Get Power Counts

Returns the power, stopping probabilities, and expected sample size for testing mean rates for negative binomial distributed event numbers in two samples at given sample sizes.

Usage

getPowerCounts(
  design = NULL,
  ...,
  directionUpper = NA,
  maxNumberOfSubjects = NA_real_,
  lambda1 = NA_real_,
  lambda2 = NA_real_,
  lambda = NA_real_,
  theta = NA_real_,
  thetaH0 = 1,
  overdispersion = 0,
  fixedExposureTime = NA_real_,
  accrualTime = NA_real_,
  accrualIntensity = NA_real_,
  followUpTime = NA_real_,
  allocationRatioPlanned = NA_real_
)

Arguments

design

The trial design. If no trial design is specified, a fixed sample size design is used. In this case, Type I error rate alpha, Type II error rate beta, twoSidedPower, and sided can be directly entered as argument where necessary.

...

Ensures that all arguments (starting from the "...") are to be named and that a warning will be displayed if unknown arguments are passed.

directionUpper

Logical. Specifies the direction of the alternative, only applicable for one-sided testing; default is TRUE which means that larger values of the test statistics yield smaller p-values.

maxNumberOfSubjects

maxNumberOfSubjects > 0 needs to be specified for power calculations or calculation of necessary follow-up (count data). For two treatment arms, it is the maximum number of subjects for both treatment arms.

lambda1

A numeric value or vector that represents the assumed rate of a homogeneous Poisson process in the active treatment group, there is no default.

lambda2

A numeric value that represents the assumed rate of a homogeneous Poisson process in the control group, there is no default.

lambda

A numeric value or vector that represents the assumed rate of a homogeneous Poisson process in the pooled treatment groups, there is no default.

theta

A numeric value or vector that represents the assumed mean ratios lambda1/lambda2 of a homogeneous Poisson process, there is no default.

thetaH0

The null hypothesis value, default is 0 for the normal and the binary case (testing means and rates, respectively), it is 1 for the survival case (testing the hazard ratio).

For non-inferiority designs, thetaH0 is the non-inferiority bound. That is, in case of (one-sided) testing of

• means: a value != 0 (or a value != 1 for testing the mean ratio) can be specified.

• rates: a value != 0 (or a value != 1 for testing the risk ratio pi1 / pi2) can be specified.

• survival data: a bound for testing H0: hazard ratio = thetaH0 != 1 can be specified.

• count data: a bound for testing H0: lambda1 / lambda2 = thetaH0 != 1 can be specified.

For testing a rate in one sample, a value thetaH0 in (0, 1) has to be specified for defining the null hypothesis H0: pi = thetaH0.

overdispersion

A numeric value that represents the assumed overdispersion of the negative binomial distribution, default is 0.

fixedExposureTime

If specified, the fixed time of exposure per subject for count data, there is no default.

accrualTime

If specified, the assumed accrual time interval(s) for the study, there is no default.

accrualIntensity

If specified, the assumed accrual intensities for the study, there is no default.

followUpTime

If specified, the assumed (additional) follow-up time for the study, there is no default. The total study duration is accrualTime + followUpTime.

allocationRatioPlanned

The planned allocation ratio n1 / n2 for a two treatment groups design, default is 1. For multi-arm designs, it is the allocation ratio relating the active arm(s) to the control. For simulating means and rates for a two treatment groups design, it can be a vector of length kMax, the number of stages. It can be a vector of length kMax, too, for multi-arm and enrichment designs. In these cases, a change of allocating subjects to treatment groups over the stages can be assessed. Note that internally allocationRatioPlanned is treated as a vector of length kMax, not a scalar.

Value

Returns a TrialDesignPlan object. The following generics (R generic functions) are available for this result object:

• names() to obtain the field names,

• print() to print the object,

• summary() to display a summary of the object,

• plot() to plot the object,

• as.data.frame() to coerce the object to a data.frame,

• as.matrix() to coerce the object to a matrix.

Details

At given design the function calculates the power, stopping probabilities, and expected sample size for testing the ratio of two mean rates of negative binomial distributed event numbers in two samples at given maximum sample size and effect. The power calculation is performed either for a fixed exposure time or a variable exposure time with fixed follow-up where the information over the stages is calculated according to the specified information rate in the design. Additionally, an allocation ratio = n1 / n2 can be specified where n1 and n2 are the number of subjects in the two treatment groups. A null hypothesis value thetaH0 can also be specified.

How to get help for generic functions

Click on the link of a generic in the list above to go directly to the help documentation of the rpact specific implementation of the generic. Note that you can use the R function methods to get all the methods of a generic and to identify the object specific name of it, e.g., use methods("plot") to get all the methods for the plot generic. There you can find, e.g., plot.AnalysisResults and obtain the specific help documentation linked above by typing ?plot.AnalysisResults.

See also

Other power functions: getPowerMeans(), getPowerRates(), getPowerSurvival()

Examples

if (FALSE) { # \dontrun{
# Fixed sample size trial where a therapy is assumed to decrease the 
# exacerbation rate from 1.4 to 1.05 (25% decrease) within an 
# observation period of 1 year, i.e., each subject has a equal 
# follow-up of 1 year.
# Calculate power at significance level 0.025 at given sample size = 180 
# for a range of lambda1 values if the overdispersion is assumed to be 
# equal to 0.5, is obtained by
getPowerCounts(alpha = 0.025, lambda1 = seq(1, 1.4, 0.05), lambda2 = 1.4, 
    maxNumberOfSubjects = 180, overdispersion = 0.5, fixedExposureTime = 1)

# Group sequential alpha and beta spending function design with O'Brien and 
# Fleming type boundaries: Power and test characteristics for N = 286, 
# under the assumption of a fixed exposure time, and for a range of 
# lambda1 values: 
getPowerCounts(design = getDesignGroupSequential(
        kMax = 3, alpha = 0.025, beta = 0.2, 
        typeOfDesign = "asOF", typeBetaSpending = "bsOF"), 
    lambda1 = seq(0.17, 0.23, 0.01), lambda2 = 0.3, 
    directionUpper = FALSE, overdispersion = 1, maxNumberOfSubjects = 286, 
    fixedExposureTime = 12, accrualTime = 6)

# Group sequential design alpha spending function design with O'Brien and 
# Fleming type boundaries: Power and test characteristics for N = 1976, 
# under variable exposure time with uniform recruitment over 1.25 months,
# study time (accrual + followup) = 4 (lambda1, lambda2, and overdispersion 
# as specified, no futility stopping):
getPowerCounts(design = getDesignGroupSequential(
        kMax = 3, alpha = 0.025, beta = 0.2, typeOfDesign = "asOF"),
    lambda1 = seq(0.08, 0.09, 0.0025), lambda2 = 0.125, 
    overdispersion = 5, directionUpper = FALSE, maxNumberOfSubjects = 1976, 
    followUpTime = 2.75, accrualTime = 1.25)
} # }