nphPower (version 1.1.0)

cal_event: Event Rate Calculation

Description

Calculate the event rate given the hazards and drop-out distribution parameters

Usage

cal_event(ratio, lambda1, lambda0, entry, fup, l_shape, l_scale)

Value

a list of components:

ep1

event rate for treatment group

ep0

event rate for control group

ep

mean event rate weighted by the randomization ratio

Arguments

ratio

allocation ratio

lambda1

hazard rate for treatment group

lambda0

hazard rate for control group

entry

enrollment period time

fup

follow-up period time

l_shape

shape parameter of weibull distribution for drop-out

l_scale

scale parameter of weibull distribution for drop-out

Details

The event rate is calculated based on the following assumptions: 1) patients are uniformly enrolled within entry time; 2) survival times for treatment and control are from exponential distribution; 3) the drop-out times for treatment and control follow the weibull distribution. The final rate is obtained via numeric integration:

$$ P=\int_{t_{fup}}^{t_{enrl}+t_{fup}} \Big \{ \int_0^{t}r(u)exp\big [-\int_0^u[r(x)+l(x)]dx \big]d(u) \Big \} \frac{1}{t_{enrl}} dt $$ where \(r(x)\) is the hazard of event and \(l(x)\) is the hazard of drop-out; \(t_{enrl}\) is the entry time and \(t_{fup}\) is the follow-up duration.

Examples

# median survival time for treatment and control: 16 months vs 12  months
# entry time: 12 months ; follow-up time: 18 months
# the shape parameter for weibull drop-out : 0.5
# median time for drop-out : 48 =>
# scale parameter: 48/log(2)^(1/0.5)=100
  RR <- 1; l1 <- log(2)/16; l0 <- log(2)/12
  t_enrl <- 12; t_fup <- 18

  cal_event(1,l1,l0,t_enrl,t_fup,0.5,100)