Randomization for Clinical Trials

Description

This tool enables the user to choose a randomization procedure based on sound scientific criteria. It comprises the generation of randomization sequences as well the assessment of randomization procedures based on carefully selected criteria. Furthermore, randomizeR provides a function for the comparison of randomization procedures.

Acknowledgement

This research is embedded in the IDeAl project, which has received funding from the European Union's Seventh Framework Programme for research, technological development and demonstration under Grant Agreement no 602552.

Author(s)

David Schindler dv.schindler@gmail.com, Diane Uschner Diane.Uschner@gmail.com, Ralf-Dieter Hilgers, Nicole Heussen, Marcia Viviane Rueckbeil marcia.rueckbeil@rwth-aachen.de

References

W. F. Rosenberger and J. M. Lachin (2002) Randomization in Clinical Trials. Wiley.

#' D. Uschner, D. Schindler, R. D. Hilgers and N. Heussen (2018). "randomizeR: An R Package for the Assessment and Implementation of Randomization in Clinical Trials." Journal of Statistical Software, 85(8), pp. 1-22. doi: 10.18637/jss.v085.i08 .

D. Schindler (2016) Assessment of Randomization Procedures in the Presence of Selection and Chronological Bias. PhD Thesis.

D. Uschner, R. D. Hilgers, N. Heussen (2018). "The impact of selection bias in randomized multi-arm parallel group clinical trials." PLOS ONE, 13(1): e0192065. doi: 10.1371/journal.pone.0192065.

M. V. Rueckbeil, R. D. Hilgers, N. Heussen (2019). "Randomization in survival studies: An evaluation method that takes into account selection and chronological bias." PLOS ONE, 14(6): e0217946. doi: 10.1371/journal.pone.0217946.

See Also

For functionality for randomization procedures, see randPar and genSeq. For the criteria for the assessment of randomization procedures, see issues. For the assessment and comparison of randomization procedures, see assess and compare.

Method defining the $ operator for the assessment class

Description

Method defining the $ operator for the assessment class

Usage

## S4 method for signature 'assessment'
x$name

Arguments

Method defining the $ operator for the assessment class

Description

Method defining the $ operator for the assessment class

Usage

## S4 method for signature 'comparison'
x$name

Arguments

Method defining the $ operator for the derFunc class

Description

Method defining the $ operator for the derFunc class

Usage

## S4 method for signature 'derFunc'
x$name

Arguments

Method defining the $ operator for the desFunc class

Description

Method defining the $ operator for the desFunc class

Usage

## S4 method for signature 'desFunc'
x$name

Arguments

Method defining the $ operator for the assessment class

Description

Method defining the $ operator for the assessment class

Usage

## S4 method for signature 'desScores'
x$name

Arguments

Method defining the $ operator for the endpoint class

Description

Method defining the $ operator for the endpoint class

Usage

## S4 method for signature 'endpoint'
x$name

Arguments

Method defining the $ operator for the evaluation class

Description

Method defining the $ operator for the evaluation class

Usage

## S4 method for signature 'evaluation'
x$name

Arguments

Method defining the $ operator for the issue class

Description

Method defining the $ operator for the issue class

Usage

## S4 method for signature 'issue'
x$name

Arguments

Method defining the $ operator for the probUnDesirable class

Description

Method defining the $ operator for the probUnDesirable class

Usage

## S4 method for signature 'probUnDesirable'
x$name

Arguments

Method defining the $ operator for the randPar class

Description

Method defining the $ operator for the randPar class

Usage

## S4 method for signature 'randPar'
x$name

Arguments

Method defining the $ operator for the randSeq class

Description

Method defining the $ operator for the randSeq class

Usage

## S4 method for signature 'randSeq'
x$name

Arguments

Calculates the Type I error for different randomization sequences from a randomization procedure for a group sequential design

Description

Calculates the Type I error for different randomization sequences from a randomization procedure for a group sequential design

Usage

GSD_allocation(
  n,
  reps,
  sfu,
  K,
  rp,
  seed = 42,
  ui = "No",
  rb = 4,
  mti = 3,
  p = 2/3
)

Arguments

Value

A list consisting of a vector of Type I errors for each randomization sequence generated from the randomization procedure and a S4 object of the class of the randomization procedure.

Examples

#Simulate a group sequential design according to O'Brien and Fleming's design with 24 patients,
#10 simulation runs,3 Stages using Random Allocation Rule as a randomization procedure.
GSD_allocation(n=24, reps=10, sfu="OF", K=3, rp="RAR")
#Simulate a group sequential design according to Lan and deMets design with a Pocock
#like alpha spending function with 18 patients, 10 simulation runs,
#3 Stages using Permuted Block Randomization with block size 4
#as a randomization procedure without updating the critical values after each stage.
library(gsDesign)
GSD_allocation(n=18, reps=10, sfu=sfLDPocock, K=3, rp="PBR", ui="no", rb=4)

Calculates the Type I error for a randomization sequence in a group sequential design

Description

Calculates the Type I error for a randomization sequence in a group sequential design

Usage

GSD_allocation_seq(sfu, K, seq, ui = "No")

Arguments

Value

A list of type I error probabilities for each stage.

Examples

#Simulate a group sequential design according to Pocock's design with 24 patients
#and the following consecutive treatment allocation:
#A, A, B, A, A, B, A, B, A, B, A, B, A, B, A, B, B, B, A, B, B, A, B, B
GSD_allocation_seq(sfu ="Pocock", K=3, seq = c(1,1,0,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,0,0))
#Simulate a group sequential design according to Lan and DeMets with O'Brien & Fleming
#like alpha spending with 24 patients and the following consecutive treatment allocation:
#A, A, B, A, A, B, A, B, A, B, A, B, A, B, A, B, B, B, A, B, B, A, B, B
library(gsDesign)
GSD_allocation_seq(sfu =sfLDOF, K=3, seq = c(1,1,0,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,0,0))

Function returning the number of trial arms slot of an S4 object

Description

Function returning the number of trial arms slot of an S4 object

Usage

K(obj)

Arguments

Value

The number of trial arms

Function returning the sample size slot of an S4 object

Description

Function returning the sample size slot of an S4 object

Usage

N(obj)

Arguments

Value

the sample size slot of an S4 object

Function returning the target value slot of an S4 object

Description

Function returning the target value slot of an S4 object

Usage

TV(obj)

Arguments

Function returning the adjusting parameter a slot of an S4 object

Description

Function returning the adjusting parameter a slot of an S4 object

Usage

a(obj)

Arguments

Value

the value of the adjusting parameter a of an S4 object

Representing Accelerated Biased Coin Design

Description

Represents the randomization procedure Accelerated Biased Coin Design.

Usage

abcdPar(N, a, groups = LETTERS[1:2])

Arguments

Details

This is a class of 'biased coins' where the probability of selecting the under-represented treatment is dependent from the absolute difference between the two treatment allocations up to the current step.

Value

S4 object of the class abcdPar.

References

A. B. Antognini and A. Giovagnoli (2004) A new 'biased coin design' for the sequential allocation of two treatments. Journal of the Royal Statistical Society. Series C (Applied Statistics) 53, No. 4, 651-664

See Also

Other randomization procedures: bbcdPar, bsdPar, chenPar, crPar, createParam(), ebcPar, gbcdPar, hadaPar, mpPar, pbrPar, rarPar, rpbrPar, rtbdPar, tbdPar, udPar

Sampling algorithm for abcd

Description

Sampling algorithm for abcd

Usage

abcdRand(N, a, K = 2)

Arguments

Value

A vector with the allocation sequence for a clinical trial. It will contain a zero (resp. 1) at position i, when patient i is allocated to treatment A (resp. B).

References

A. B. Antognini and A. Giovagnoli (2004) A new 'biased coin design' for the sequential allocation of two treatments. Journal of the Royal Statistical Society. Series C (Applied Statistics) 53, No. 4, 651-664

Creates stratified sequences Compares stratified sequences to their respective non-stratified version under the influence of bias.

Description

Creates stratified sequences Compares stratified sequences to their respective non-stratified version under the influence of bias.

Arguments

Details

Stratified and Non-stratified versions of a randomization sequence behave differently with respect to issues like selection bias, chronological bias or combined bias. The analyse function creates both versions of a sequence for each of the specified randomization procedures and analyses them in relation to the bias created according to the theta and eta values. The first argument should specify the total sample size of patients. The second argument should be one of class normEndp describing a normally distributed endpoint. The third argument should be the allocation ratio for the different strata. The fourth argument should be the number of strata in the clinical trial. The fifth and sixth arguments should be the selection bias effect eta and the time trend theta. The seventh argument should be a vector of strings representing different randomization procedures. The strings should be given as described by the getDesign function. Any additional parameters should be given after the design name of the procedure encapsulated in parenthesis.

Value

The function returns a matrix that summarizes the performance of the randomization procedures. The values for each randomization procedure represent the percentage of sequences that kept the 5

Assessing randomization sequences

Description

Assesses randomization sequences based on specified issues in clinical trials.

Usage

assess(randSeq, ..., endp)

## S4 method for signature 'randSeq,missing'
assess(randSeq, ..., endp)

## S4 method for signature 'randSeq,endpoint'
assess(randSeq, ..., endp)

Arguments

Details

Randomization sequences behave differently with respect to issues like selection bias, chronological bias, or loss in power estimation. The assess function evaluates the behavior of randomization sequences with respect to these issues. The first argument should be a result of one of the functions genSeq or getAllSeq. The second argument should be any number of issues arising in a clinical trial. The last argument endp may be provided if the assessment should take the distribution of the treatment groups into account, e.g. for power evaluation.

Value

S4 object of class assessment summarizing the assessment of the randomization procedure.

See Also

Representation of randomization procedures: randPar

Generation of randomization sequences: genSeq

issues for the assessment of randomization sequences

Examples

# assess the full set of Random Allocation Rule for N=4 patients
sequences <- getAllSeq(rarPar(4))
issue1 <- corGuess("CS")
issue2 <- corGuess("DS")
issue3 <- imbal("imb")
issue4 <- imbal("maxImb")
assess(sequences, issue1, issue2, issue3, issue4)

# assess one sequence of the Big Stick Design with respect to correct guesses
sequence <- genSeq(bsdPar(10, 2), seed = 1909)
assess(sequence, issue1)

# assess the same sequence with respect to selection bias and power for a normal endpoint
endp <- normEndp(c(2, 2), c(1, 1))
issue5 <- selBias("CS", 4, "exact")
issue6 <- setPower(2, "exact")
assess(sequence, issue1, issue5, issue6, endp = endp)

# assess the same sequence with respect to selection bias for an exponential endpoint
endp <- expEndp(lambda = c(0.5, 0.5), cenRate=0.1, accrualTime=1, cenTime=5)
issue7 <- selBias("CS", 0.1, "exact")
assess(sequence, issue1, issue7, endp = endp)

# recommended plot for the assessment of rejection probabilities
RP <- getAllSeq(crPar(6))
cB <- chronBias(type = "linT", theta = 1/6, method = "exact")
sB <- selBias(type=  "CS", eta = 1/4, method = "exact")
normEndp <- normEndp(c(0, 0), c(1, 1))
A <- assess(RP, cB, sB, endp = normEndp)
D <- A$D
desiredSeq <- round(sum(D[,2][D[,3] <= 0.05 & D[,4] <= 0.05]), digits = 4)
colnames(D) <- c("Seq", "Prob", "SB", "linT")
g <- ggplot(D, aes(x = SB, y = linT))
g <- g + annotate("rect", xmin = 0, xmax = 0.05, ymin = 0, ymax = 0.05,
alpha=0.2, fill="green") 
g <- g + geom_point(alpha = 1/10, size = 3, col = "orange")
g <- g <- g + geom_vline(xintercept = 0.05, col = "red")
g <- g + geom_hline(yintercept = 0.05, col = "red")
g  <- g + geom_text(data = NULL, x = 0, y = 0,
label = paste("Proportion:", desiredSeq), hjust=0, vjust=0, size = 7)
g

Representing Bayesian Biased Coin Design

Description

Represents the randomization procedure Bayesian Biased Coin Design.

Usage

bbcdPar(N, a, groups = LETTERS[1:2])

Arguments

Details

Extension of Efron's biased coin design.

Value

S4 object of the class bbcdPar.

References

A. B. Antognini and Maroussa Zagoraiou (2014) Balance and randomness in sequential clinical trials: the dominant biased coin design. Pharmaceutical Statistics 13(2), 119-127

See Also

Other randomization procedures: abcdPar, bsdPar, chenPar, crPar, createParam(), ebcPar, gbcdPar, hadaPar, mpPar, pbrPar, rarPar, rpbrPar, rtbdPar, tbdPar, udPar

Sampling algorithm for bbcd

Description

Sampling algorithm for bbcd

Usage

bbcdRand(N, a, K = 2)

Arguments

Value

A vector with the allocation sequence for a clinical trial. It will contain a zero (resp. 1) at position i, when patient i is allocated to treatment A (resp. B).

References

A. B. Antognini and Maroussa Zagoraiou (2014) Balance and randomness in sequential clinical trials: the dominant biased coin design. Pharmaceutical Statistics 13(2), 119-127

Function returning the block slot of an S4 object

Description

Function returning the block slot of an S4 object

Usage

blocks(obj)

Arguments

Value

a vector with the lenghts of each block of a pbrPar object

Representing Big Stick Design

Description

Represents the randomization procedure Big Stick Design.

Usage

bsdPar(N, mti, groups = LETTERS[1:2])

Arguments

Details

Tossing a fair coin as long as the difference in group sizes does not exceed the mti. If the mti is reached a deterministic allocation is done, so that the difference in group sizes is reduced.

Value

S4 object of the class bsdPar.

References

J. F. Soares and C. F. Jeff Wu (1983) Some Restricted Randomization Rules in Sequential Designs. Comm. in Stat., 12, 2017-34.

See Also

Other randomization procedures: abcdPar, bbcdPar, chenPar, crPar, createParam(), ebcPar, gbcdPar, hadaPar, mpPar, pbrPar, rarPar, rpbrPar, rtbdPar, tbdPar, udPar

Sampling algorithm for BSD

Description

Sampling algorithm for BSD

Usage

bsdRand(N, mti, K = 2)

Arguments

Value

A vector with the allocation sequence for a clinical trial. It will contain a zero (resp. 1) at position i, when patient i is allocated to treatment A (resp. B).

References

J. F. Soares and C. F. Jeff Wu (1983) Some Restricted Randomization Rules in Sequential Designs. Comm. in Stat., 12, 2017-34.

Representing Chen's Design

Description

Represents the randomization procedure Chen's Design.

Usage

chenPar(N, mti = N, p = 0.5, groups = LETTERS[1:2])

Arguments

Details

Flip a biased coin with probability p in favor of the treatment which is allocated less frequently as long as the difference in group sizes does not exceed the mti. If the mti is reached a deterministic allocation is done, so that the difference in group sizes is reduced. If both treatments have been assigned equally often a fair coin is tossed.

Value

S4 object of the class chenPar.

References

Chen Yung-Pin (1999) Biased coin design with imbalance tolerance. Comm. in Stat., 15, 953-975.

See Also

Other randomization procedures: abcdPar, bbcdPar, bsdPar, crPar, createParam(), ebcPar, gbcdPar, hadaPar, mpPar, pbrPar, rarPar, rpbrPar, rtbdPar, tbdPar, udPar

Representing Chen's Design

Description

Representing Chen's Design

Usage

chenRand(N, mti, p, K = 2)

Arguments

Value

A vector with the allocation sequence for a clinical trial. It will contain a zero (resp. 1) at position i, when patient i is allocated to treatment A (resp. B).

References

Chen Yung-Pin (1999) Biased coin design with imbalance tolerance. Comm. in Stat., 15, 953-975.

Representing chronological bias

Description

Represents the issue of chronological bias in a clinical trial.

Usage

chronBias(type, theta, method, saltus, alpha = 0.05)

Arguments

Details

Chronological bias can be an issue in the design of a clinical trial. The chronBias function is a constructor function for an S4 object of the class chronBias representing the issue of chronological bias, s.a. time trends, in a clinical trial. It supports two possible modes, method="sim" and method="exact", and three different types of trend.

If method="sim", the object represents the simulated type-I-error rate given the level alpha, the selection effect eta and the biasing strategy type. When calling assess for a chronBias object with method="sim", one test decision is computed for each sequence of randSeq. The type-I-error rate (power) is the proportion of falsely (correctly) rejected null hypotheses.

If method="exact", the object represents the exact type-I-error probability given the level alpha, the selection effect eta and the biasing strategy type. When calling assess for a chronBias object with method="exact", the p-value of each randomization sequence is computed. For normal endpoints and two treatment groups these p-values are exact values which can be calculated from the sum of the corresponding quantiles of the doubly noncentral t-distribution. For more than two treatment groups, exact p-values are computed using a doubly noncentral F distribution. For exponential endpoints the p-values are obtained using an approximation formula.

Types of chronological bias

type = "linT"

Represents linear time trend. Linear time trend means that the time trend function of the patients, i.e. expected response for normal endpoints, increases evenly by theta/(N-1) with every patient included in the study, until reaching theta after N patients. Linear time trend may occur as a result of gradually relaxing in- or exclusion criteria throughout the trial. It can be represented by the formula:

f(i) = (i-1)/(N-1) \theta

type = "logT"

Represents logarithmic time trend. Logarithmic time trend means that the time trend function of the patients, i.e. expected response for normal endpoints, increases logarithmically in the patient index by theta/log(N) with every patient included in the study, until reaching theta after N patients. Logarithmic time trend may occur as a result of a learning curve, i.e. in a surgical trial. It can be represented by the formula:

\log(i)/\log(N) \theta

type = "stepT"

Represents step trend. Step trend means that the expected response of the patients increases by theta after a given point ("saltus") in the allocation process. Step trend may occur if a new device is used after the point c = "saltus", or if the medical personal changes after this point. Step time trend can be represented by the formula:

f(i) = 1_{c < i \leq N} \theta

Value

S4 object of class chronBias, a formal representation of the issue of chronological bias in a clinical trial.

References

G. K. Rosenkranz (2011) The impact of randomization on the analysis of clinical trials. Statistics in Medicine, 30, 3475-87.

M. Tamm and R.-D. Hilgers (2014) Chronological bias in randomized clinical trials under different types of unobserved time trends. Methods of Information in Medicine, 53, 501-10.

See Also

Other issues: combineBias(), corGuess, imbal, issue, selBias, setPower()

Examples

# create a linear time trend with theta = 0.5 for which the exact rejection probabilities
# are calculated
cbias <- chronBias("linT", 0.5, "exact")

# create a stepwise time trend with theta = 1 after 10 allocations for which the test
# decision is simulated
cbias <- chronBias("stepT", 1, "sim", 10)

Function returning the coin slot of an S4 object

Description

Function returning the coin slot of an S4 object

Usage

coin(obj)

Arguments

Value

The success probability of the biased coin

Combined bias criterion

Description

This class combines a selBias object and a chronBias object to a new object. In the analysis within the new object the two types of bias are treated as additive effect for normal endpoints and as multiplicative effect for exponential endpoints.

Usage

combineBias(selBias, chronBias)

Arguments

Value

A combined bias object that combines a selBias and a chronBias object

See Also

Other issues: chronBias, corGuess, imbal, issue, selBias, setPower()

Examples

chronBias <- chronBias(type="linT", theta=1, method="sim")
selBias <- selBias(type="CS", eta=1, method="sim")
combineBias(selBias, chronBias)

Comparison of randomization procedures

Description

Compares randomization procedures based on a specified issue in clinical trials.

Usage

compare(issue, ..., endp)

## S4 method for signature 'issue,missing'
compare(issue, ..., endp)

## S4 method for signature 'issue,endpoint'
compare(issue, ..., endp)

Arguments

Details

Randomization procedures behave differently with respect to issues like selection bias, chronological bias, or loss in power estimation. The compare function evaluates the behavior of randomization procedures with respect to one issue. Its first argument should represent one of the implemented issues. The second argument should be any number of objects of the class randSeq. These objects represent the randomization procedures for the planned comparison. The last argument endp may be provided if the assessment should take the distribution of the treatment groups into account, e.g. for power evaluation.

Value

S4 object of class comparison summarizing the comparison of the randomization procedures.

See Also

Representation of randomization procedures: randPar

Generation of randomization sequences: genSeq

issues for the assessment of randomization sequences

Examples

# compare Random Allocation Rule and Big Stick for N = 4 with respect to
# correct guesses
RAR <- getAllSeq(rarPar(4))
BSD <- getAllSeq(bsdPar(4, mti = 2))
corGuess <- corGuess("CS")
(comp <- compare(corGuess, RAR, BSD))
plot(comp)

# compare the same procedures with respect to selection bias for a normal endpoint
endp <- normEndp(c(2, 2), c(1, 1))
selBias <- selBias("CS", 4, "exact")
(comp <- compare(selBias, RAR, BSD, endp = endp))
plot(comp)

# compare the same procedures with respect to selection bias for an exponential endpoint
endp <- expEndp(lambda = c(0.5, 0.5), cenRate=0.1, accrualTime=1, cenTime=5)
selBias <- selBias("CS", 0.1, "exact")
(comp <- compare(selBias, RAR, BSD, endp = endp))
plot(comp)

Representing the expected number of correct guesses

Description

Represents the expected number of correct guesses of randomization sequences.

Usage

corGuess(type)

Arguments

Details

Selection bias can be an issue in the design of a clinical trial. The expected number of correct guesses is one measure for selection bias. The corGuess function is a constructor function for an S4 object of the class corGuess representing the issue of correct guesses in a clinical trial. The parameter type takes the following values:

"CS"

refers to "convergence strategy", i.e. the investigator predicts the treatment which has hitherto occurred less often.

"DS"

refers to "divergence strategy", i.e. the investigator predicts the treatment which has hitherto occurred more often.

Value

S4 object of class corGuess, a formal representation of the issue of correct guesses in a clinical trial.

References

D. Blackwell and J.L. Hodges Jr. (1957) Design for the control of selection bias. Annals of Mathematical Statistics, 25, 449-60.

See Also

Other issues: chronBias, combineBias(), imbal, issue, selBias, setPower()

Representing Complete Randomization

Description

Represents the randomization procedure Complete Randomization.

Usage

crPar(N, K = 2, ratio = rep(1, K), groups = LETTERS[1:K])

Arguments

Details

Toss a fair coin N times in case K=2 and assign the treatments according to the result of the coin. In case of K>2, replace the coin by a die with K sides.

Value

S4 object of the class crPar.

References

W. F. Rosenberger and J. M. Lachin (2002) Randomization in Clinical Trials. Wiley.

See Also

Other randomization procedures: abcdPar, bbcdPar, bsdPar, chenPar, createParam(), ebcPar, gbcdPar, hadaPar, mpPar, pbrPar, rarPar, rpbrPar, rtbdPar, tbdPar, udPar

Representing any randomization procedure

Description

Represents any randomization procedure for a two-armed clinical trial.

Usage

createParam(method, N, mti, bc, rb, p, ini, add, filledBlock)

Arguments

Details

Depending on the input of the user, createParam creates an object representing a randomization procedures for a two-armed clinical trial (see also randPar).

Value

S4object of the corresponding randomization procedure class.

See Also

Other randomization procedures: abcdPar, bbcdPar, bsdPar, chenPar, crPar, ebcPar, gbcdPar, hadaPar, mpPar, pbrPar, rarPar, rpbrPar, rtbdPar, tbdPar, udPar

Query to create a randomization sequence of a particular randomization procedure

Description

This function is a query to create an corresponding randomization sequence for a two-armed clinical trial. If file is defined, the generated sequence is automatically saved to the corresponding path.

Usage

createSeq(file)

Arguments

Value

an object Param, which is available

Representing Derringer-Suich desirability functions

Description

Represents the Derringer-Suich desirability approach.

Usage

derFunc(TV, SLs, b)

Arguments

Details

derFunc represents the framework for left, right and two-sided desirability functions introduced by Derringer and Suich (1980). For all three different kinds of desirability functions the parameter TV must be specified. If the parameter SLs has length 1, either the left- or right-sided desirability function is created depending from whether the value is smaller (left-sided) or greater (right-sided) than the target value. By specifying SLs as a vector of length 2 a two-sided desirability function is created where the lower specified border is determined as the smaller value of SLs and thus the upper specified border is determined as the greater value. If there are no values specified for the weights, then they are automatically set to 1 (linear loss).

Value

S4 object of class derFunc, a formal representation of desirability functions introduced by Derringer and Suich.

References

Derringer, G., and Suich, R., (1980) Simultaneous Optimization of Several Response Variables. Journal of Quality Technology, 12, 214-219.

See Also

Other desirability topics: evaluate(), getDesScores(), plotDes(), plotEv(), probUnDes()

Examples

# create an object of a left-sided desirability function
dLeft <- derFunc(0.5, 0.3, 2)

# create an object of a right-sided desirability function
dRight <- derFunc(0.5, 0.8, 1)

# create an object of a two-sided desirability function
dLR <- derFunc(0.5, c(0.3, 0.9), c(3, 1))

Desirability functions within the scope of clinical trials

Description

Illustrates the interplay between functions related to desirability indices.

Details

Currently, randomizeR encompasses the class of desirability functions introduced by Derringer and Suich (1980) and corresponding functions to evaluate and compare randomization sequences which have been assessed on the basis of desirability indices of specific issues:

• derFunc represents the class of desirability functions according to Derringer-Suich (1980).

• getDesScores can be applied to an object of class assessment together with prespecified desirability functions to compare the behavior of randomization sequences (on a common scale \[0,1\]).

• plotDes plots a desScores object on a radar chart.

• evaluate performs a comparison of sequences from different randomization sequences on the basis of object of the class desScores.

• plotEv plots an evaluation object on a radar chart.

• probUnDes computes the probability of undesired randomization sequences with respect to certain issues and desirability functions.

Examples

# perform a comparison of randomization sequences from different randomization procedures 
# with the help of desirability functions

issue1 <- corGuess("CS")
issue2 <- chronBias(type = "linT", theta = 1/4, method = "exact")
RAR <- getAllSeq(rarPar(4))
BSD <- getAllSeq(bsdPar(4, mti = 2))
A1 <- assess(RAR, issue1, issue2, endp = normEndp(c(0,0), c(1,1)))
A2 <- assess(BSD, issue1, issue2, endp = normEndp(c(0,0), c(1,1)))

d1 <- derFunc(TV = 0.5, 0.75, 2)
d2 <- derFunc(0.05, c(0, 0.1), c(1, 1))

# apply the getDesScores function to the assessment output with the specified desirability
# functions to evaluate the behaviour of randomization sequences on a [0,1] scale

DesScore <- getDesScores(A1, d1, d2, weights = c(5/6, 1/6))
DesScore2 <- getDesScores(A2, d1, d2, weights = c(5/6, 1/6))

# plotting the desScores objects
plotDes(DesScore, quantiles = TRUE)
plotDes(DesScore2, quantiles = TRUE)

# summarize the results of getDesScore with respect to the statistic "mean"
evaluate(DesScore, DesScore2)

# plot the evaluation objects for a visualized comparison
plotEv(evaluate(DesScore, DesScore2))

# display which randomzation procedure produces more undesired randomization sequences 
# with respect to certain issues and desirability functions
probUnDes(DesScore)
probUnDes(DesScore2)

Distribution function of the non central F-distribution

Description

Distribution function of the non central F-distribution

Usage

doublyF_opt(x, df1, df2, lambda1, lambda2, acc = 100, ex = 5)

Arguments

Value

Probability of observing a value larger than x

Rejection probability for one sequence in the presence of selection bias

Description

Rejection probability for one sequence in the presence of selection bias

Usage

doublyF_value(R, bias, endp)

Arguments

Value

data frame containing the non centrality parameters, the degrees of freedom, the 1-alpha quantile corresponding to the central f distribution and a numeric value for probability of false rejection of the null hypothesis of no difference in the presence of selection bias.

Rejection probability in case of selection bias in multi-arm trials

Description

calculates the non-centrality parameters of the F-distribution under third order selection bias.

Usage

doublyF_values(randSeq, bias, endp)

Arguments

Value

data frame with the sequences and their corresponding ncps and rejection probabilities.

Approximation of the distribution function of the doubly noncentral t-distribution

Description

Computes the value of the distribution function of the doubly noncentral t-distribution at x.

Usage

doublyT(x, df, lambda1, lambda2, lb = 0, ub)

Arguments

Value

Distribution value of the doubly noncentral t-distribution at x.

Calculation of the biased type-one-error probability (resp. power) of Student's t-test

Description

Computes the biased type-one-error probability (resp. power) of Student's t-test due to shifts in the expectation vectors in both treatment groups.

Usage

doublyTValues(randSeq, bias, endp)

Arguments

Value

the biased type-one-error probability (resp. power) of all randomization sequences.

Representing Efron's Biased Coin Design

Description

Represents the randomization procedure Efron's Biased Coin Design.

Usage

ebcPar(N, p, groups = LETTERS[1:2])

Arguments

Details

Flip a biased coin with probability p in favor of the treatment which is allocated less frequently. If both treatments have been assigned equally often a fair coin is tossed.

Value

S4 object of the class ebcPar.

References

B. Efron (1971) Forcing a sequential experiment to be balanced. Biometrika, 58, 403-17.

See Also

Other randomization procedures: abcdPar, bbcdPar, bsdPar, chenPar, crPar, createParam(), gbcdPar, hadaPar, mpPar, pbrPar, rarPar, rpbrPar, rtbdPar, tbdPar, udPar

Evaluation of several randomization procedures with respect to certain desirability functions applied to specified issues.

Description

Evaluation of several randomization procedures with respect to certain desirability functions applied to specified issues.

Usage

evaluate(..., statistic)

## S4 method for signature 'missing'
evaluate(..., statistic)

## S4 method for signature 'character'
evaluate(..., statistic)

Arguments

Details

The evaluate function allows the user to compare and evaluate different randomization procedures. It expects a number of objects that result when applying the getDesScores function to an assess object and specified desirability functions. The evaluate function summarizes the desirability scores of each randomization procedure on the basis of a prespecified statistic and incorporates them into a data frame. If no statistic is specified then it is automatically set to mean. If the function is applied to only one object it corresponds simply to summary(getDesScores(...)).

Value

S4 object of class evaluation Comparison of randomization procedures with respect to desirability functions applied to specified issues, summarized by a prespecified statistic.

References

D. Schindler Assessment of Randomization Procedures in the Presence of Selection and Chronological Bias. PhD Thesis.

See Also

Representation of randomization procedures: randPar

Generation of randomization sequences: genSeq

issues for the desirability of randomization sequences

Other desirability topics: derFunc, getDesScores(), plotDes(), plotEv(), probUnDes()

Examples

# compare Random Allocation Rule to Big Stick Design with respect to different issues
# and their corresponding desirability functions
issue1 <- corGuess("CS")
issue2 <- corGuess("DS")
RAR <- getAllSeq(rarPar(4))
BSD <- getAllSeq(bsdPar(4, mti = 2))
A1 <- assess(RAR, issue1, issue2)
A2 <- assess(BSD, issue1, issue2)

d1 <- derFunc(TV = 0.1, 0.7, 2)
d2 <- derFunc(0.5, c(0.3, 0.8), c(1, 1))
DesScore <- getDesScores(A1, d1, d2, weights = c(5/6, 1/6))
DesScore2 <- getDesScores(A2, d1, d2, weights = c(5/6, 1/6))

evaluate(DesScore, DesScore2)
evaluate(DesScore, DesScore2, statistic = "max")

Representation of exponentially distributed endpoints

Description

Represents exponentially distributed endpoints in clinical trials.

Usage

expEndp(lambda, cenRate, accrualTime = 0, cenTime)

Arguments

Details

The expEnd function is a constructor function for an S4 object of the class expEnd representing an exponentially distributed endpoint in a clinical trial. In conjunction with the assess function, exponential endpoints admit the calculation of the 'exact' type-I-error probability and power using an approximation formula.

Value

A S4 object representing an exponentially distributed endpoint in a clinical trial.

See Also

Compute exact or simulated type-I-error: assess.

Other endpoint types: normEndp, survEndp

Examples

# set the parameters of two exponentially distributed endpoints
endp <- expEndp(lambda = c(1, 2), cenTime = 10, cenRate = 0.01)

Representing Generalized Biased Coin Design

Description

Represents the randomization procedure Generalized Biased Coin Design.

Usage

gbcdPar(N, rho, groups = LETTERS[1:2])

Arguments

Details

Generalization of Wei's urn and Efron's biased coin design.

Value

S4 object of the class gbcdPar.

References

R. L. Smith (1984) Sequential treatment allocation using biased coin designs. Journal of the Royal Statistical Society B, 46, 519-543.
W. F. Rosenberger and J. M. Lachin (2002) Randomization in Clinical Trials. Wiley, 64-65

See Also

Other randomization procedures: abcdPar, bbcdPar, bsdPar, chenPar, crPar, createParam(), ebcPar, hadaPar, mpPar, pbrPar, rarPar, rpbrPar, rtbdPar, tbdPar, udPar

Sampling algorithm for gbcd

Description

Sampling algorithm for gbcd

Usage

gbcdRand(N, rho, K = 2)

Arguments

Value

A vector with the allocation sequence for a clinical trial. It will contain a zero (resp. 1) at position i, when patient i is allocated to treatment A (resp. B).

References

R. L. Smith (1984) Sequential treatment allocation using biased coin designs. Journal of the Royal Statistical Society B, 46, 519-543.
W. F. Rosenberger and J. M. Lachin (2002) Randomization in Clinical Trials. Wiley, 64-65

Calculation of the NCPs of each randomization sequence for the doubly noncentral t-distribution

Description

Computes the noncentrality parameters delta and lambda for the doubly noncentral t-distribution of each randomization sequence.

Usage

genNcps(randSeq, bias, endp)

Arguments

Value

matrix containing the noncentrality parameters delta and lambda of all randomization sequences.

Calculation of the NCPs of each randomization sequence for the doubly noncentral t-distribution

Description

Computes the noncentrality parameters delta and lambda for the doubly noncentral t-distribution of each randomization sequence.

Usage

genNcps_new(randSeq, bias, endp, weight = FALSE)

Arguments

Value

a list containing the noncentrality parameters delta and lambda of all randomization sequences.

Complete set of randomization sequences

Description

Computes all randomization sequences for the given randomization procedure, and stores them in an object along with the parameters belonging to the randomization procedure.

Usage

getAllSeq(obj)

## S4 method for signature 'pbrPar'
getAllSeq(obj)

## S4 method for signature 'rarPar'
getAllSeq(obj)

## S4 method for signature 'abcdPar'
getAllSeq(obj)

## S4 method for signature 'bbcdPar'
getAllSeq(obj)

## S4 method for signature 'ebcPar'
getAllSeq(obj)

## S4 method for signature 'bsdPar'
getAllSeq(obj)

## S4 method for signature 'chenPar'
getAllSeq(obj)

## S4 method for signature 'crPar'
getAllSeq(obj)

## S4 method for signature 'gbcdPar'
getAllSeq(obj)

## S4 method for signature 'hadaPar'
getAllSeq(obj)

## S4 method for signature 'mpPar'
getAllSeq(obj)

## S4 method for signature 'tbdPar'
getAllSeq(obj)

## S4 method for signature 'udPar'
getAllSeq(obj)

Arguments

Details

getAllSeq is a generic function which dispatches different methods depending on the type of input. The set of sequences of a procedure is computed by enumerating all possible sequences and eliminating those that are not possible in the randomization procedure specified by obj. The parameters of the randomization procedure are saved along with the sequences to ensure reproducibility of the results.

Value

An object inheriting from randSeq, representing the set of randomization sequences for the given parameters. The output consists of the parameters used for the generation of the randomization sequences (see createParam) and the matrix M that stores the randomization sequences in its rows.

See Also

createParam

Examples

# all randomization sequences of Efron's Biased Coin Design with p = 0.667 for N = 6
myPar <- ebcPar(6, 0.667)
getAllSeq(myPar)

# all randomization sequences of Big Stick Design with mti = 2 for N = 6
myPar <- bsdPar(6, 2)
getAllSeq(myPar)

# all randomization sequences of Permuted Block Randomization with block sizes 4 and 2
myPar <- pbrPar(c(4, 2))
getAllSeq(myPar)

Generate random sequences

Description

Generates randomization sequences from a given randomization procedure.

Usage

genSeq(obj, r, seed)

## S4 method for signature 'pbrPar,missing,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'pbrPar,numeric,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'pbrPar,missing,missing'
genSeq(obj, r, seed)

## S4 method for signature 'pbrPar,numeric,missing'
genSeq(obj, r, seed)

## S4 method for signature 'rarPar,numeric,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'rarPar,missing,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'rarPar,numeric,missing'
genSeq(obj, r, seed)

## S4 method for signature 'rarPar,missing,missing'
genSeq(obj, r, seed)

## S4 method for signature 'abcdPar,numeric,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'abcdPar,numeric,missing'
genSeq(obj, r, seed)

## S4 method for signature 'abcdPar,missing,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'abcdPar,missing,missing'
genSeq(obj, r, seed)

## S4 method for signature 'bbcdPar,numeric,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'bbcdPar,numeric,missing'
genSeq(obj, r, seed)

## S4 method for signature 'bbcdPar,missing,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'bbcdPar,missing,missing'
genSeq(obj, r, seed)

## S4 method for signature 'ebcPar,numeric,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'ebcPar,missing,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'ebcPar,numeric,missing'
genSeq(obj, r, seed)

## S4 method for signature 'ebcPar,missing,missing'
genSeq(obj, r, seed)

## S4 method for signature 'bsdPar,numeric,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'bsdPar,numeric,missing'
genSeq(obj, r, seed)

## S4 method for signature 'bsdPar,missing,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'bsdPar,missing,missing'
genSeq(obj, r, seed)

## S4 method for signature 'chenPar,numeric,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'chenPar,numeric,missing'
genSeq(obj, r, seed)

## S4 method for signature 'chenPar,missing,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'chenPar,missing,missing'
genSeq(obj, r, seed)

## S4 method for signature 'crPar,numeric,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'crPar,missing,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'crPar,numeric,missing'
genSeq(obj, r, seed)

## S4 method for signature 'crPar,missing,missing'
genSeq(obj, r, seed)

## S4 method for signature 'gbcdPar,numeric,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'gbcdPar,numeric,missing'
genSeq(obj, r, seed)

## S4 method for signature 'gbcdPar,missing,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'gbcdPar,missing,missing'
genSeq(obj, r, seed)

## S4 method for signature 'hadaPar,numeric,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'hadaPar,missing,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'hadaPar,numeric,missing'
genSeq(obj, r, seed)

## S4 method for signature 'hadaPar,missing,missing'
genSeq(obj, r, seed)

## S4 method for signature 'mpPar,numeric,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'mpPar,missing,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'mpPar,numeric,missing'
genSeq(obj, r, seed)

## S4 method for signature 'mpPar,missing,missing'
genSeq(obj, r, seed)

## S4 method for signature 'rpbrPar,missing,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'rpbrPar,numeric,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'rpbrPar,missing,missing'
genSeq(obj, r, seed)

## S4 method for signature 'rpbrPar,numeric,missing'
genSeq(obj, r, seed)

## S4 method for signature 'tbdPar,numeric,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'tbdPar,missing,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'tbdPar,numeric,missing'
genSeq(obj, r, seed)

## S4 method for signature 'tbdPar,missing,missing'
genSeq(obj, r, seed)

## S4 method for signature 'rtbdPar,numeric,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'rtbdPar,missing,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'rtbdPar,numeric,missing'
genSeq(obj, r, seed)

## S4 method for signature 'rtbdPar,missing,missing'
genSeq(obj, r, seed)

## S4 method for signature 'udPar,numeric,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'udPar,missing,numeric'
genSeq(obj, r, seed)

## S4 method for signature 'udPar,numeric,missing'
genSeq(obj, r, seed)

## S4 method for signature 'udPar,missing,missing'
genSeq(obj, r, seed)

Arguments

Details

genSeq generates randomization sequences for a randomization procedure as defined by the input parameters. genSeq has two modes, according to the input.

1. genSeq(obj,r): gives r random sequences from the design specified by obj, along with the parameters stored in obj.

2. genSeq(obj): gives one random sequences from the design specified by obj, along with the parameters stored in obj.

The sequences are generated by using the Monte-Carlo sampling technique to sample from the true distribution of the sequences according to the randomization procedure specified by obj. The parameters of the randomization procedure are saved along with the sequences to ensure reproducibility of the results.

Value

An object inheriting from randSeq, representing the r randomization sequences generated at random for the specified randomization procedure. The output consists of the parameters used for the generation of the randomization sequences (see createParam) and the matrix M that stores the randomization sequences in its r rows. If r is missing, one sequence is generated by default.

Examples

# generate randomization sequences using Complete Randomization for N = 10
myPar <- crPar(10)
genSeq(myPar, 4)
genSeq(myPar)

# generate randomization sequences using the Random Allocation Rule for N = 10
myPar <- rarPar(10)
genSeq(myPar, 4)
genSeq(myPar)

# generate randomization sequences using the Maximal Procedure with mti = 2 and N = 10
myPar <- mpPar(10, 2)
genSeq(myPar, 4)
genSeq(myPar)

Matrix of the guesses of the investigator

Description

Calculates the guesses of the investigator of a randomization list following the specified guessing strategy.

Usage

getCorGuesses(randSeq, guessing)

Arguments

Value

Matrix of the guesses of the investigator following the specified guessing strategy. No guess is abbreviated with "nG".

Examples

myPar <- bsdPar(10, 2)
M <- genSeq(myPar, 2)
type <- corGuess("CS")
getCorGuesses(M, type)

Type of Desirability function

Description

Generates a character vector which specifies the used desirability function and its parameters

Usage

getDesFunc(obj)

## S4 method for signature 'derringerLs'
getDesFunc(obj)

## S4 method for signature 'derringerRs'
getDesFunc(obj)

## S4 method for signature 'derringerTs'
getDesFunc(obj)

Arguments

Value

A character vector which specifies the used desirability function and its parameters

Applying desirability functions on issues of individual randomization sequences

Description

Applying desirability function on issues of individual randomization sequences.

Usage

getDesScores(assess, ..., weights)

## S4 method for signature 'assessment,missing'
getDesScores(assess, ..., weights)

## S4 method for signature 'assessment,numeric'
getDesScores(assess, ..., weights)

Arguments

Details

Randomization sequences behave differently with respect to issues like selection bias, chronological bias, or loss in power estimation. The getDesScores function evaluates the behavior of randomization sequences with respect to these issues. The difference to the assess function is that it scales them to \[0,1\] and makes them easier interpretable. The first argument should be a result of the assess function. The second argument should be any number of derFunc objects that represent the desirability functions. The last argument weights may be provided if the desirability functions should be weighted differently.

Value

S4 object of class desirability summarizing the desirability of the randomization procedure.

See Also

Representation of randomization procedures: randPar

Generation of randomization sequences: genSeq

issues for the desirability of randomization sequences

Other desirability topics: derFunc, evaluate(), plotDes(), plotEv(), probUnDes()

Examples

# compute the desire-function for the full set of Random Allocation Rule for N = 4
sequences <- getAllSeq(rarPar(4))
issue1 <- corGuess("CS")
issue2 <- chronBias("linT", 0.25, "exact")
endp <- normEndp(mu = c(0,0), sigma = c(1,1))
A <- assess(sequences, issue1, issue2, endp = endp)
d1 <- derFunc(0.5, 0.75, 1)
d2 <- derFunc(0.05, 0.1, 1)

D1 <- getDesScores(A, d1, d2)
summary(D1)

D2 <- getDesScores(A, d1, d2, weights = c(3/4, 1/4))
summary(D2)

Design of a randomization procedure

Description

Generates a character vector which specifies the used randomization method

Usage

getDesign(obj)

## S4 method for signature 'pbrPar'
getDesign(obj)

## S4 method for signature 'rarPar'
getDesign(obj)

## S4 method for signature 'rarSeq'
getDesign(obj)

## S4 method for signature 'abcdPar'
getDesign(obj)

## S4 method for signature 'abcdSeq'
getDesign(obj)

## S4 method for signature 'bbcdPar'
getDesign(obj)

## S4 method for signature 'bbcdSeq'
getDesign(obj)

## S4 method for signature 'ebcPar'
getDesign(obj)

## S4 method for signature 'bsdPar'
getDesign(obj)

## S4 method for signature 'bsdSeq'
getDesign(obj)

## S4 method for signature 'chenPar'
getDesign(obj)

## S4 method for signature 'chenSeq'
getDesign(obj)

## S4 method for signature 'crPar'
getDesign(obj)

## S4 method for signature 'crSeq'
getDesign(obj)

## S4 method for signature 'ebcSeq'
getDesign(obj)

## S4 method for signature 'gbcdPar'
getDesign(obj)

## S4 method for signature 'gbcdSeq'
getDesign(obj)

## S4 method for signature 'hadaPar'
getDesign(obj)

## S4 method for signature 'hadaSeq'
getDesign(obj)

## S4 method for signature 'mpPar'
getDesign(obj)

## S4 method for signature 'mpSeq'
getDesign(obj)

## S4 method for signature 'pbrSeq'
getDesign(obj)

## S4 method for signature 'rRtbdSeq'
getDesign(obj)

## S4 method for signature 'rRpbrSeq'
getDesign(obj)

## S4 method for signature 'rpbrPar'
getDesign(obj)

## S4 method for signature 'tbdPar'
getDesign(obj)

## S4 method for signature 'rtbdPar'
getDesign(obj)

## S4 method for signature 'tbdSeq'
getDesign(obj)

## S4 method for signature 'udPar'
getDesign(obj)

## S4 method for signature 'udSeq'
getDesign(obj)

Arguments

Value

the name of the randomization procedure used

Get distribution parameters of a randomization list

Description

Generates a matrix of the distribution parameters of the included patients in the clinical trial.

Usage

getDistributionPars(randSeq, issue, endp)

## S4 method for signature 'randSeq,missing,survEndp'
getDistributionPars(randSeq, endp)

## S4 method for signature 'randSeq,chronBias,survEndp'
getDistributionPars(randSeq, issue, endp)

## S4 method for signature 'randSeq,selBias,survEndp'
getDistributionPars(randSeq, issue, endp)

## S4 method for signature 'randSeq,combinedBias,survEndp'
getDistributionPars(randSeq, issue, endp)

## S4 method for signature 'randSeq,combinedBiasStepTrend,survEndp'
getDistributionPars(randSeq, issue, endp)

Arguments

Value

a matrix of the distribution parameters of the included patients in the clinical trial.

Examples

# return the shape and scale parameters of a Weibull distribution
endp <- survEndp(shape = c(1,1), scale = c(0.5,1), cenTime = 10, cenRate = 0.01)
biasSB <- selBias("CS", log(2), "exact")
randSeq <- genSeq(rpbrPar(rb = 2, N = 12))
getDistributionPars(randSeq,biasSB,endp)

Get expectations of a randomization list

Description

Generates a matrix of the expectations of the included patients in the clinical trial.

Usage

getExpectation(randSeq, issue, endp)

## S4 method for signature 'randSeq,missing,survEndp'
getExpectation(randSeq, endp)

## S4 method for signature 'randSeq,missing,expEndp'
getExpectation(randSeq, endp)

## S4 method for signature 'randSeq,missing,normEndp'
getExpectation(randSeq, endp)

## S4 method for signature 'randSeq,power,normEndp'
getExpectation(randSeq, issue, endp)

## S4 method for signature 'randSeq,chronBias,normEndp'
getExpectation(randSeq, issue, endp)

## S4 method for signature 'randSeq,chronBias,expEndp'
getExpectation(randSeq, issue, endp)

## S4 method for signature 'randSeq,chronBias,survEndp'
getExpectation(randSeq, issue, endp)

## S4 method for signature 'randSeq,chronBias,missing'
getExpectation(randSeq, issue)

## S4 method for signature 'randSeq,selBias,normEndp'
getExpectation(randSeq, issue, endp)

## S4 method for signature 'randSeq,selBias,expEndp'
getExpectation(randSeq, issue, endp)

## S4 method for signature 'randSeq,selBias,survEndp'
getExpectation(randSeq, issue, endp)

## S4 method for signature 'randSeq,selBias,missing'
getExpectation(randSeq, issue)

## S4 method for signature 'randSeq,combinedBias,normEndp'
getExpectation(randSeq, issue, endp)

## S4 method for signature 'randSeq,combinedBias,expEndp'
getExpectation(randSeq, issue, endp)

## S4 method for signature 'randSeq,combinedBias,survEndp'
getExpectation(randSeq, issue, endp)

## S4 method for signature 'randSeq,combinedBiasStepTrend,normEndp'
getExpectation(randSeq, issue, endp)

## S4 method for signature 'randSeq,combinedBiasStepTrend,expEndp'
getExpectation(randSeq, issue, endp)

## S4 method for signature 'randSeq,combinedBiasStepTrend,survEndp'
getExpectation(randSeq, issue, endp)

Arguments

Details

It is assumed that the expectations of the included patients in a clinical trial can be influenced in three different ways:

• The strength of selection bias and the guessing strategy of the investigator (see selBias).

• The strength of a linear time trend, which is described by an object of the class chronBias.

• The expectations of the investigated treatment groups can be different (see e.g. normEndp).

Value

A matrix of the expectations of the included patients in the clinical trial.

Examples

# get Expectation for a normal endpoint
myPar <- bsdPar(10, 2)
M <- genSeq(myPar, 2)
cs <- selBias("CS", 2, "sim")
endp <- normEndp(mu = c(2, 2), sigma = c(1, 1))
getExpectation(M, cs, endp)

# get Expectation for an exponential endpoint
cs <- selBias("CS", 0.1 , "sim")
endp <- expEndp(lambda = c(0.5, 1), cenTime = 10, cenRate = 0.01)
getExpectation(M, cs, endp)

Theoretical probability for randomization sequences

Description

Calculate theoretical probability for observed randomization sequences

Usage

getProb(obj)

## S4 method for signature 'rarSeq'
getProb(obj)

## S4 method for signature 'abcdSeq'
getProb(obj)

## S4 method for signature 'bbcdSeq'
getProb(obj)

## S4 method for signature 'bsdSeq'
getProb(obj)

## S4 method for signature 'chenSeq'
getProb(obj)

## S4 method for signature 'crSeq'
getProb(obj)

## S4 method for signature 'ebcSeq'
getProb(obj)

## S4 method for signature 'gbcdSeq'
getProb(obj)

## S4 method for signature 'hadaSeq'
getProb(obj)

## S4 method for signature 'mpSeq'
getProb(obj)

## S4 method for signature 'pbrSeq'
getProb(obj)

## S4 method for signature 'tbdSeq'
getProb(obj)

## S4 method for signature 'udSeq'
getProb(obj)

Arguments

Value

a matrix with theoretical probabilities for observed randomization sequences

Examples

myPar <- bsdPar(10, 2)
M <- genSeq(myPar, 2)
getProb(M)

# all Sequences
par <- pbrPar(bc=c(2,2))
refSet <- getAllSeq(myPar)
probs <- getProb(refSet)

# sequences with probabilities
cbind(probs, refSet$M)

Accessor function for the randomization list

Description

Get the randomization list coded in its groups.

Usage

getRandList(obj)

Arguments

Value

A matrix with all randomization sequences of a S4 object

Examples

myPar <- bsdPar(10, 2)
M <- genSeq(myPar, 2)
getRandList(M)

Calculating p values

Description

Computes the p values based on the noncentrality parameters delta and lambda for the doubly noncentral t-distribution

Usage

get_p_values_new(delta, lambda, N, alpha = 0.05, df = sum(N - 2))

Arguments

Value

a p value

Biasing Policy for a Group of Favored Treatments

Description

Calculate vector with the selection bias for each patient

Usage

getbiasCS1(R, K, pref)

Arguments

Value

vector with the selection bias for each patient

Biasing Policy for Avoiding the Placebo Treatment

Description

Calculate vector with the selection bias for each patient

Usage

getbiasCS2(R, K, avoid)

Arguments

Value

vector with the selection bias for each patient

Representing Hadamard Randomization

Description

Represents the randomization procedure Hadamard Randomization.

Usage

hadaPar(N, groups = LETTERS[1:2])

Arguments

Details

Hadamard randomization has been proposed by R.A. Bailey. The key idea is to use the columns of a special Hadamard Matrix as a randomization scheme. The implemented algorithm uses the Hadamard Matrix with N=12 columns proposed in the paper, see references.

Value

S4 object of the class hadaPar.

Note

getProb and getAllSeq are currently only supported for hadaPar with total sample size N=12.

References

R.A. Bailey and P.R. Nelson (2003) Hadamard Randomization: A valid restriction of random permuted blocks. Biometrical Journal, 45, 554-60.

See Also

Other randomization procedures: abcdPar, bbcdPar, bsdPar, chenPar, crPar, createParam(), ebcPar, gbcdPar, mpPar, pbrPar, rarPar, rpbrPar, rtbdPar, tbdPar, udPar

Check function for occurrence of all treatment groups in the sequence

Description

checks whether each group has its value coming up at least once in the sequence

Usage

hasAllGroups(seq, K)

Arguments

Value

TRUE if all groups represented, FAlSE otherwise

Calculate hat matrix

Description

Calculate hat matrix

Usage

hatMatrix(M)

Arguments

Value

Hat matrix, i.e. M * (M^T M)^{-1} M^T

Representing the allocation imbalance

Description

Represents the imbalance of the treatment assignments of patients in a clinical trial.

Usage

imbal(type)

Arguments

Details

Balance of the treatment assignment of patients can be an issue in the design of a clinical trial. The imbal function is a constructor function for an S4 object of class imbal representing the issue of imbalance of a clinical trial. The parameter type can take the following values: The type

"imb"

the final imbalance, i.e. difference in group sizes at the end of a trial

"absImb"

the absolute value of the final imbalance

"loss"

the loss in power estimation, i.e. imb^2/N

"maxImb"

the maximal attained imbalance during the trial

Value

S4 object of class imbal, a formal representation of the issue of imbalance in a clinical trial.

References

A.C. Atkinson (2014) Selecting a biased coin design. Statistical Science, 29, Vol. 1, 144-163.

See Also

Other issues: chronBias, combineBias(), corGuess, issue, selBias, setPower()

Assessment criteria for clinical trials

Description

Summarizes the criteria for the assessment of randomization procedures.

Details

Randomization in clinical trials is supposed to control certain properties in clinical trials. In the randomizeR package, these properties are called issues. It is crucial to decide which of the issues is relevant in the present clinical trial, because a randomization procedure that manages well one issue might behave very badly for another. The issues include

• Selection bias can occur if future treatment allocations are predictable due to restricted randomization and unmasking of past treatment assignments. The influence of selection bias on the test decision is represented by the selBias class. The measure for the predictability of a randomization procedure is implemented in the corGuess class representing the expected number of correct guesses.

• Chronological bias can occur if a time trend is present in the data. Time trends occur due to learning curves, relaxed inclusion/ exclusion criteria or new co-medication. Chronological bias is represented by the chronBias class.

• Additive combination of chronological and selection bias may occur if a time trend and selection bias are present in the data. The combined bias is represented by the combineBias class.

• Balance is important in order to ensure proper power estimation properties of the treatments. However, a high degree of balance favors selection bias. Depending on the clinical context, a randomization procedure should be chosen that admits a suitable imbalance. Imbalance bias is represented by the imbal class. The power loss due to imbalance can be assessed directly via the setPower class

See Also

Representation of randomization procedures: randPar

Generation of randomization sequences: genSeq

Assessment of randomization sequences: assess

Comparison of randomization sequences: compare

Other issues: chronBias, combineBias(), corGuess, imbal, selBias, setPower()

Method returning the rate parameter of an expEndp S4 object

Description

Method returning the rate parameter of an expEndp S4 object

Usage

lambda(obj)

Arguments

Calculate first non centrality parameter of the doubly non central F-distribution

Description

Calculate first non centrality parameter of the doubly non central F-distribution

Usage

lambda1(H, EY)

Arguments

Value

First non centrality parameter, a single numeric value

Calculate second non centrality parameter of the doubly non central F-distribution

Description

Calculate second non centrality parameter of the doubly non central F-distribution

Usage

lambda2(H, EY)

Arguments

Value

Second non centrality parameter, a single numeric value

logRankDecSim

Description

logRankDecSim

Usage

logRankDecSim(randSeq, bias, endp)

Arguments

Value

a simulated test decision for each randomization sequence.

Approximation of the biased type I error probability (resp. power) of the log rank test

Description

Computes the biased type I error probability (resp. power) of the log rank test due to shifts in the expectation vectors in both treatment groups.

Usage

logRankRejectionProb(randSeq, bias, endp)

Arguments

Value

the rejection probability (type I error probability resp. power) of all randomization sequences.

Calculate Expectation vector

Description

Calculate Expectation vector

Usage

makeBiasedExpectation(R, mu, bias)

Arguments

Value

vector of length N with the biased expectation for each patient.

Design Matrix

Description

Calculate Design Matrix from randomization sequence

Usage

makeDesignMatrix(R)

Arguments

Value

makeDesignMatrix converts the randomization sequence R to its Matrix form. The resulting matrix has K columns, one for each treatment group, and N rows, one for each subject. If a subject i is randomized to a certain treatment j, the entry of (i,j) of the matrix will be one, and all other entries in this row will be zero.

Function returning the method of an S4 object

Description

Function returning the method of an S4 object

Usage

method(obj)

Arguments

Value

The method of an S4 object

Representing Maximal Procedure

Description

Represents the Maximal Procedure.

Usage

mpPar(N, mti, ratio = c(1, 1), groups = LETTERS[1:2])

Arguments

Details

Fix the total sample size N and the mti. Afterwards, the patients are assigned to each treatment arm according to the ratio. All randomization sequences are equiprobable.

Value

S4 object of the class mpPar.

References

V.W. Berger, A. Ivanova and M.D. Knoll (2003) Minimizing predictability while retaining balance through the use of less restrictive randomization procedures. Statistics in Medicine, 19, 3017-28.

See Also

Other randomization procedures: abcdPar, bbcdPar, bsdPar, chenPar, crPar, createParam(), ebcPar, gbcdPar, hadaPar, pbrPar, rarPar, rpbrPar, rtbdPar, tbdPar, udPar

Function returning the MTI slot of an S4 object

Description

Function returning the MTI slot of an S4 object

Usage

mti(obj)

Arguments

Access the expectation value slot of a normEndp S4 object

Description

Access the expectation value slot of a normEndp S4 object

Usage

mu(obj)

Arguments

Representation of normally distributed endpoints

Description

Represents normally distributed endpoints in clinical trials.

Usage

normEndp(mu, sigma)

Arguments

Details

The normEnd function is a constructor function for an S4 object of the class normEnd representing a normally distributed endpoint in a clinical trial. In conjunction with the assess function, normal endpoints admit the calculation of the exact type-I-error probability and power.

Value

A S4 object that represents a normally distributed endpoint in a clinical trial

See Also

Compute exact or simulated type-I-error: assess.

Other endpoint types: expEndp, survEndp

Examples

# set the parameters of two normally distributed endpoints
endp <- normEndp(mu = c(1, 2), sigma = c(1, 1))

Overview over the parameters used in the randomizeR package

Description

This list of parameters yields a comprehensive overview of the parameters used in the randomizeR package.

Arguments

Representing Permuted Block Randomization

Description

Represents the randomization procedure Permuted Block Randomization.

Usage

pbrPar(bc, K = 2, ratio = rep(1, K), groups = LETTERS[1:K])

Arguments

Details

Fix the block constellation bc, the number of treatment groups K, and the vector of the ratio. Afterwards, in each block the patients are assigned according to the ratio to the corresponding treatment groups. All generated randomization sequences are equiprobable.

Value

S4 object of the class pbrPar.

References

W. F. Rosenberger and J. M. Lachin (2002) Randomization in Clinical Trials. Wiley.

See Also

Other randomization procedures: abcdPar, bbcdPar, bsdPar, chenPar, crPar, createParam(), ebcPar, gbcdPar, hadaPar, mpPar, rarPar, rpbrPar, rtbdPar, tbdPar, udPar

Generic plotting of comparison objects

Description

Generic plotting of comparison objects

Usage

plot(x, y, ...)

## S4 method for signature 'comparison,character'
plot(x, y)

## S4 method for signature 'comparison,missing'
plot(x, y)

Arguments

Details

Creates a box- or violinplot of an object x of the class comparison.

Value

A plot created with the additional package ggplot2.

See Also

compare for creating S4 objects of the class comparison

Examples

# compare Random Allocation Rule and Big Stick for N = 4 with respect to
# correct guesses
RAR <- getAllSeq(rarPar(4))
BSD <- getAllSeq(bsdPar(4, mti = 2))
corGuess <- corGuess("CS")
comp <- compare(corGuess, RAR, BSD)
plot(comp)

desScore plotting

Description

Plot of an desScore object.

Usage

plotDes(desScore, labels, colAv = "red", quantiles = FALSE)

Arguments

Value

a plot of an desScore object

See Also

Other desirability topics: derFunc, evaluate(), getDesScores(), plotEv(), probUnDes()

Examples

# compute the desirability scores of the full set of PBR(4)
sequences <- getAllSeq(rarPar(4))
issue1 <- corGuess("CS")
issue2 <- chronBias("linT", 1/4, "exact")
endp <- normEndp(mu = c(0,0), sigma = c(1,1))
A <- assess(sequences, issue1, issue2, endp = endp)
d1 <- derFunc(0.5, 0.75, 1)
d2 <- derFunc(0.05, 0.1, 1)

D <- getDesScores(A, d1, d2)
summary(D)
plotDes(D)
plotDes(D, quantiles = TRUE)

Evaluation plotting

Description

Plot of an evaluation object.

Usage

plotEv(evaluation, labels, cols)

Arguments

Value

A plot of an evaluation object

See Also

Other desirability topics: derFunc, evaluate(), getDesScores(), plotDes(), probUnDes()

Examples

# compare Random Allocation Rule to Big Stick Design with respect to different issues
# and their corresponding desirability functions
issue1 <- corGuess("CS")
issue2 <- chronBias(type = "linT", theta = 1/4, method = "exact")
RAR <- getAllSeq(rarPar(4))
BSD <- getAllSeq(bsdPar(4, mti = 2))
A1 <- assess(RAR, issue1, issue2, endp = normEndp(c(0,0), c(1,1)))
A2 <- assess(BSD, issue1, issue2, endp = normEndp(c(0,0), c(1,1)))

d1 <- derFunc(TV = 0.5, 0.75, 2)
d2 <- derFunc(0.05, c(0, 0.1), c(1, 1))
DesScore <- getDesScores(A1, d1, d2, weights = c(5/6, 1/6))
DesScore2 <- getDesScores(A2, d1, d2, weights = c(5/6, 1/6))

E <- evaluate(DesScore, DesScore2)
plotEv(E)

Sequence plotting

Description

Plot all randomization sequences of a randSeq object

Usage

plotSeq(sequences, plotAllSeq = FALSE, emph = NA, rs = NA)

Arguments

Value

A plot of all randomization sequences of a randSeq object.

Computing the probability of having desirability scores of zero

Description

Computing the probability of having desirability scores of zero for each desirability function applied to an issue.

Usage

probUnDes(desScore)

## S4 method for signature 'desScores'
probUnDes(desScore)

Arguments

Details

The function probUnDes expects an object that results from the getDesScores function. For each issue it computes the probability that it achieves an undesirable score, i.e. a desirability score of 0. In doing so, it weights the zero desirability scores with the probability that the sequence occurs.

Value

S4 object of class probUnDesirable computing the probability of getting undesirable scores, i.e. desirability scores of 0.

See Also

Representation of randomization procedures: randPar

Generation of randomization sequences: genSeq

issues for the desirability of randomization sequences

Other desirability topics: derFunc, evaluate(), getDesScores(), plotDes(), plotEv()

Examples

# compare Random Allocation Rule to Big Stick Design with respect to different issues
# and their corresponding desirability functions
RAR <- getAllSeq(rarPar(4))
issue1 <- corGuess("CS")
issue2 <- corGuess("DS")
A1 <- assess(RAR, issue1, issue2)

d1 <- derFunc(TV = 0.1, 0.7, 2)
d2 <- derFunc(0.5, c(0.3, 0.8), c(1, 1))
DesScore <- getDesScores(A1, d1, d2, weights = c(5/6, 1/6))

probUnDes(DesScore)

Function returning the block slot of an S4 object

Description

Function returning the block slot of an S4 object

Usage

randBlocks(obj)

Arguments

Value

a vector with the lengths of each random block of a pbrPar object

Settings for randomization procedures

Description

Randomization procedures in randomizeR are represented by objects that inherit from randPar. The representation can then be used in order to generate randomization sequences. In order generate a representation of a randomization procedure, call createParam or one of the following functions.

Supported randomization procedures

• Complete Randomization (crPar)

• Random Allocation Rule (rarPar)

• Permuted Block Randomization (pbrPar)

• Permuted Block Randomization with random block length (rpbrPar)

• Truncated Binomial Design (tbdPar)

• Truncated Binomial Design with random block length (rtbdPar)

• Efron's Biased Coin Design (ebcPar)

• Big Stick Design (bsdPar)

• Maximal Procedure (mpPar)

• Wei's Urn Design (udPar)

• Chen's Design (chenPar)

• Generalized Biased Coin Design (gbcdPar)

• Accelerated Biased Coin Design (abcdPar)

• Bayesian Biased Coin Design (bbcdPar)

• Hadamard Randomization (hadaPar)

See Also

Generate randomization sequences genSeq. Calculate the the complete set of randomization sequences of a randomization procedure. getAllSeq.

An S4 Class for the representation of randomization sequences

Description

This set of classes provides functionality of storing randomization sequences of different randomization procedures along with the parameters representing the design.

Slots

N

total number of patients included in the trial

M

matrix containing randomization sequences of length N in its rows.

K

number of treatment groups

groups

character string of length K defining the names of the treatment groups

ratio

ratio of patients between the different groups

Representing Random Allocation Rule

Description

Represents the randomization procedure Random Allocation Rule.

Usage

rarPar(N, K = 2, ratio = rep(1, K), groups = LETTERS[1:K])

Arguments

Details

Fix a total sample size N the number of treatment groups K, and the vector of the ratio. Afterwards, all patients are assigned according to the ratio to the corresponding treatment groups. All randomization sequences are equiprobable.

Value

S4 object of the class rarPar.

References

W. F. Rosenberger and J. M. Lachin (2002) Randomization in Clinical Trials. Wiley.

See Also

Other randomization procedures: abcdPar, bbcdPar, bsdPar, chenPar, crPar, createParam(), ebcPar, gbcdPar, hadaPar, mpPar, pbrPar, rpbrPar, rtbdPar, tbdPar, udPar

Function returning the allocation ratio slot of an S4 object

Description

Function returning the allocation ratio slot of an S4 object

Usage

ratio(obj)

Arguments

Value

A vector containng the allocation ratio of an S4 object

Function returning the adjusting parameter rho slot of an S4 object

Description

Function returning the adjusting parameter rho slot of an S4 object

Usage

rho(obj)

Arguments

Value

the value of the rho parameter of an S4 object

Representing Randomized Permuted Block Randomization

Description

Represents the randomization procedure Randomized Permuted Block Randomization.

Usage

rpbrPar(
  N,
  rb,
  K = 2,
  ratio = rep(1, K),
  groups = LETTERS[1:K],
  filledBlock = FALSE
)

Arguments

Details

Fix the possible random block lengths rb, the number of treatment groups K, the sample size N and the vector of the ratio. Afterwards, one block length is randomly selected of the random block lengths. The patients are assigned according to the ratio to the corresponding treatment groups. This procedure is repeated until N patients are assigned. Within each block all possible randomization sequences are equiprobable.

Value

S4 object of the class rpbrPar.

References

W. F. Rosenberger and J. M. Lachin (2002) Randomization in Clinical Trials. Wiley.

See Also

Other randomization procedures: abcdPar, bbcdPar, bsdPar, chenPar, crPar, createParam(), ebcPar, gbcdPar, hadaPar, mpPar, pbrPar, rarPar, rtbdPar, tbdPar, udPar

Representing Randomized Truncated Binomial Design

Description

Represents the randomization procedure Randomized Truncated Binomial Design.

Usage

rtbdPar(N, rb = N, groups = LETTERS[1:2], filledBlock = FALSE)

Arguments

Details

Fix the possible random block lengths rb and the sample size of the trial N. Afterwards, one block length is randomly selected of the random block lengths. In this block a fair coin is tossed for the patient assignments until half of the patients have been assigned to one of the treatment arms. Afterwards, the block is filled with the other treatment. This procedure is repeated until N patients are assigned.

Value

S4 object of the class rtbdPar.

References

W. F. Rosenberger and J. M. Lachin (2002) Randomization in Clinical Trials. Wiley.

See Also

Other randomization procedures: abcdPar, bbcdPar, bsdPar, chenPar, crPar, createParam(), ebcPar, gbcdPar, hadaPar, mpPar, pbrPar, rarPar, rpbrPar, tbdPar, udPar

Saving an assess object

Description

Saves the full information of an assess object in a .csv data sheet.

Usage

saveAssess(obj, file = "assessObject.csv")

Arguments

Value

Creates a .csv data in the home folder.

See Also

Other saving functions: saveRand()

Saving a randomization lists

Description

Saves the parameters of a randSeq object in a .csv data sheet.

Usage

saveRand(obj, file = "randList.csv")

Arguments

Value

Creates a .csv data in the home folder and saves the randomization list as a column vector.

See Also

Other saving functions: saveAssess()

Method returning the scale parameter of an survEndp S4 object

Description

Method returning the scale parameter of an survEndp S4 object

Usage

scale(obj)

Arguments

Function returning the allocation seed slot of an object

Description

Returns the seed that was either generated at random or user specified. The seed can be specified for any random operation e.g. genSeq.

Usage

seed(obj)

Arguments

Representing selection bias

Description

Represents the issue of selection bias in a clinical trial.

Usage

selBias(type, eta, method, alpha = 0.05, delta = 0)

Arguments

Details

Selection bias can be an issue in the design of a clinical trial. The selBias function is a constructor function for an S4 object of the class selBias representing the issue of third order selection bias in a clinical trial. It supports two possible modes, method="sim" and method="exact". This representation is particularly useful in interaction with the assess function.

method="sim"

Represents the simulated type-I-error rate given the level alpha, the selection effect eta and the biasing strategy type. When calling assess for a selBias object with method="sim", one test decision is computed for each sequence of randSeq. The type-I-error rate (power) is the proportion of falsely (correctly) rejected null hypotheses.

method="exact"

Represents the exact type-I-error probability given the level alpha, the selection effect eta and the biasing strategy type. When calling assess for a selBias object with method="exact", the p-value of each randomization sequence is computed. For normal endpoints and two treatment groups these p-values are exact values which can be calculated from the sum of the corresponding quantiles of the doubly noncentral t-distribution. For more than two treatment groups, exact p-values are computed using a doubly noncentral F distribution. For exponential endpoints the p-values are obtained using an approximation formula.

It also supports three types of selection bias:

type="DS"

Refers to the divergence strategy according to Blackwell and Hodges (1957). Under this guessing strategy, the investigator guesses that the upcoming treatment is the one that has so far been allocated *more* frequently.

type="CS"

Refers to the convergence strategy according to Blackwell and Hodges (1957). Under this guessing strategy, the investigator guesses that the upcoming treatment is the one that has so far been allocated *less* frequently. In multi-arm trials, type="CS" refers to the first generalization of the convergence strategy according to Uschner et al (2018). The investigator guesses the treatment that had been allocated less frequently whenever all the treatments of the opposite group are larger than the smallest of the present group.

type="CS2"

In trials with two treatment arms, type="CS2" is equivalent to type="CS". In multi-arm trials, type="CS2" refers to the second generalization of convergence strategy according to Uschner et al (2018). The investigator guesses the treatment that had been allocated less frequently whenever all the treatments of the opposite group are larger than the smallest of the present group.

Value

S4 object of class selBias, a formal representation of the issue of selection bias in a clinical trial.

References

D. Blackwell and J.L. Hodges Jr. (1957) Design for the control of selection bias. Annals of Mathematical Statistics, 25, 449-60.

M. Proschan (1994) Influence of selection bias on the type-I-error rate under random permuted block designs. Statistica Sinica, 4, 219-31.

D. Uschner, R.-D. Hilgers, N. Heussen (2018) The impact of selection bias in randomized multi-arm parallel group clinical trials PLOS ONE, 13(1), 1-18.

See Also

Compute exact or simulated rejection probability: assess.

Other issues: chronBias, combineBias(), corGuess, imbal, issue, setPower()

Examples

# create a selection bias of the convergency strategy type with eta = 0.25 for which
# the exact rejection probabilities are calculated
sbias <- selBias("CS", 0.25, "exact")

Representing the power

Description

Represents the expected power of the individual randomization sequences.

Usage

setPower(d, method, alpha = 0.05)

Arguments

Details

The attained power of an individual randomization sequence can be an issue in the design of a clinical trial. The power of a randomization sequence is computed depending on the effect size d and the difference in group sizes.

If method="sim", the object represents the simulated power of an individual randomization sequence. When calling assess for a power object with method="sim", one test decision is computed for each randomization sequence of randSeq. The power is the proportion of falsely (correctly) rejected null hypotheses.

If method="exact", the object represents the exact power of an individual randomization sequence. When calling assess for a power object with method="exact", the exact p-value of each randomization sequence is computed. So far, this is only supported for normal endpoints. Then the power is the sum of the corresponding quantiles of the noncentral t-distribution.

Value

S4 object of class power, a formal representation of the issue of power in a clinical trial.

See Also

Other issues: chronBias, combineBias(), corGuess, imbal, issue, selBias

Method returning the shape parameter of an survEndp S4 object

Description

Method returning the shape parameter of an survEndp S4 object

Usage

shape(obj)

Arguments

Function returning the standard deviation slot of a normEndp S4 object

Description

Function returning the standard deviation slot of a normEndp S4 object

Usage

sigma(obj)

Arguments

Summary of assessments of a randomization procedure

Description

Summary of assessments of a randomization procedure

Summary of desirability scores of a randomization procedure

Usage

summary(object, ...)

## S4 method for signature 'assessment'
summary(object)

summary(object, ...)

## S4 method for signature 'desScores'
summary(object)

Arguments

Details

For each issue the assessment of the sequences is summarized to permit a design-based assessment of the randomization procedure. This approach uses the sequence-wise values of the assessment and the probabilities in order to give an overall summary.

For each issue the desirability score of the sequences is summarized to permit a design-based desirability score of the randomization procedure. This approach uses the sequence-wise values of the desirability and the probabilities in order to give an overall summary.

Value

Data frame with a summary of the assessment object.

Data frame with a summary of the desirability scores object.

Examples

# assess the full set of PBR(4)
seq <- getAllSeq(pbrPar(4))
issue <- corGuess("CS")
A <- assess(seq, issue)
summary(A)

# compute the desirability scores of the full set of PBR(4)
seq <- getAllSeq(pbrPar(4))
issue1 <- corGuess("CS")
issue2 <- corGuess("DS")
A <- assess(seq, issue1, issue2)
d1 <- derFunc(0.5, c(0.1, 0.8), c(1, 1))
d2 <- derFunc(0.1, 0.7, 2)
D <- getDesScores(A, d1, d2, weights = c(5/6, 1/6))
summary(D)

Representation of survival endpoints

Description

Represents survival endpoints in clinical trials.

Usage

survEndp(
  cenRate,
  accrualTime = 0,
  cenTime,
  shape,
  scale,
  weights = c(0, 0),
  maxcombo = FALSE
)

Arguments

Details

The survEnd function is a constructor function for an S4 object of the class survEnd representing a survival endpoint in a clinical trial.

Value

A S4 object representing a survival endpoint in a clinical trial.

See Also

Compute exact or simulated type-I-error: assess.

Other endpoint types: expEndp, normEndp

Representing Truncated Binomal Design

Description

Represents the Truncated Binomial Design.

Usage

tbdPar(bc = N, groups = LETTERS[1:2])

Arguments

Details

A fair coin is tossed until half of the patients have been assigned to one of the treatment arms. Afterwards, the randomization list is filled with the other treatment.

Value

S4 object of the class tbdPar.

References

W. F. Rosenberger and J. M. Lachin (2002) Randomization in Clinical Trials. Wiley.

See Also

Other randomization procedures: abcdPar, bbcdPar, bsdPar, chenPar, crPar, createParam(), ebcPar, gbcdPar, hadaPar, mpPar, pbrPar, rarPar, rpbrPar, rtbdPar, udPar

Get type of an object

Description

Accesses the type slot of an S4 object

Usage

type(obj)

Arguments

Value

Character string specifying the type of bias obj represents, e.g. "linT" in case of chronological bias.

Representing Wei's Urn Design

Description

Represents Wei's Urn Design.

Usage

udPar(N, ini, add, groups = LETTERS[1:2])

Arguments

Details

An urn is filled with a number of ini balls of both of the treatments. Afterwards, a ball is drawn randomly from the urn. Finally, add balls are added to the urn from the opposite treatment. This procedure is repeated until N patients are assigned.

Value

S4 object of the class udPar.

References

L.J. Wei (1977) A Class of Designs for Sequential Clinical Trials. Journal of the American Statistical Association, 72, 382-6.

See Also

Other randomization procedures: abcdPar, bbcdPar, bsdPar, chenPar, crPar, createParam(), ebcPar, gbcdPar, hadaPar, mpPar, pbrPar, rarPar, rpbrPar, rtbdPar, tbdPar