Table 2.

Power for Addressing Secondary Objectives of Design A

	True TE parameters			Null hypotheses tested
Scenario	TE-Vaccine (%)	TE-NVPM (%)	TE-Vaccine+NVPM (%)	TE-Vaccine ≤0%	TE-NVPM ≤30%	TE-Vaccine+NVPM ≤30%	TE-Vaccine=TE-NVPM	TE-Vaccine=TE-Vaccine+NVPM	Vaccine and NVPM Additive
Additivity	40	60	76	90	90	100	53	99	5
Synergy	40	60	88	90	90	100	53	100	53
Antagonism	40	60	64	90	90	96	53	72	31
Additivity	40	70	82	90	100	100	91	100	5
Synergy	40	70	91	90	100	100	91	100	45
Antagonism	40	70	73	90	100	100	91	96	27
Additivity	40	80	88	90	100	100	100	100	5
Synergy	40	80	94	90	100	100	100	100	33
Antagonism	40	80	82	90	100	100	100	100	22

Power (%) for evaluating the treatment efficacy of the combination intervention (TE-Vaccine+NVPM) and the NVPM alone (TE-NVPM), comparing active treatment arms head-to-head, and testing for vaccine and NVPM synergy/antagonism under Design A of Table 1. Under TE-NVPM=60%, 70%, or 80%, Design A requires 7,600 participants (1,900 per treatment arm) for 90% power to detect TE-Vaccine=40% and the level of TE-Vaccine+NVPM shown assuming Vaccine and NVPM additivity, and to compare TE-Vaccine vs. TE-Vaccine+NVPM, rejecting the null hypotheses: TE-Vaccine ≤0%, TE-Vaccine+NVPM ≤30%, and TE-Vaccine=TE-Vaccine+NVPM using one-sided 0.025-level log-rank tests, respectively. Power is shown under vaccine and NVPM additivity, synergy (a 50% decrease in relative risk), and antagonism (a 50% increase in relative risk). Evidence for synergy/antagonism is evaluated using a two-sided 0.05-level likelihood ratio test under the Cox proportional hazards model.

TE, treatment efficacy.