Statistica Sinica 15(2005), 1015-1032

QUANTIFYING PQL BIAS IN ESTIMATING

CLUSTER-LEVEL COVARIATE EFFECTS

IN GENERALIZED LINEAR MIXED MODELS

FOR GROUP-RANDOMIZED TRIALS

Scarlett L. Bellamy$^1$, Yi Li$^2$, Xihong Lin$^2$ and Louise M. Ryan$^2$

$^1$University of Pennsylvania and $^2$Harvard School of Public Health

Abstract: We derive the asymptotic bias and variance of the penalized quasilikelihood (PQL) estimator of the cluster-level covariate effect in generalized linear mixed models for group-randomized trials where the number of clusters $n$ is small and the cluster size $m$ is large. We show that the asymptotic bias is of order $\hbox {O}_p(1/m)$ and the asymptotic variance is of order $O_p(1/n)+O_p\{1/(nm)\}$. The practical implication of our results is that the PQL method works well in settings involving small numbers of large clusters which are typical in grouped randomized trials. We illustrate the results using simulation studies.

Key words and phrases: Asymptotic bias, asymptotic variance, generalized linear mixed models, Penalized quasilikelihood.