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Hypothesis testing is a fundamental statistical tool that begins with the assumption that the null hypothesis H0 is true. During this process, two types of errors can occur: Type I and Type II. A Type I error refers to the incorrect rejection of a true null hypothesis, while a Type II error involves the failure to reject a false null hypothesis.
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Type I error control for cluster randomized trials under varying small sample structures.

Joshua R Nugent1, Ken P Kleinman2

  • 1Department of Biostatistics and Epidemiology, School of Public Health and Health Sciences, University of Massachusetts Amherst, 715 North Pleasant Street, Amherst, 01003, Massachusetts, USA.

BMC Medical Research Methodology
|April 4, 2021
PubMed
Summary
This summary is machine-generated.

For cluster randomized trials (CRTs), the likelihood ratio test (LRT) can inflate Type I errors with small clusters, while Wald tests with Satterthwaite DF offer better control. Choose hypothesis tests carefully for accurate CRT analysis.

Keywords:
Likelihood ratio testLinear mixed modelsType I errorWald test

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Area of Science:

  • Statistics
  • Biostatistics
  • Clinical Trials

Background:

  • Linear mixed models (LMM) are standard for cluster randomized trials (CRTs).
  • Inference methods like Wald tests and likelihood ratio tests (LRT) can yield inaccurate Type I error rates in finite samples.
  • Limited research exists on how cluster size, number of clusters, intraclass correlation coefficient (ICC), and analysis approach impact Type I errors in CRTs.

Purpose of the Study:

  • To investigate the impact of various factors on Type I error rates in LMM for CRTs.
  • To compare the performance of LRT and Wald tests under different simulation conditions.

Main Methods:

  • Simulations were conducted using a random-intercept LMM structure.
  • Type I error rates were evaluated for LRT and Wald tests with different degrees of freedom (DF) choices.
  • Simulations varied cluster size, number of clusters, and ICC.

Main Results:

  • The LRT demonstrated anti-conservative behavior (inflated Type I errors) with large ICC and small numbers of clusters, especially with larger cluster sizes.
  • Wald tests using between-within DF or Satterthwaite DF approximation maintained Type I error control.
  • These Wald tests showed conservatism when cluster number, size, and ICC were small.

Conclusions:

  • The choice of hypothesis testing approach in CRTs should be tailored to the data structure to ensure appropriate Type I error rates.
  • Wald tests with Satterthwaite DF approximation are generally reliable.
  • In specific scenarios, the LRT may provide Type I error rates closer to the nominal level.