Get Sample Size Rates

Returns the sample size for testing rates in one or two samples.

Usage

getSampleSizeRates(
  design = NULL,
  ...,
  groups = 2L,
  normalApproximation = TRUE,
  riskRatio = FALSE,
  thetaH0 = ifelse(riskRatio, 1, 0),
  pi1 = c(0.4, 0.5, 0.6),
  pi2 = 0.2,
  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.

groups

The number of treatment groups (1 or 2), default is 2.

normalApproximation

If FALSE, the sample size for the case of one treatment group is calculated exactly using the binomial distribution, default is TRUE.

riskRatio

If TRUE, the sample size for one-sided testing of H0: pi1 / pi2 = thetaH0 is calculated, default is FALSE.

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.

pi1

A numeric value or vector that represents the assumed probability in the active treatment group if two treatment groups are considered, or the alternative probability for a one treatment group design, default is seq(0.2, 0.5, 0.1) (power calculations and simulations) or seq(0.4, 0.6, 0.1) (sample size calculations).

pi2

A numeric value that represents the assumed probability in the reference group if two treatment groups are considered, default is 0.2.

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 stage-wise and maximum sample size for testing rates. In a two treatment groups design, additionally, an allocation ratio = n1 / n2 can be specified where n1 and n2 are the number of subjects in the two treatment groups. If a null hypothesis value thetaH0 != 0 for testing the difference of two rates or thetaH0 != 1 for testing the risk ratio is specified, the sample size formula according to Farrington & Manning (Statistics in Medicine, 1990) is used. Critical bounds and stopping for futility bounds are provided at the effect scale (rate, rate difference, or rate ratio, respectively) for each sample size calculation separately. For the two-sample case, the calculation here is performed at fixed pi2 as given as argument in the function.

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: getSampleSizeCounts(), getSampleSizeMeans(), getSampleSizeSurvival()

Examples

if (FALSE) { # \dontrun{
# Calculate the stage-wise sample sizes, maximum sample sizes, and the optimum 
# allocation ratios for a range of pi1 values when testing 
# H0: pi1 - pi2 = -0.1 within a two-stage O'Brien & Fleming design;
# alpha = 0.05 one-sided, power 1 - beta = 90%:
getSampleSizeRates(getDesignGroupSequential(kMax = 2, alpha = 0.05,  
    beta = 0.1), groups = 2, thetaH0 = -0.1, pi1 = seq(0.4, 0.55, 0.025), 
    pi2 = 0.4, allocationRatioPlanned = 0)

# Calculate the stage-wise sample sizes, maximum sample sizes, and the optimum 
# allocation ratios for a range of pi1 values when testing 
# H0: pi1 / pi2 = 0.80 within a three-stage O'Brien & Fleming design;
# alpha = 0.025 one-sided, power 1 - beta = 90%:
getSampleSizeRates(getDesignGroupSequential(kMax = 3, alpha = 0.025, 
    beta = 0.1), groups = 2, riskRatio = TRUE, thetaH0 = 0.80, 
    pi1 = seq(0.3, 0.5, 0.025), pi2 = 0.3, allocationRatioPlanned = 0)
} # }