Abstract
Adjustments of sample size formulas are given for varying cluster sizes in cluster randomized trials with a binary outcome when testing the treatment effect with mixed effects logistic regression using second-order penalized quasi-likelihood estimation (PQL). Starting from first-order marginal quasi-likelihood (MQL) estimation of the treatment effect, the asymptotic relative efficiency of unequal versus equal cluster sizes is derived. A Monte Carlo simulation study shows this asymptotic relative efficiency to be rather accurate for realistic sample sizes, when employing second-order PQL. An approximate, simpler formula is presented to estimate the efficiency loss due to varying cluster sizes when planning a trial. In many cases sampling 14 per cent more clusters is sufficient to repair the efficiency loss due to varying cluster sizes. Since current closed-form formulas for sample size calculation are based on first-order MQL, planning a trial also requires a conversion factor to obtain the variance of the second-order PQL estimator. In a second Monte Carlo study, this conversion factor turned out to be 1.25 at most.
Original language | English |
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Pages (from-to) | 1488-1501 |
Number of pages | 14 |
Journal | Statistics in Medicine |
Volume | 29 |
Issue number | 14 |
DOIs | |
Publication status | Published - 30 Jun 2010 |
Keywords
- cluster randomized trials
- mixed effects logistic regression
- quasi-likelihood estimation
- sample size
- varying cluster sizes
- OPTIMAL EXPERIMENTAL-DESIGNS
- RELATIVE EFFICIENCY
- MULTICENTER TRIALS
- MODELS
- PERFORMANCE