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Modelling the hierarchical structure in datasets with very small clusters: a simulation study to explore the effect of the proportion of clusters when the outcome is continuous
Author(s) -
Sauzet O.,
Wright K.C.,
Marston L.,
Brocklehurst P.,
Peacock J.L.
Publication year - 2012
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.5638
Subject(s) - statistics , cluster analysis , linear regression , linear model , cluster (spacecraft) , mixed model , outcome (game theory) , contrast (vision) , regression , type i and type ii errors , multilevel model , generalized linear mixed model , econometrics , hierarchical clustering , random effects model , mathematics , computer science , meta analysis , artificial intelligence , medicine , programming language , mathematical economics
In cluster‐randomised trials, the problem of non‐independence within clusters is well known, and appropriate statistical analysis documented. Clusters typically seen in cluster trials are large in size and few in number, whereas datasets of preterm infants incorporate clusters of size two (twins), size three (triplets) and so on, with the majority of infants being in ‘clusters’ of size one. In such situations, it is unclear whether adjustment for clustering is needed or even possible. In this paper, we compared analyses allowing for clustering (linear mixed model) with analyses ignoring clustering (linear regression). Through simulations based on two real datasets, we explored estimation bias in predictors of a continuous outcome in different size datasets typical of preterm samples, with varying percentages of twins. Overall, the biases for estimated coefficients were similar for linear regression and mixed models, but the standard errors were consistently much less well estimated when using a linear model. Non‐convergence was rare but was observed in approximately 5% of mixed models for samples below 200 and percentage of twins 2% or less. We conclude that in datasets with small clusters, mixed models should be the method of choice irrespective of the percentage of twins. If the mixed model does not converge, a linear regression can be fitted, but standard error will be underestimated, and so type I error may be inflated. Copyright © 2012 John Wiley & Sons, Ltd.