cal_event: Event Rate Calculation

In hcheng99/nphPower: Sample Size Calculation under Non-Proportional Hazards

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)

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.

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

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)

hcheng99/nphPower documentation built on March 31, 2024, 10:42 a.m.