Analysis of multicenter clinical trials with very low event rates

Table 5 Reanalysis of the motivating five-arm smoking cessation trial [3]

Study arm^a	Randomized (n)	6-month cessation (n (%))	No adjustment	Random intercept	MH	GEE	GEE-small sample correction
Usual care	813	1 (0.1%)	0.12 (0.02 to 0.90)	0.12 (0.02 to 0.90)	0.14 (0.02 to 1.24)	0.14 (0.02 to 0.87)	Model did not converge
Free cessation aids	1587*	8 (0.5%)	0.51 (0.21 to 1.26)	0.51 (0.21 to 1.25)	1.95 (0.81 to 4.7)	0.53 (0.22 to 1.24)
Free e-cigarettes	1199	12 (1.0%)	Reference	Reference	Reference	Reference
Rewards plus free cessation aids	1198	24 (2.0%)	2.02 (1.01 to 4.06)	2.02 (1.01 to 4.07)	2.05 (1.02 to 4.14)	1.96 (1.00 to 3.84)
Redeemable deposit plus free cessation aids	1207*	35 (2.9%)	2.95 (1.52 to 5.71)	2.97 (1.53 to 5.76)	2.96 (1.53 to 5.72)	2.84 (1.50 to 5.37)
Total	6004 (100%)	80 (1.3%)	6004 (100%)	6004 (100%)	552/2012 (27.44%)^b 1025/2786 (36.79%)^b 1497/2397 (62.45%)^b 1701/2406 (70.70%)^b	6004 (100%)

Results are reported as odds ratios and 95% confidence intervals unless otherwise specified. All models are additionally adjusted for study wave (first or second) according to the primary analysis plan
GEE generalized estimating equations, MH Mantel–Haenszel, RE random-effects (i.e., random center intercept)
*A total of 6006 participants were randomized, though for 2 participants (n = 1 in each study arm with an asterisk) who did not meet the criteria for the primary outcome, we did not have information on their employer
^aDetails about the interventions examined in this smoking cessation trial are detailed in the primary trial report [3]
^bBecause odds ratios were calculated by each study arm using the e-cigarettes group as the reference group, we have reported the total number for each analysis to illustrate the dropout that occurred when using the Mantel–Haenszel approach

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