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Shojania KG, Ranji SR, Shaw LK, et al. Closing the Quality Gap: A Critical Analysis of Quality Improvement Strategies (Vol. 2: Diabetes Care). Rockville (MD): Agency for Healthcare Research and Quality (US); 2004 Sep. (Technical Reviews, No. 9.2.)

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Closing the Quality Gap: A Critical Analysis of Quality Improvement Strategies (Vol. 2: Diabetes Care).

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Appendix FCalculation of effective sample sizes for trials with clustering

A substantial number of studies exhibited “clustering,” in that the units of analysis were patient level outcomes but the unit of allocation had been clusters of patients (e.g., randomization involved providers or clinics). The significance of clustering is that patients within a cluster are not independent - i.e., patients at one clinic have greater resemblance to each other than to patients at other sites or cared for by other providers in the trial. Unit of analysis errors do not affect point estimates for effect sizes, but they may spuriously narrow the associated confidence interval, potentially leading to a false-positive result in a trial.18 To avoid the same inflation of precision in our analysis, we calculated an effective sample size* for each study. Importantly, from the point of view of our analysis, the degree to which investigators acknowledged or accounted for cluster effects did not affect our analysis, except in so far as investigators who did consider cluster effects in the design or analysis of the trial were more likely to report data such as the number of providers randomized, rather than just the total numbers of patients in each group, as well as provide more technical details, such as values for the intra-cluster coefficient (ICC). 911

The table below compares the effective and originally reported sample sizes for effective sample sizes. Only values at baseline in the control and intervention groups are shown, but the same calculations were carried out for reported sample sizes in the post-intervention period for all study groups. Because so few studies reported ICC values,911 we imputed values based on published estimates. Specifically, we used ICC=0.03 for the HbA1c outcome and ICC=0.10 for measures of provider adherence, based no the midpoints of published values for process and outcome measures in primary care settings. 3 As a sensitivity analysis, we re-ran the effective sample size calculations and regression analyses with the upper bounds of these ranges (ICC=0.10 and ICC=0.33, for outcome and process measures, respectively), with no substantial impacts no the results.

Table F1Reported vs. effective sample sizes for clustered studies evaluating reduction in HbA1c

No. of clustersReported N(patients)Effective N(patients)Percent reduction (%)
Benjamin 199912 21064657
Boucher 199713 618310543
Olivarius 200114 4848748572
de Sonnaville 199715 2856337633
Frijling 20029 1231430112821
Groeneveld 200116 1522416526
Hetlevik 200017 3073345238
Hirsch 200218 21094658
Kiefe 200119 84135297428
Kinmonth 199810 4224019718
Kogan 200320 4428324912
Litzelman 199321 435311169
Mazzuca 198622 1312710418
McDermott 200123 2167838044
Meigs 200311 6659837737
O'Connor 199624 22416075
Ovhed 200025 23946683
Reed 200126 918912335
Renders 200127 2738929125
Wagner 200128 3460942530
Walker 200129 23456581
Deeb 198830 663617373
Feder 199531 2421210
Legorreta 199632 22055872
Hartmann 199533 1737624635
Walker 200129 23456581
Legorreta 199632 21855570
Branger 199934 3227522717
Mazzuca 198622 1412010116

Effective N equals sample size adjusted for presence of clustering. It was calculated as NEffective = (k*m) / (1 + (m-1)*r), where 'k 'is the number of clusters, ‘m’ is the number of patients per cluster, and ‘r’ is the intracluster coefficient (ICC). When r = 0, then NEffective = k*m (i.e., the reported sample size) When r = 1, then NEffective = k(i.e., the number of clusters) 18

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