Table 2:

Key notation used in theoretical development. Full data parameters refer to summaries of the population when no right-censoring is present. Observed data parameters refer to summaries of the observed population, which includes participants with right-censored outcome data. In the text, a subscript n denotes an estimate of the relevant quantity.

Quantity	Expression	Description
Full data parameters
Fj,z(t0)	${\text{pr}}_{{\mathbb{P}}_0}\{T\le t_0,J=j\mid Z=z\}$	cumulative incidence at time t0 of type j endpoints in arm z
V Ej(t0)	1 − Fj,1(t0)/Fj,0(t0)	vaccine efficacy against type j endpoints at time t0
V S E(t0)	(1 − V E1(t0))/(1 − V E2(t0))	vaccine sieve effect at time t0
Observed data parameters
μt(h(t − 1))	EP0{μt + 1(H(t)) ∣ Z = 1, C(t − 1) = 0, H(t − 1) = h(t − 1)}	iterated mean at time t given history h(t − 1)
G(w)	prP0{W ≤ w}	distribution function of baseline covariates
$\stackrel{‒}{\mu }$	∫ μ1 (w)dG(w)	mean of μ1; under assumptions, equals F1,1 (t0)
ζ(w)	prP0{Z = 1 ∣ W = w}	probability of receiving vaccine given covariate value w
πt(w)	prP0 {C(t) = 0 ∣ Z = 1, N(t − 1) = 0, M(t − 1) = 0, C(t − 1) = 0, W = w}	probability of remaining under study at time t given at risk at t − 1 and covariate value w