designSafeLogrank {safestats}

Designs a Safe Logrank Test Experiment

Description

A designed experiment requires (1) an anticipated number of events nEvents, or even better nPlan, the number of participants to be recruited in the study, and (2) the parameter of the safe test, i.e., thetaS. Provided with a clinically relevant minimal hazard ratio hrMin, this function outputs thetaS = hrMin as the safe test defining parameter in accordance to the GROW criterion. If a tolerable type II error beta is provided then nEvents can be sampled. The sampled nEvents is then the smallest nEvents for which hrMin is found with power of at least 1 - beta under optional stopping. If exact equal FALSE, then the computations exploit the local asymptotic normal approximation to sampling distribution of the logrank test derived by Schoenfeld (1981).

Usage

designSafeLogrank(
  hrMin = NULL,
  beta = NULL,
  nEvents = NULL,
  h0 = 1,
  alternative = c("twoSided", "greater", "less"),
  alpha = 0.05,
  ratio = 1,
  exact = TRUE,
  tol = 1e-05,
  m0 = 50000L,
  m1 = 50000L,
  nSim = 1000L,
  nBoot = 10000L,
  parameter = NULL,
  groupSizePerTimeFunction = returnOne,
  pb = TRUE,
  ...
)

Arguments

hrMin

numeric that defines the minimal relevant hazard ratio, the smallest hazard ratio that we want to detect.

beta

numeric in (0, 1) that specifies the tolerable type II error control necessary to calculate both "n" and "phiS". Note that 1-beta defines the power.

nEvents

numeric > 0, targetted number of events.

h0

numeric > 0, represents the null hypothesis, default h0=1.

alternative

a character string specifying the alternative hypothesis, which must be one of "twoSided" (default),"greater" or "less". The alternative is pitted against the null hypothesis of equality of the survival distributions. More specifically, let lambda1 be the hazard rate of group 1 (i.e., placebo), and lambda2 the hazard ratio of group 2 (i.e., treatment), then the null hypothesis states that the hazard ratio theta = lambda2/lambda1 = 1. If alternative = "less", the null hypothesis is compared to theta < 1, thus, lambda2 < lambda1, that is, the hazard of group 2 (i.e., treatment) is less than that of group 1 (i.e., placebo), hence, the treatment is beneficial. If alternative = "greater", then the null hypothesis is compared to theta > 1, thus, lambda2 > lambda1, hence, harm.

alpha

numeric in (0, 1) that specifies the tolerable type I error control –independent on n– that the designed test has to adhere to. Note that it also defines the rejection rule e10 > 1/alpha.

ratio

numeric > 0 representing the randomisation ratio of condition 2 (Treatment) over condition 1 (Placebo), thus, m1/m0. Note that m1 and m0 are not used to specify ratio. Ratio is only used when zApprox=TRUE, which ignores m1 and m0.

exact

a logical indicating whether the design should be based on the exact safe logrank test based on the hypergeometric likelihood. Default is TRUE, if FALSE then the design is based on a safe z-test.

tol

a number that defines the stepsizes between the lowParam and highParam.

m0

Number of subjects in the control group 0/1 at the beginning of the trial, i.e., nPlan[1].

m1

Number of subjects in the treatment group 1/2 at the beginning of the trial, i.e., nPlan[2].

nSim

integer > 0, the number of simulations needed to compute power or the number of events for the exact safe logrank test under continuous monitoring

nBoot

integer > 0 representing the number of bootstrap samples to assess the accuracy of the approximation of power or nEvents for the exact safe logrank test under continuous monitoring

parameter

Numeric > 0, represents the safe tests defining thetaS. Default NULL so it's decided by the algorithm, typically, this equals hrMin, which corresponds to the GROW choice.

groupSizePerTimeFunction

A function without parameters and integer output. This function provides the number of events at each time step. For instance, if rpois(1, 7) leads to a random number of events at each time step.

pb

logical, if TRUE, then show progress bar.

...

further arguments to be passed to or from methods.

Value

Returns a safeDesign object that includes:

nEvents

the anticipated number of events, either (1) specified by the user, or (2) computed based on beta and thetaMin.

parameter

the parameter that defines the safe test. Here log(thetaS).

esMin

the minimally clinically relevant hazard ratio specified by the user.

alpha

the tolerable type I error provided by the user.

beta

the tolerable type II error provided by the user.

alternative

any of "twoSided", "greater", "less" provided by the user.

testType

"logrank".

ratio

default is 1. It defines the ratio between the planned randomisation of condition 2 over condition 1.

pilot

FALSE to indicate that the design is not a pilot study.

call

the expression with which this function is called.

References

Schoenfeld, D. (1981). The asymptotic properties of nonparametric tests for comparing survival distributions. Biometrika, 68(1), 316-319.

Examples

designSafeLogrank(hrMin=0.7)
designSafeLogrank(hrMin=0.7, zApprox=TRUE)
designSafeLogrank(hrMin=0.7, beta=0.3, nSim=10)
designSafeLogrank(hrMin=0.7, nEvents=190, nSim=10)