getAnalysisResults {rpact}

Get Analysis Results

Description

Calculates and returns the analysis results for the specified design and data.

Usage

getAnalysisResults(
  design,
  dataInput,
  ...,
  directionUpper = TRUE,
  thetaH0 = NA_real_,
  nPlanned = NA_real_,
  allocationRatioPlanned = 1,
  stage = NA_integer_,
  maxInformation = NULL,
  informationEpsilon = NULL
)

Arguments

design

The trial design.

dataInput

The summary data used for calculating the test results. This is either an element of DatasetMeans, of DatasetRates, or of DatasetSurvival and should be created with the function getDataset(). For more information see getDataset().

...

Further arguments to be passed to methods (cf., separate functions in "See Also" below), e.g.,

thetaH1 and stDevH1 (or assumedStDev / assumedStDevs), pi1, pi2, or piTreatments, piControl(s)

The assumed effect size, standard deviation or rates to calculate the conditional power if nPlanned is specified. For survival designs, thetaH1 refers to the hazard ratio. For one-armed trials with binary outcome, only pi1 can be specified, for two-armed trials with binary outcome, pi1 and pi2 can be specified referring to the assumed treatment and control rate, respectively. In multi-armed or enrichment designs, you can specify a value or a vector with elements referring to the treatment arms or the sub-populations, respectively. For testing rates, the parameters to be specified are piTreatments and piControl (multi-arm designs) and piTreatments and piControls (enrichment designs).
If not specified, the conditional power is calculated under the assumption of observed effect sizes, standard deviations, rates, or hazard ratios.

iterations

Iterations for simulating the power for Fisher's combination test. If the power for more than one remaining stages is to be determined for Fisher's combination test, it is estimated via simulation with specified
iterations, the default is 1000.

seed

Seed for simulating the conditional power for Fisher's combination test. See above, default is a random seed.

normalApproximation

The type of computation of the p-values. Default is FALSE for testing means (i.e., the t test is used) and TRUE for testing rates and the hazard ratio. For testing rates, if normalApproximation = FALSE is specified, the binomial test (one sample) or the exact test of Fisher (two samples) is used for calculating the p-values. In the survival setting, normalApproximation = FALSE has no effect.

equalVariances

The type of t test. For testing means in two treatment groups, either the t test assuming that the variances are equal or the t test without assuming this, i.e., the test of Welch-Satterthwaite is calculated, default is TRUE.

intersectionTest

Defines the multiple test for the intersection hypotheses in the closed system of hypotheses when testing multiple hypotheses. Five options are available in multi-arm designs: "Dunnett", "Bonferroni", "Simes", "Sidak", and "Hierarchical", default is "Dunnett". Four options are available in population enrichment designs: "SpiessensDebois" (one subset only), "Bonferroni", "Simes", and "Sidak", default is "Simes".

varianceOption

Defines the way to calculate the variance in multiple treatment arms (> 2) or population enrichment designs for testing means. For multiple arms, three options are available: "overallPooled", "pairwisePooled", and "notPooled", default is "overallPooled". For enrichment designs, the options are: "pooled", "pooledFromFull" (one subset only), and "notPooled", default is "pooled".

stratifiedAnalysis

For enrichment designs, typically a stratified analysis should be chosen. For testing means and rates, also a non-stratified analysis based on overall data can be performed. For survival data, only a stratified analysis is possible (see Brannath et al., 2009), default is TRUE.

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.

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.

nPlanned

The additional (i.e., "new" and not cumulative) sample size planned for each of the subsequent stages. The argument must be a vector with length equal to the number of remaining stages and contain the combined sample size from both treatment groups if two groups are considered. For survival outcomes, it should contain the planned number of additional events. For multi-arm designs, it is the per-comparison (combined) sample size. For enrichment designs, it is the (combined) sample size for the considered sub-population.

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.

stage

The stage number (optional). Default: total number of existing stages in the data input.

maxInformation

Positive integer value specifying the maximum information.

informationEpsilon

Positive integer value specifying the absolute information epsilon, which defines the maximum distance from the observed information to the maximum information that causes the final analysis. Updates at the final analysis in case the observed information at the final analysis is smaller ("under-running") than the planned maximum information maxInformation, default is 0. Alternatively, a floating-point number > 0 and < 1 can be specified to define a relative information epsilon.

Details

Given a design and a dataset, at given stage the function calculates the test results (effect sizes, stage-wise test statistics and p-values, overall p-values and test statistics, conditional rejection probability (CRP), conditional power, Repeated Confidence Intervals (RCIs), repeated overall p-values, and final stage p-values, median unbiased effect estimates, and final confidence intervals.

For designs with more than two treatments arms (multi-arm designs) or enrichment designs a closed combination test is performed. That is, additionally the statistics to be used in a closed testing procedure are provided.

The conditional power is calculated if the planned sample size for the subsequent stages (nPlanned) is specified. The conditional power is calculated either under the assumption of the observed effect or under the assumption of an assumed effect, that has to be specified (see above).
For testing rates in a two-armed trial, pi1 and pi2 typically refer to the rates in the treatment and the control group, respectively. This is not mandatory, however, and so pi1 and pi2 can be interchanged. In many-to-one multi-armed trials, piTreatments and piControl refer to the rates in the treatment arms and the one control arm, and so they cannot be interchanged. piTreatments and piControls in enrichment designs can principally be interchanged, but we use the plural form to indicate that the rates can be differently specified for the sub-populations.

Median unbiased effect estimates and confidence intervals are calculated if a group sequential design or an inverse normal combination test design was chosen, i.e., it is not applicable for Fisher's p-value combination test design. For the inverse normal combination test design with more than two stages, a warning informs that the validity of the confidence interval is theoretically shown only if no sample size change was performed.

A final stage p-value for Fisher's combination test is calculated only if a two-stage design was chosen. For Fisher's combination test, the conditional power for more than one remaining stages is estimated via simulation.

Final stage p-values, median unbiased effect estimates, and final confidence intervals are not calculated for multi-arm and enrichment designs.

Value

Returns an AnalysisResults 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.

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

getObservedInformationRates()

Other analysis functions: getClosedCombinationTestResults(), getClosedConditionalDunnettTestResults(), getConditionalPower(), getConditionalRejectionProbabilities(), getFinalConfidenceInterval(), getFinalPValue(), getRepeatedConfidenceIntervals(), getRepeatedPValues(), getStageResults(), getTestActions()

Examples

## Not run: 
# Example 1 One-Sample t Test
# Perform an analysis within a three-stage group sequential design with
# O'Brien & Fleming boundaries and one-sample data with a continuous outcome
# where H0: mu = 1.2 is to be tested
dsnGS <- getDesignGroupSequential()
dataMeans <- getDataset(
    n = c(30, 30),
    means = c(1.96, 1.76),
    stDevs = c(1.92, 2.01)
)
getAnalysisResults(design = dsnGS, dataInput = dataMeans, thetaH0 = 1.2)

# You can obtain the results when performing an inverse normal combination test
# with these data by using the commands
dsnIN <- getDesignInverseNormal()
getAnalysisResults(design = dsnIN, dataInput = dataMeans, thetaH0 = 1.2)

# Example 2 Use Function Approach with Time to Event Data
# Perform an analysis within a use function approach according to an
# O'Brien & Fleming type use function and survival data where
# where H0: hazard ratio = 1 is to be tested. The events were observed
# over time and maxInformation = 120, informationEpsilon = 5 specifies
# that 116 > 120 - 5 observed events defines the final analysis.
design <- getDesignGroupSequential(typeOfDesign = "asOF")
dataSurvival <- getDataset(
    cumulativeEvents = c(33, 72, 116),
    cumulativeLogRanks = c(1.33, 1.88, 1.902)
)
getAnalysisResults(design,
    dataInput = dataSurvival,
    maxInformation = 120, informationEpsilon = 5
)

# Example 3 Multi-Arm Design
# In a four-stage combination test design with O'Brien & Fleming boundaries
# at the first stage the second treatment arm was dropped. With the Bonferroni
# intersection test, the results together with the CRP, conditional power
# (assuming a total of 40 subjects for each comparison and effect sizes 0.5
# and 0.8 for treatment arm 1 and 3, respectively, and standard deviation 1.2),
# RCIs and p-values of a closed adaptive test procedure are
# obtained as follows with the given data (treatment arm 4 refers to the
# reference group; displayed with summary and plot commands):
data <- getDataset(
    n1 = c(22, 23),
    n2 = c(21, NA),
    n3 = c(20, 25),
    n4 = c(25, 27),
    means1 = c(1.63, 1.51),
    means2 = c(1.4, NA),
    means3 = c(0.91, 0.95),
    means4 = c(0.83, 0.75),
    stds1 = c(1.2, 1.4),
    stds2 = c(1.3, NA),
    stds3 = c(1.1, 1.14),
    stds4 = c(1.02, 1.18)
)
design <- getDesignInverseNormal(kMax = 4)
x <- getAnalysisResults(design,
    dataInput = data, intersectionTest = "Bonferroni",
    nPlanned = c(40, 40), thetaH1 = c(0.5, NA, 0.8), assumedStDevs = 1.2
)
summary(x)
if (require(ggplot2)) plot(x, thetaRange = c(0, 0.8))
design <- getDesignConditionalDunnett(secondStageConditioning = FALSE)
y <- getAnalysisResults(design,
    dataInput = data,
    nPlanned = 40, thetaH1 = c(0.5, NA, 0.8), assumedStDevs = 1.2, stage = 1
)
summary(y)
if (require(ggplot2)) plot(y, thetaRange = c(0, 0.4))

# Example 4 Enrichment Design
# Perform an two-stage enrichment design analysis with O'Brien & Fleming boundaries
# where one sub-population (S1) and a full population (F) are considered as primary
# analysis sets. At interim, S1 is selected for further analysis and the sample
# size is increased accordingly. With the Spiessens & Debois intersection test,
# the results of a closed adaptive test procedure together with the CRP, repeated
# RCIs and p-values are obtained as follows with the given data (displayed with
# summary and plot commands):
design <- getDesignInverseNormal(kMax = 2, typeOfDesign = "OF")
dataS1 <- getDataset(
    means1 = c(13.2, 12.8),
    means2 = c(11.1, 10.8),
    stDev1 = c(3.4, 3.3),
    stDev2 = c(2.9, 3.5),
    n1 = c(21, 42),
    n2 = c(19, 39)
)
dataNotS1 <- getDataset(
    means1 = c(11.8, NA),
    means2 = c(10.5, NA),
    stDev1 = c(3.6, NA),
    stDev2 = c(2.7, NA),
    n1 = c(15, NA),
    n2 = c(13, NA)
)
dataBoth <- getDataset(S1 = dataS1, R = dataNotS1)
x <- getAnalysisResults(design,
    dataInput = dataBoth,
    intersectionTest = "SpiessensDebois",
    varianceOption = "pooledFromFull",
    stratifiedAnalysis = TRUE
)
summary(x)
if (require(ggplot2)) plot(x, type = 2)

## End(Not run)