Get Sample Size Counts

Returns the sample size for testing the ratio of mean rates of negative binomial distributed event numbers in two samples at given effect.

Usage

getSampleSizeCounts(
  design = NULL,
  ...,
  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_,
  maxNumberOfSubjects = NA_integer_,
  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.

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.

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.

allocationRatioPlanned

The planned allocation ratio n1 / n2 for a two treatment groups design, default is 1. If allocationRatioPlanned = 0 is entered, the optimal allocation ratio yielding the smallest overall sample size is determined.

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 information, and stage-wise and maximum sample size for testing mean rates of negative binomial distributed event numbers in two samples at given effect. The sample size calculation is performed either for a fixed exposure time or a variable exposure time with fixed follow-up. For the variable exposure time case, at given maximum sample size the necessary follow-up time is calculated. The planned calendar time of interim stages is calculated if an accrual time is defined. 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 sample size functions: getSampleSizeMeans(), getSampleSizeRates(), getSampleSizeSurvival()

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 an equal follow-up of 1 year.
# The sample size that yields 90% power at significance level 0.025 for 
# detecting such a difference, if the overdispersion is assumed to be 
# equal to 0.5, is obtained by
getSampleSizeCounts(alpha = 0.025, beta = 0.1, lambda2 = 1.4, 
    theta = 0.75, overdispersion = 0.5, fixedExposureTime = 1)

# Noninferiority test with blinded sample size reassessment to reproduce 
# Table 2 from Friede and Schmidli (2010):
getSampleSizeCounts(alpha = 0.025, beta = 0.2, lambda = 1, theta = 1,
    thetaH0 = 1.15, overdispersion = 0.4, fixedExposureTime = 1)

# Group sequential alpha and beta spending function design with O'Brien and 
# Fleming type boundaries: Estimate observation time under uniform 
# recruitment of patients over 6 months and a fixed exposure time of 12 
# months (lambda1, lambda2, and overdispersion as specified):
getSampleSizeCounts(design = getDesignGroupSequential(
        kMax = 3, alpha = 0.025, beta = 0.2, 
        typeOfDesign = "asOF", typeBetaSpending = "bsOF"), 
    lambda1 = 0.2, lambda2 = 0.3, overdispersion = 1, 
    fixedExposureTime = 12, accrualTime = 6)

# Group sequential alpha spending function design with O'Brien and Fleming 
# type boundaries: Sample size for variable exposure time with uniform 
# recruitment over 1.25 months and study time (accrual + followup) = 4 
# (lambda1, lambda2, and overdispersion as specified, no futility stopping):
getSampleSizeCounts(design = getDesignGroupSequential(
        kMax = 3, alpha = 0.025, beta = 0.2, typeOfDesign = "asOF"),
    lambda1 = 0.0875, lambda2 = 0.125, overdispersion = 5, 
    followUpTime = 2.75, accrualTime = 1.25)
} # }