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Area of Science:

  • Statistics
  • Biostatistics
  • Psychometrics

Background:

  • Multilevel logistic regression is widely used but estimating statistical power is challenging.
  • Power estimation is complicated by the need for computer simulations and the influence of predictor distributions.
  • Existing methods often lack user-friendly tools for power analysis in complex models.

Purpose of the Study:

  • To investigate the impact of predictor distributions on statistical power in multilevel logistic regression.
  • To develop and provide a user-friendly web application for conducting power analysis in these models.
  • To offer guidance on sample size determination considering predictor characteristics.

Main Methods:

  • Computer simulations were used to estimate statistical power.
  • Simulations varied the number of clusters, cluster sample sizes, and predictor distributions (non-normal, non-symmetrical).
  • Power curves were generated to assess the effects of predictor distributions on detecting effects.

Main Results:

  • Skewed continuous and unbalanced binary predictors necessitate larger sample sizes at both levels compared to normal or balanced predictors.
  • In extreme cases of imbalance and skewness, even substantial sample sizes (110 Level 2 units, 100 Level 1 units) were insufficient to achieve 80% power for all predictors.
  • Power often hovered around 50% under highly skewed or imbalanced conditions.

Conclusions:

  • Generic sample size recommendations for multilevel logistic regression are insufficient due to complex interactions between sample size, effect size, and predictor distributions.
  • Larger sample sizes are consistently required when predictor distributions are asymmetric or unbalanced.
  • A web-based application using R simulations is provided to assist researchers in tailored power analysis for multilevel logistic regression studies.