natrisk: Number of Subjects at Risk

In lrstat: Power and Sample Size Calculation for Non-Proportional Hazards and Beyond

Number of Subjects at Risk

Description

Obtains the number of subjects at risk at given analysis times for each treatment group.

Usage

natrisk(
  t = NA_real_,
  allocationRatioPlanned = 1,
  accrualTime = 0L,
  accrualIntensity = NA_real_,
  piecewiseSurvivalTime = 0L,
  lambda1 = NA_real_,
  lambda2 = NA_real_,
  gamma1 = 0L,
  gamma2 = 0L,
  accrualDuration = NA_real_,
  maxFollowupTime = NA_real_,
  time = NA_real_
)

Arguments

t	A vector of analysis times at which to calculate the number of patients at risk.
allocationRatioPlanned	Allocation ratio for the active treatment versus control. Defaults to 1 for equal randomization.
accrualTime	A vector that specifies the starting time of piecewise Poisson enrollment time intervals. Must start with 0, e.g., c(0, 3) breaks the time axis into 2 accrual intervals: [0, 3) and [3, \infty).
accrualIntensity	A vector of accrual intensities. One for each accrual time interval.
piecewiseSurvivalTime	A vector that specifies the starting time of piecewise exponential survival time intervals. Must start with 0, e.g., c(0, 6) breaks the time axis into 2 event intervals: [0, 6) and [6, \infty). Defaults to 0 for exponential distribution.
lambda1	A vector of hazard rates for the event for the active treatment group. One for each analysis time interval.
lambda2	A vector of hazard rates for the event for the control group. One for each analysis time interval.
gamma1	The hazard rate for exponential dropout, or a vector of hazard rates for piecewise exponential dropout for the active treatment group.
gamma2	The hazard rate for exponential dropout, or a vector of hazard rates for piecewise exponential dropout for the control group.
accrualDuration	Duration of the enrollment period.
maxFollowupTime	Follow-up time for the first enrolled subject. For fixed follow-up, maxFollowupTime = minFollowupTime. For variable follow-up, maxFollowupTime = accrualDuration + minFollowupTime.
time	Calendar time for the analysis.

Details

For a given treatment group g and calendar time \tau, the number of patients at risk at analysis time t is calculated as

\phi_g A(\tau - t) S_g(t) G_g(t),

where \phi_g is the probability of randomization to treatment group g, A(\tau - t) is the number of patients enrolled by calendar time \tau - t, S_g(t)G_g(t) is the probability of being at risk at analysis time t for a patient in treatment group g after enrollment. Obviously, t < \min(\tau, T_{\rm{fmax}}).

Value

A matrix of the number of patients at risk at the specified analysis times (row) for each treatment group (column).

Author(s)

Kaifeng Lu, [e-mail]

Examples

# Piecewise accrual, piecewise exponential survivals, and 5% dropout by
# the end of 1 year.

natrisk(t = c(9, 24), allocationRatioPlanned = 1,
        accrualTime = c(0, 3), accrualIntensity = c(10, 20),
        piecewiseSurvivalTime = c(0, 6),
        lambda1 = c(0.0533, 0.0309), lambda2 = c(0.0533, 0.0533),
        gamma1 = -log(1-0.05)/12, gamma2 = -log(1-0.05)/12,
        accrualDuration = 12, maxFollowupTime = 30, time = 30)

lrstat documentation built on May 13, 2026, 9:06 a.m.