computeN {CoRpower}

Estimation of Size and Numbers of Cases and Controls in the Target Population of Active Treatment Recipients At Risk at the Biomarker Sampling Timepoint

Description

If the power calculation is done at the study design stage, the function estimates the size and numbers of cases and controls in the target population of active treatment recipients observed to be at risk at the biomarker sampling timepoint.

Usage

computeN(
  Nrand,
  tau,
  taumax,
  VEtauToTaumax,
  VE0toTau,
  risk0,
  dropoutRisk,
  propCasesWithS
)

Arguments

Nrand

the number of participants randomized to the active treatment group

tau

the biomarker sampling timepoint after randomization

taumax

the time after randomization marking the end of the follow-up period for the clinical endpoint

VEtauToTaumax

the treatment (vaccine) efficacy level between \tau and \tau_{max}

VE0toTau

the treatment (vaccine) efficacy between 0 and \tau

risk0

the overall placebo-group endpoint risk between \tau and \tau_{max}

dropoutRisk

the risk of participant dropout between 0 and \tau_{max}

propCasesWithS

the proportion of observed cases with a measured biomarker response

Details

The function estimates design parameters that are required as input to computePower. If the power calculation is done after the follow-up was completed, the estimates are replaced by the observed counterparts for use as input parameters in computePower.

The calculations include options to account for participant dropout by specifying dropoutRisk as well as for incomplete sample storage by specifying propCasesWithS.

The estimation procedure considers the standard survival analysis framework with failure and censoring times denoted by T and C, respectively, and makes the following assumptions:

1. T and C are independent.

2. T|Z=0 follows an exponential distribution with rate \theta_t and C|Z=0 follows an exponential distribution with rate \theta_c

3. RR_{\tau-\tau_{max}} := P(T <= \tau_{max}|T> \tau, Z=1)/P(T <= \tau_{max}|T> \tau, Z=0) is assumed to be equal to P(T <= t|T> \tau, Z=1)/P(T <= t|T> \tau, Z=0) for all t \in (\tau,\tau_{max}].

Value

A list with the following components:

• N: the total estimated number of active treatment recipients observed to be at risk at \tau

• nCases: the estimated number of clinical endpoint cases observed between \tau and \tau_{max} in the active treatment group

• nControls: the estimated number of controls observed to complete follow-up through \tau_{max} endpoint-free in the active treatment group

• nCasesWithS: the estimated number of clinical endpoint cases observed between \tau and \tau_{max} in the active treatment group with an available biomarker response

See Also

computePower

Examples

Nrand = 4100
tau = 3.5
taumax = 24
VEtauToTaumax = 0.75
VE0toTau = 0.75/2
risk0 = 0.034
dropoutRisk = 0.1
propCasesWithS = 1
computeN(Nrand, tau, taumax, VEtauToTaumax, VE0toTau, risk0, dropoutRisk, propCasesWithS)