seqopr: Compute Operating Characteristics for Group Sequential...

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

Compute Operating Characteristics for Group Sequential Designs

Description

Computes operating characteristics (seqopr) and sample size (seqss) for group sequential logrank tests in the setting of phase III studies with failure time endpoints.

Usage

seqopr(
  acc.per,
  acc.rate,
  control.rate = NULL,
  pct.imp = NULL,
  a.times,
  prop.strat = rep(1, length(control.rate)),
  alpha = 0.025,
  alphal = 0,
  p.con = 0.5,
  use = 6,
  usel = 6,
  oftr = alpha/50,
  oftrl = alphal/50,
  control.med = NULL,
  pct.reduc = NULL
)

Arguments

acc.per	In sequse and lr.inf, the planned accrual period for the study. In seqss, a vector of length 2 giving the min and max values of the range of possible accrual periods over which to search.
acc.rate	Expected accrual rate
control.rate	Vector giving the hazard rate on the control treatment in each stratum
pct.imp	The percent improvement in the median failure time for the experimental treatment over the control
a.times	Planned chronological times of interim analyses. Must be positive and in increasing order.
prop.strat	Vector giving the proportion of the total sample in each stratum. The vector is renormalized to sum to 1, so the values only need to be proportional to the proportions.
alpha	The one-sided significance level of the group sequential test
alphal	The one-sided significance level used in the RCI monitoring for stopping in favor of the null. The confidence level of the RCI is 1-2*alphal. If alphal <= 0, only the upper boundary is used.
p.con	The proportion of subjects to be randomized to the control group
use	the type of use function: 1=O'Brien-Fleming, 2=Pocock, 3=linear, 4=one and a half, 5=quadratic, 6=truncated O'Brien-Fleming
usel	The use function for determining critical values for the RCI lower boundary (same codes as use)
oftr	The significance level at which the truncated O-F boundary is truncated (upper boundary)
oftrl	The significance level at which the truncated O-F boundary is truncated (RCI lower boundary)
control.med	Vector giving the median failure times on the control treatment in each stratum (may be given instead of control.rate)
pct.reduc	The percent reduction in the hazard rate for the experimental treatment relative to the control (may be given instead of pct.imp)
power	The desired power for the study
add.fu	The additional follow-up planned after the end of accrual before the final analysis will be conducted
anal.int	Interim analyses are planned to take place every anal.int time units on the chronological time scale, beginning at first.anal
first.anal	Time of the first planned interim analysis

Details

Assumes accrual is uniform at the rate acc.rate for acc.per units of time, so the total number of subjects is acc.rate * acc.per, with interim analyses to be performed at the times in a.times. The final analysis is assumed to take place at the final time in a.times. Significance levels at the analyses are determined from the error spending rate function approach (see sequse for more details). Optionally, an asymmetric lower boundary for early stopping in favor of the null can be included by specifying a value of alphal > 0. An approximate lower boundary based on repeated confidence intervals is used (see sequse). Failure times are assumed to be exponentially distributed, with the exponential failure hazard rates specified through the control.rate parameter, or alternately the control.med parameter. A stratified sample with different failure rates in the strata can be specified by giving a vector of control group hazard rates corresponding to the different strata, and specifying the stratum proportions in prop.strata. These functions assume proportional hazards alternatives. The improvement from using the experimental treatment instead of control is specified as the PERCENT improvement in the median time to failure. This is related to the hazard ratio through hazard ratio = 1/(1+pct.imp/100). Alternately, the percent reduction in the hazard rate (pct.reduc) can be specified.

Given the specifications above, seqopr computes the boundaries, power, boundary crossing probabilities and expected stopping times. The expected stopping times under the null are computed using the specified calendar times of analysis and the null failure rates, but using the information times and boundaries based on the expected information at these times as determined under the alternative. They therefore do not typically give the correct expected stopping times under the design as it will be implemented in practice.

In seqss, the desired power is specified, and a range is given for the accrual period. The program then searches for the accrual period that gives the desired power. The timing of the final analysis after the completion of accrual (parameter add.fu) is kept fixed. Since the study duration is variable, an approximate interim analysis schedule is specified through the parameters anal.int and first.anal. When early stopping in favor of the null is included, it is possible that some designs examined in the search will have incompatible specifications. If this happens, try reducing the upper limit on acc.per. If the range of acc.per specified does not include a solution, then the algorithm should give an error message stating that the values at the end points are not of opposite signs. If this occurs, try increasing the width of the interval.

Given accrual and follow-up information and failure rates, lr.inf computes the total planned information and the Brownian motion mean parameter eta. The main use of this function is to get the value of eta for computing the lower boundary in sequse.

Value

seqopr returns a list with the following components (except acc.per). seqss returns a list with the following components computed from the final design.

Expected.inf	A matrix giving the expected information times at the planned analysis times and the expected number of failures under the null and alternative and the sample size at each analysis.
Boundaries	A matrix giving the boundaries on the standard normal test statistic scale at the expected information at the planned analysis times, plus columns giving the upper and lower boundary crossing probabilities under H0 and H1 at each analysis
Rej.Probs	A vector of 4 values giving the size and power (upper boundary crossing probabilities under H0 and H1) and the total lower boundary crossing probabilities under H0 and H1.
stop.times	A 2 x 4 matrix of expected stopping times
eta	The Brownian motion mean parameter
call	The call to seqopr
acc.per	The accrual period that gives the desired power

lr.inf returns a vector giving the values of the Brownian motion mean parameter eta and the expected number of failures under the alternative.

See Also

sequse; powlgrnk6; seqp

Examples

seqopr(3, 200, 0.1, 50, c(2, 3, 4, 5))
seqss(0.8, c(2, 6), 200, 2, 0.5, 2, 0.1, 50)
lr.inf(3, 200, 2, 0.1, 50)

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