMEs.
  • An illustrative example from clinical psychology was used to demonstrate the methods.

Main Results:

  • The fixed-covariate approach is reliable only when treatment effects are homogeneous (no treatment-covariate interactions).
  • Stochastic-covariate approaches are preferable when there is heterogeneity in interindividual treatment effects.
  • Underestimation of AME standard errors occurs with the fixed-covariate approach under certain conditions.

Conclusions:

  • Stochastic-covariate approaches provide more accurate standard errors for AMEs in psychological RCTs with binary outcomes, especially with treatment-effect heterogeneity.
  • Careful consideration of covariate sampling uncertainty is crucial for reliable statistical inference in RCTs.
  • The findings have implications for the analysis of psychological interventions and clinical trial design.