Table 1.

Summary of data generation scenarios, see Supplementary Text 2 for more details.

Parameter	Phase one	Phase two
Control prevalence in the first measurement occasion	30%	30%
Time trend	Linear, odds ratio = 1.05 for each measurement occasion (6 occasions for all trial designs)	Linear, odds ratio = 1.05 for each measurement occasion (6 occasions for all trial designs)
Intervention effect	Odds ratio = 1.3	Odds ratio = 1.3
ICC within measurement occasion ($\mathit{\rho }$)	0.01, 0.1	0.01, 0.05, 0.1
Correlation structures between measurement occasions	Exchangeable	Exchangeable
	AR(1) r = 0.6	AR(1) r = 0.6
	AR(1) r = 0.8	AR(1) r = 0.8
	AR(1) r = 0.8 with 50% less correlation between control and intervention	AR(1) r = 0.8 with 50% less correlation between control and intervention
Number of sequences	3,6	3,6
Number of clusters (C)	18	6,12,18, 24,
		42,48, 54
Cluster size	24, 60	24, 60,300a
Coefficient of variation (CV) of cluster size	0, 0.4	0, 0.4

^aThe scenario with cluster size of 300 was only run with exchangeable within cluster correlation, 12, 24, and 42 clusters, and no variability in cluster size.