Type I error control for cluster randomized trials under varying small sample structures

Joshua R Nugent,Ken P Kleinman

doi:10.1186/s12874-021-01236-7

Joshua R Nugent, Ken P Kleinman

Open Access

https://doi.org/10.1186/s12874-021-01236-7

Copy DOI

Abstract

BackgroundLinear mixed models (LMM) are a common approach to analyzing data from cluster randomized trials (CRTs). Inference on parameters can be performed via Wald tests or likelihood ratio tests (LRT), but both approaches may give incorrect Type I error rates in common finite sample settings. The impact of different combinations of cluster size, number of clusters, intraclass correlation coefficient (ICC), and analysis approach on Type I error rates has not been well studied. Reviews of published CRTs find that small sample sizes are not uncommon, so the performance of different inferential approaches in these settings can guide data analysts to the best choices.MethodsUsing a random-intercept LMM stucture, we use simulations to study Type I error rates with the LRT and Wald test with different degrees of freedom (DF) choices across different combinations of cluster size, number of clusters, and ICC.ResultsOur simulations show that the LRT can be anti-conservative when the ICC is large and the number of clusters is small, with the effect most pronouced when the cluster size is relatively large. Wald tests with the between-within DF method or the Satterthwaite DF approximation maintain Type I error control at the stated level, though they are conservative when the number of clusters, the cluster size, and the ICC are small.ConclusionsDepending on the structure of the CRT, analysts should choose a hypothesis testing approach that will maintain the appropriate Type I error rate for their data. Wald tests with the Satterthwaite DF approximation work well in many circumstances, but in other cases the LRT may have Type I error rates closer to the nominal level.

Highlights

Linear mixed models (LMM) are a common approach to analyzing data from cluster randomized trials (CRTs)
When the response variable of interest is continuous, linear mixed models (LMMs), which require that observations are independent only after conditioning on cluster membership, are a common approach to the data analysis
Our work aims to add to this literature by examining in more detail the Type I error (TIE) control of several LMM inference approaches in a variety of plausible CRT scenarios

Summary

Introduction

Linear mixed models (LMM) are a common approach to analyzing data from cluster randomized trials (CRTs). These groups, rather than the subjects directly, are randomized to the trial interventions [1] In these studies, outcomes within a cluster – for example, patients within hospitals or students within classrooms – are almost certainly correlated with one another. Outcomes within a cluster – for example, patients within hospitals or students within classrooms – are almost certainly correlated with one another This clustering complicates data analysis because the common regression assumption that observations are independent is violated. CRTs are a widely used experimental design (see for example [2,3,4]), and LMMs are an attractive option for data analysis Some reasons for this attractiveness are that LMMs are robust to certain missing data mechanisms and can flexibly accommodate nested levels of clustering and/or varying cluster sizes [5]

Methods

Results

Conclusion