Sample size requirements to detect an intervention by time interaction in longitudinal cluster randomized clinical trials with random slopes

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13 Citations (Scopus)

Abstract

In longitudinal cluster randomized clinical trials (cluster-RCT), subjects are nested within a higher level unit such as clinics and are evaluated for outcome repeatedly over the study period. This study design results in a three level hierarchical data structure. When the primary goal is to test the hypothesis that an intervention has an effect on the rate of change in the outcome over time and the between-subject variation in slopes is substantial, the subject-specific slopes are often modeled as random coefficients in a mixed-effects linear model. In this paper, we propose approaches for determining the samples size for each level of a 3-level hierarchical trial design based on ordinary least squares (OLS) estimates for detecting a difference in mean slopes between two intervention groups when the slopes are modeled as random. Notably, the sample size is not a function of the variances of either the second or the third level random intercepts and depends on the number of second and third level data units only through their product. Simulation results indicate that the OLS-based power and sample sizes are virtually identical to the empirical maximum likelihood based estimates even with varying cluster sizes. Sample sizes for random versus fixed slope models are also compared. The effects of the variance of the random slope on the sample size determinations are shown to be enormous. Therefore, when between-subject variations in outcome trends are anticipated to be significant, sample size determinations based on a fixed slope model can result in a seriously underpowered study.

Original languageEnglish (US)
Pages (from-to)169-178
Number of pages10
JournalComputational Statistics and Data Analysis
Volume60
Issue number1
DOIs
StatePublished - 2013

Fingerprint

Randomized Clinical Trial
Size determination
Slope
Sample Size
Requirements
Interaction
Sample Size Determination
Ordinary Least Squares
Maximum likelihood
Data structures
Linear Mixed Effects Model
Hierarchical Data
Least Squares Estimate
Unit
Random Coefficients
Empirical Likelihood
Rate of change
Intercept
Hierarchical Structure
Maximum Likelihood

Keywords

  • Effect size
  • Longitudinal cluster RCT
  • Power
  • Random slope
  • Sample size
  • Three level data

ASJC Scopus subject areas

  • Computational Mathematics
  • Computational Theory and Mathematics
  • Statistics and Probability
  • Applied Mathematics

Cite this

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abstract = "In longitudinal cluster randomized clinical trials (cluster-RCT), subjects are nested within a higher level unit such as clinics and are evaluated for outcome repeatedly over the study period. This study design results in a three level hierarchical data structure. When the primary goal is to test the hypothesis that an intervention has an effect on the rate of change in the outcome over time and the between-subject variation in slopes is substantial, the subject-specific slopes are often modeled as random coefficients in a mixed-effects linear model. In this paper, we propose approaches for determining the samples size for each level of a 3-level hierarchical trial design based on ordinary least squares (OLS) estimates for detecting a difference in mean slopes between two intervention groups when the slopes are modeled as random. Notably, the sample size is not a function of the variances of either the second or the third level random intercepts and depends on the number of second and third level data units only through their product. Simulation results indicate that the OLS-based power and sample sizes are virtually identical to the empirical maximum likelihood based estimates even with varying cluster sizes. Sample sizes for random versus fixed slope models are also compared. The effects of the variance of the random slope on the sample size determinations are shown to be enormous. Therefore, when between-subject variations in outcome trends are anticipated to be significant, sample size determinations based on a fixed slope model can result in a seriously underpowered study.",
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