powlgrnk: Computes the power of the logrank test

In raredd/desmon: Functions for design and monitoring of clinical trials

Computes the power of the logrank test

Description

Computes the power of the two-group logrank test for arbitrary failure time distributions in a standard clinical trials setting.

Usage

powlgrnk(
  acc.per,
  acc.rate,
  add.fu,
  alpha = 0.025,
  p.con = 0.5,
  hazcon = function(x, lc, pc, ...) {
     u <- (1 - pc) * exp(-lc * x)
     lc * u/(pc +
    u)
 },
  survcon = function(x, lc, pc, ...) pc + (1 - pc) * exp(-lc * x),
  haztst = function(x, lt, pt, ...) {
     u <- (1 - pt) * exp(-lt * x)
     lt * u/(pt +
    u)
 },
  survtst = function(x, lt, pt, ...) pt + (1 - pt) * exp(-lt * x),
  control.rate = NULL,
  test.rate = NULL,
  control.cure = 0,
  test.cure = 0,
  ...
)

Arguments

acc.per	Planned duration of accrual
acc.rate	Number of patients expected to be entered per time unit
add.fu	Additional follow-up between the end of accrual and the time of analysis
alpha	The one-sided type I error of the test
p.con	The proportion randomized to the control arm
hazcon	A function evaluating the control group hazard function at a vector of times
survcon	A function evaluating the control group survivor function at a vector of times
haztst	A function evaluating the experimental or test group hazard function at a vector of times
survtst	A function evaluating the experimental or test group survivor function at a vector of times
control.rate	Exponential hazard rate in control group for non-cured
test.rate	Exponential hazard rate in test group for non-cured
control.cure	Cure fraction in control group
test.cure	Cure fraction in test group
...	additional arguments passed to survival and hazard functions

Details

The calculations assume that n=acc.rate*acc.per patients are entered uniformly over the period [0,acc.per], with follow-up continuing for an addition add.fu time units, so censoring will be uniform on [add.fu,add.fu+acc.per]. The failure probability under the specified failure distribution is then computed, as is the expected number of failures, n*fail.prob.

hazcon must be the hazard function corresponding to the survivor function in survcon (and similarly for haztst and survtst). The program does not check for consistency of these functions, though. One way to check would be to compare survcon(x) to exp(-integrate(hazcon,0,x)$value) for various values x. The default functions are for the exponential cure rate model, which reduces to the two-sample exponential when the cure fractions are 0.

If custom hazcon, survcon, haztst, and survtst functions are given, the arguments should match those in the default functions (ie x,lc,pc,... for hazcon, etc). The values of lc, pc, lt, and pt are specified in the control.rate, control.cure, test.rate, and test.cure arguments and passed through to these functions.

The calculations are performed by using the integrate function to approximate the expectations of the logrank score and the logrank variance estimator and the variance of the logrank score under the specified conditions, and then using a normal approximation to the distribution of the logrank statistic.

This function only computes power for a single analysis, and does not consider group sequential tests.

Caution: consistent time units must be used for all quantities; eg if the accrual rate is given in patients/month, then the hazard rates must be in units of events/month and acc.per and add.fu must be in months.

Value

Returns a vector giving the power of the test under the specified conditions (power), the total sample size (n) and the expected number of events (nd).

See Also

powlgrnk6

Examples

# Exponential distributions
powlgrnk(5, 200, 3, control.rate = 0.1, test.rate = 0.075)

# Cure rate
powlgrnk(3, 200, 3, control.rate = log(2) / 3, test.rate = log(2) / 4,
         control.cure = 0.3, test.cure = 0.4)

# Exponential cure-rate with proportional hazards alternative
ht <- function(x, rat, ...) rat * hc(x, ...)
st <- function(x, rat, ...) sc(x, ...) ^ rat
sc <- function(x, pic, lic, ...) pic + (1 - pic) * exp(-lic * x)
hc <- function(x, pic, lic, ...) {
  u <- (1 - pic) * exp(-lic * x); lic * u / (pic + u)
}
powlgrnk(5, 200, 3, hazcon = hc, survcon = sc, haztst = ht,
         survtst = st, lic = log(2) / 3, pic = 0.3, rat = 0.5)

raredd/desmon documentation built on May 7, 2024, 3:46 p.m.