
A Practical Guide to Cluster Randomised Trials in Health Services Research
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"There are several unique strengths to this book. Inparticular the authors are very experienced statisticians havingworked for many years in the design and analysis of clusterrandomized trials and have written excellent methodologicalarticles many of which are cited in their book." (Journal of Biopharmaceutical Statistics, 2012)More details
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Subscripts
i Represents clusters j Represents individuals 1 Represents intervention arm 2 Represents control armFrequently used notation
k Number of clusters in each arm N Sample size (total number of individuals analysed or number of person years) for individually randomised trial Nc Sample size (total number of individuals analysed or number of person years) for cluster randomised trial m Cluster size (numbers analysed) if cluster sizes are fixed mi Number of individuals in the ith cluster Mean cluster size ? Intra-cluster correlation coefficient (ICC) ? Mean of outcome ?b2 Between-cluster variance (?b between-cluster standard deviation) ?w2 Within-cluster variance (?w within-cluster standard deviation) ? Probability of ‘success’ ? RateNotation in Chapter 4
p Proportion of successes in sample s Observed total standard deviation of outcome between participantsNotation in Chapter 6
? Constant in generalised estimating equations or mixed effects models ? Effect size eij Residual for jth individual in the ith cluster xij Dummy variable indicating intervention arm. When there are only two arms, xij takes the value 1 when the ith cluster is in the intervention arm, and 0 when the ith cluster is in the control arm Yij Value of outcome for the jth individual in the ith cluster Yi Mean value of outcome in the ith cluster ?i Mean effect of being in the ith cluster for cluster-specific models ?ij Probability of ‘success’ for the ith individual in the jth clusterNotation in Chapter 7
?m Correlation between matched pairs cvc Coefficient of variation of cluster sizes, cvcs Coefficient of variation of cluster sizes within strata sc Standard deviation of cluster sizes cv Coefficient of variation for the outcome, or cvm Coefficient of variation for the outcome within a matched pair t Number of person years per cluster th Harmonic mean of the number of person years per cluster S Number of strata Deff Design effect ma ?b1 Between-cluster standard deviation in the intervention arm ?b2 Between-cluster standard deviation in the control arm ?bm Between-cluster standard deviation for clusters within a matched pair ?w Within-cluster standard deviation (consistent with Donner) ?1 Mean in the intervention arm (note the subscripts for ? and ? have a different meaning in Chapter 7 from their meaning in Chapters 6 and 8, although the usage in each chapter is consistent with the subscripts section at the top of this list ) ?2 Mean in the control arm (see note above) ?1 Proportion in the intervention arm (see note above) ?2 Proportion in the control arm (see note above) ?1 Rate in the intervention arm (see note above) ?2 Rate in the control arm (see note above)Notation in Chapter 8
ps Probability that any two subjects from the same cluster have the same outcome po Probability that any two subjects from different clusters have the same outcome MSB Mean square between clusters MSW Mean square within clusters L Total number of intervention arms Ns Total number of individuals in a single population Nl Total number of individuals in arm l of a trial Yli Mean outcome in cluster i in intervention arm l Yl Mean outcome in intervention arm l Yij Value of the outcome for the jth individual in the ith cluster Yli Mean outcome in cluster i in intervention arm l Yl Mean outcome in intervention arm l L Total number of intervention arms Ns Total number of individuals in a single population Nl Total number of individuals in arm l of a trial mli Number of individuals in ith cluster in intervention arm l ?2 Total variance ? Constant in generalised estimating equations or mixed effects...System requirements
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