nevent: Number of Subjects Having an Event by Calendar Time

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

Number of Subjects Having an Event by Calendar Time

Description

Obtains the number of subjects having an event by given calendar times for each treatment group.

Usage

nevent(
  time = 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_
)

Arguments

time	A vector of calendar times at which to calculate the number of patients having an event.
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.

Details

For a given treatment group g and calendar time \tau, the number of patients having an event by calendar time \tau is calculated as I_1 + I_2, where

I_1 = \phi_g A(\tau - T_{\rm{fmax}}) P_g(T_{\rm{fmax}}),

and

I_2 = \phi_g \int_{\tau - T_{\rm{fmax}}}^{\tau} a(u) P_g(\tau - u) du,

where \phi_g is the probability of randomization to treatment group g, A(\tau - T_{\rm{fmax}}) is the number of patients enrolled by calendar time \tau - T_{\rm{fmax}}, P_g(T_{\rm{fmax}}) is the probability of having an event by the maximum follow-up time T_{\rm{fmax}} for a patient in treatment group g after enrollment, a(u) is the accrual intensity at calendar time u, and P_g(\tau - u) is the probability of having an event by calendar time \tau for a patient in treatment group g enrolled at calendar time u.

Value

A matrix of the number of patients having an event at the specified calendar 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.
nevent(time = 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)

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