Package 'BDP2' reference manual

Title:	Bayesian Adaptive Designs for Phase II Trials with Binary Endpoint
Description:	Tools and workflow to choose design parameters in Bayesian adaptive single-arm phase II trial designs with binary endpoint (response, success) with possible stopping for efficacy and futility at interim analyses. Also contains routines to determine and visualize operating characteristics. See Kopp-Schneider et al. (2018) <doi:10.1002/bimj.201700209>.
Authors:	Annette Kopp-Schneider, Manuel Wiesenfarth, Ulrich Abel
Maintainer:	Manuel Wiesenfarth <[email protected]>
License:	GPL-2
Version:	0.1.3
Built:	2024-10-30 04:46:10 UTC
Source:	https://github.com/wiesenfa/bdp2

Bayesian Adaptive Designs for Phase II Trials with Binary Endpoint

Description

Tools and workflow to choose design parameters in Bayesian adaptive single-arm phase II trial designs with binary endpoint (response, success) with possible stopping for efficacy and futility at interim analyses. Also contains routines to determine and visualize operating characteristics. See Kopp-Schneider et al. (2018) <doi:10.1002/bimj.201700209>.

Details

The DESCRIPTION file:

Package:	BDP2
Type:	Package
Title:	Bayesian Adaptive Designs for Phase II Trials with Binary Endpoint
Version:	0.1.3
Date:	2018-07-31
Author:	Annette Kopp-Schneider, Manuel Wiesenfarth, Ulrich Abel
Maintainer:	Manuel Wiesenfarth <[email protected]>
Description:	Tools and workflow to choose design parameters in Bayesian adaptive single-arm phase II trial designs with binary endpoint (response, success) with possible stopping for efficacy and futility at interim analyses. Also contains routines to determine and visualize operating characteristics. See Kopp-Schneider et al. (2018) <doi:10.1002/bimj.201700209>.
License:	GPL-2
Depends:	rmarkdown, shiny, shinyBS
LazyData:	TRUE
Suggests:	knitr
VignetteBuilder:	knitr
Repository:	https://wiesenfa.r-universe.dev
RemoteUrl:	https://github.com/wiesenfa/bdp2
RemoteRef:	HEAD
RemoteSha:	f674d39ef8686ab7a7cfe7e2c969ace4e2dbdb76

Index of help topics:

BDP2                    Operating characteristics of a single-arm trial
                        with a binary endpoint
BDP2-package            Bayesian Adaptive Designs for Phase II Trials
                        with Binary Endpoint
BDP2_simulate           Simulated operating characteristics of a
                        single-arm trial with a binary endpoint for
                        different types of futility criteria
BDP2_simulateEF_PredPow
                        internal functions
BDP2workflow            Shiny app for workflow
crit_general            Calculates CritBoundaries for different types
                        of futility criteria
pFstop                  Operating characteristics of a single-arm trial
                        with a binary endpoint with futility stopping
pFstopEcall             operating characteristics of a single-arm trial
                        with a binary endpoint with futility stopping
                        and calling efficacy at interim
pFstopEstop             Operating characteristics of a single-arm trial
                        with a binary endpoint with stopping for
                        futility and stopping for efficacy
plot.cE_vs_pEcall       Plot objects returned by plotBDP2()
plotBDP2                Plots

Main functions: BDP2workflow, BDP2 and plotBDP2. BDP2workflow provides an interactive shiny app which also generates Word/pdf/html reports.

Author(s)

Annette Kopp-Schneider, Manuel Wiesenfarth, Ulrich Abel

Maintainer: Manuel Wiesenfarth <[email protected]>

References

Kopp-Schneider, A., Wiesenfarth, M., Witt, R., Edelmann, D., Witt, O. and Abel, U. (2018).
Monitoring futility and efficacy in phase II trials with Bayesian posterior distributions - a calibration approach. Biometrical Journal, to appear.

Examples

## Not run: 
# Starts Shiny app
  BDP2workflow()

## End(Not run)
## Not run: 
# Starts Shiny app
  BDP2workflow()

## End(Not run)

Operating characteristics of a single-arm trial with a binary endpoint

Description

Determines the operating characteristics of a single-arm trial with a binary endpoint (response, success) and interim efficacy and futility analyses. Declaration of efficacy and futility (including possibly early stopping) is based on the posterior probability that the true response rate is at least pE , pF respectively.

Usage

BDP2(n, interim.at, ptrue, 
      eff.stop = FALSE, 
      pF, cF, pE = NULL, cE = NULL, 
      type="PostProb", alpha=0.05,
      shape1F, shape2F, shape1E = NULL, shape2E = NULL, 
      simulate = FALSE, nsim = 10000)
BDP2(n, interim.at, ptrue, 
      eff.stop = FALSE, 
      pF, cF, pE = NULL, cE = NULL, 
      type="PostProb", alpha=0.05,
      shape1F, shape2F, shape1E = NULL, shape2E = NULL, 
      simulate = FALSE, nsim = 10000)

Arguments

`n`	sample size at the final analysis
`interim.at`	vector of sample sizes at the interim analyses
`ptrue`	true (assumed) response rate used for analytical evaluations or simulating the trial
`eff.stop`	`FALSE`: No evaluation of efficacy. `"call"`: no stop for efficacy; in this case the program merely calculates the probability that the efficicacy criterion is satisfied (possibly triggering a notification of the DMC and the start of the planning of a subsequent trial). `"stop"`: the study ends if the efficacy criterion is reached at an interim analysis.
`pF`	response rate used for the futility criterion (may be identical to pE)
`cF`	critical level of posterior probabilities used for declaring futility
`pE`	response rate used for the efficacy criterion
`cE`	critical level of posterior probabilities used for declaring efficacy
`type`	"PostProb" for decisions based on posterior probabilities (default) or "PredictivePower" for decisions based on predictive power (currently only implemented for `simulate==TRUE`)
`alpha`	significance level for final test (only for `simulate==TRUE & type=="PredictivePower"`)
`shape1F`	first parameter of the Beta prior for futility analysis
`shape2F`	second parameter of the Beta prior for futility analysis
`shape1E`	first parameter of the Beta prior for efficacy analysis
`shape2E`	second parameter of the Beta prior for efficacy analysis
`simulate`	`FALSE` for analytical evaluation and `TRUE` for simulation
`nsim`	number of simulation runs (only used if `simulate==TRUE`)

Details

Assumptions: Endpoint (response/no response) data available for all study patients. Beta-binomial model. Prior distribution = Beta(shape1, shape2).

Decisions based on posterior probabilities

The posterior distribution at interim analysis with n.int patients and k.int successes is Beta(k.int + shape1F, n.int + shape2F - k.int) and Beta(k.int + shape1E, n.int + shape2E - k.int), respectively. Efficacy is declared if the posterior probability P(true response rate > pE) is >= cE. Futility is declared if the posterior probability P(true success rate > pF) is < cF. cF, cE translate into futility/efficacy boundaries (maximum number of responses leading to early termination for futility/ minimum number of responses leading to declaring of, or early termination for, efficacy).

Decisions based on predictive power

Given the results of the interim analysis, the predictive power at the final analysis (n patients, critical number of successes k.crit) is P(X >= k.crit - k.int), where X follows a beta-binomial distribution with parameters n'= n - n.int, a = k.int + shape1, and b = n.int - k.int + shape2.

Efficacy is declared if the predictive power is >= cE (cE must be high, e.g. 0.70). Futility is declared if the predictive power is < cF (cF must be small, e.g. 0.10). cE, cF translate into futility/efficacy boundaries (maximum number of responses leading to early termination for futility/ minimum number of responses leading to declaring of, or early termination for, efficacy).

References

Examples

# Operating characteristics with calling for efficacy
BDP2(n=20, interim.at = c(3,9,13,18), ptrue = 0.3, 
      eff.stop = "call",
      pF=0.3, cF=0.01, pE=0.12, cE = 0.9, 
      type="PostProb", 
      shape1F=0.3, shape2F=0.7, shape1E=0.12, shape2E=0.88)

# Operating characteristics with stopping for efficacy
BDP2(n=20, interim.at = c(3,9,13,18), ptrue = 0.3, 
      eff.stop = "stop",
      pF=0.3, cF=0.01, pE=0.12, cE = 0.9, 
      type="PostProb", 
      shape1F=0.3, shape2F=0.7, shape1E=0.12, shape2E=0.88)



# Operating characteristics with calling for efficacy
BDP2(n=20, interim.at = c(3,9,13,18), ptrue = 0.3, 
      eff.stop = "call",
      pF=0.3, cF=0.01, pE=0.12, cE = 0.9, 
      type="PostProb", 
      shape1F=0.3, shape2F=0.7, shape1E=0.12, shape2E=0.88)

# Operating characteristics with stopping for efficacy
BDP2(n=20, interim.at = c(3,9,13,18), ptrue = 0.3, 
      eff.stop = "stop",
      pF=0.3, cF=0.01, pE=0.12, cE = 0.9, 
      type="PostProb", 
      shape1F=0.3, shape2F=0.7, shape1E=0.12, shape2E=0.88)

Simulated operating characteristics of a single-arm trial with a binary endpoint for different types of futility criteria

Description

NOTE: Usually function BDP2 will be preferred.

Determines the operating characteristics of a single-arm trial with a binary endpoint (success - failure) and interim futility analyses. The user can choose among 10 futility criteria, which are based on predictive or conditional power (the latter either assuming H1 or the MLE), posterior or predictive probabilities, tail probabilites (under H0 or H1), constant success rates, or arbitrary user-defined futility bounds.

Assumptions: Endpoint (success/no success) data available for all study patients. In case of Bayesian analysis: Beta-binomial model. Prior distribution = Beta(shape1,shape2) (uniform if prior.mean=0.5,prior.sampleSize=2) In case of predictive or conditional power, tail probabilities, or rates: One-sided testing in the final analysis.

Usage

BDP2_simulate(n, vn.int, p, p0, p1, 
              alpha = 0.05, crit, type = 5, nsim, 
              shape1 = 1, shape2 = 1)
BDP2_simulate(n, vn.int, p, p0, p1, 
              alpha = 0.05, crit, type = 5, nsim, 
              shape1 = 1, shape2 = 1)

Arguments

`n`	sample size at the final analysis
`vn.int`	vector of sample sizes at the interim analyses (the vector may be equal to 1:(n-1) = continuous monitoring of futility)
`p`	true (assumed) success rate used for simulating the trial
`p0`	success rate corresponding to H0
`p1`	success rate corresponding to H1 (p1 > p0)
`alpha`	nominal probability of type 1 error used for the final test
`crit`	critical level(s) of predictive/conditional power, (posterior) probabilities, rates, or patient numbers used for early termination. crit translates into futility boundaries (maximum number of successes leading to early termination). If simple rates are used for monitoring futility (type=7), crit is the critical success rate. Rates or probabilites must be input as percentages (???). In case of type 10 analyses, crit must be a vector of numbers of successes indicating futility bounds at each (interim or final)analysis.
`type`	type of futility analysis: 1=predictive power; 2=conditional power under H1; 3=conditional power under the MLE; 4=posterior probability of a success rate > p0; 5=posterior probability of a success rate >= p1; 6=predictive probability of reaching a "positive" final study result, where "positive" is defined in terms of the posterior probability of a success rate > p0. (Here, the ciritcal level must be >= 1- alpha). 7=estimated success rate; 8=p-values; 9="p-values under H1"; 10=user- defined bounds (a vector of critical numbers of successes for each analysis)
`nsim`	number of simulation runs
`shape1`	shape parameter for prior distribution
`shape2`	shape parameter for prior distribution

Details

Some methodological details on the 10 types of futility criteria:

Type 1: Predictive power. Given the results of the interim analysis the predictive power at the final analysis (n patients, critical number of successes k.crit) is P(X >= k.crit - k.int), where X follows a beta-binomial distribution with parameters n'= n - n.int, a = k.int + shape1, and b= n.int - k.int + shape2.

Type 2,3: Conditional power. The conditional power at the interim analysis is P(X >= k.crit - k.int), where X follows a binomial distribution with parameters n'= n - n.int, and success probability either equal to p1 (futility analysis type 2) or to the estimated success rate (MLE) at the interim analysis (type 3.)

Type 4,5:Posterior probabilities. The posterior distribution at interim analysis with n.int patients and k.int successes is Beta(k.int + shape1, n + shape2 - k.int) Type 4: Futility is declared if the posterior probability P(true success rate > p0) is < crit. (Here, crit must be large,e.g. 70%). Type 5: Futility is declared if the posterior probability P(true success rate >= p1) is < crit. (Here, crit must be small, e.g. 10%).

Type 6: Predictive probability combined with posterior probability. Futility is declared if the posterior predictive probability that the study will be a success is < crit (e.g. 10%). Here, the success is defined by the total number of successes in the trial yielding a posterior probability of at least 1 - alpha (when evaluated in the final analysis) that the true success rate is > p0.

Type 7: Estimated success rates. Futility is declared if the success rate is smaller than a fixed benchmark crit. The final analysis is test-based.

Type 8,9: Tail probabilites under H0,H1. Type 8: The futility criterion uses an alpha level crit that is constant across all interim analysis. The final analysis is test-based. Futility is declared if the p-value (upper tail) is >= crit. Type 8 futility analyses should only be used if the number of patients at the first interim analysis is not too low (say, at least 5 to 10). The value of crit is not identicalt o the alpha level used in the final test. Generally, a fairly high value of crit will be appropriate (e.g. 70%). Type 9: Similar to type 8, but with lower-tail probabilites calculated under H1 ("p-values under H1"). I.e., futility is declared if, under H1, the probability of obtaining at most as many successes as the observed number is < crit ("observed number of successes "too low" to be compatible with H1 at one-sided significance level = crit). Generally, a small value of crit (e.g. 5% or 10%) should be chosen.

Type 10: User-defined boundaries. Here, the futility boundaries (maximum numbers of successes leading to early termination) are directly input by the user. crit ist the vector of these boundaries at each (interim or final) analysis. The study is terminated if the number of successes is at analysis no. m is <= the crit[m].

Examples

BDP2_simulate(n=30, vn.int=c(10,20), 
              p=0.2, p0=0.1, p1=0.3, crit=0.1, type=5, nsim=1000,shape1=1,shape2=1)
BDP2_simulate(n=30, vn.int=c(10,20), 
              p=0.2, p0=0.1, p1=0.3, crit=0.1, type=5, nsim=1000,shape1=1,shape2=1)

Shiny app for workflow

Description

Starts a shiny app in the web browser. It provides a workflow to choose design parameters single-arm trial with a binary endpoint (response, success) and interim efficacy and futility analyses as well as routines to determine and visualize operating characteristics. Also Word/pdf/html reports can be generated.

Usage

BDP2workflow(display.mode = "normal")
BDP2workflow(display.mode = "normal")

Arguments

display.mode

display.mode passed to shiny::runApp()

References

Examples

## Not run: 
# Starts Shiny app
  BDP2workflow()

## End(Not run)
## Not run: 
# Starts Shiny app
  BDP2workflow()

## End(Not run)

Calculates CritBoundaries for different types of futility criteria

Description

Calculates CritBoundaries for different types of futility criteria

Usage

crit_general(n, p0, p1, vn.int, alpha, crit, type=5, shape1 = 1, shape2 = 1)
crit_general(n, p0, p1, vn.int, alpha, crit, type=5, shape1 = 1, shape2 = 1)

Arguments

`n`	sample size at the final analysis
`p0`	success rate corresponding to H0
`p1`	success rate corresponding to H1 (p1 > p0)
`vn.int`	vector of sample sizes at the interim analyses (the vector may be equal to 1:(n-1) = continuous monitoring of futility)
`alpha`	nominal probability of type 1 error used for the final test
`crit`	critical level(s) of predictive/conditional power, (posterior) probabilities, rates, or patient numbers used for early termination. crit translates into futility boundaries (maximum number of successes leading to early termination). If simple rates are used for monitoring futility (type=7), crit is the critical success rate. Rates or probabilites must be input as percentages. In case of type 10 analyses, crit must be a vector of numbers of successes indicating futility bounds at each (interim or final)analysis.
`type`	see `BDP2_simulate` for details. Type of futility analysis: 1=predictive power; 2=conditional power under H1; 3=conditional power under the MLE; 4=posterior probability of a success rate > p0; 5=posterior probability of a success rate >= p1; 6=predictive probability of reaching a "positive" final study result, where "positive" is defined in terms of the posterior probability of a success rate > p0. (Here, the ciritcal level must be >= 1- alpha). 7=estimated success rate; 8=p-values; 9="p-values under H1"; 10=user- defined bounds (a vector of critical numbers of successes for each analysis)
`shape1`	for prior distribution
`shape2`	for prior distribution

internal functions

Operating characteristics of a single-arm trial with a binary endpoint with futility stopping

Description

Determines the operating characteristics of a single-arm trial with a binary endpoint (success - failure) on the basis of analytical derivations. The design allows for futility stopping. Outputs are

probability of futility stopping (P.futil) at each interim analysis
cumulative stopping probability up to the interim (P.futil.cum).

Usage

pFstop(p, vn.int, v.crit)
pFstop(p, vn.int, v.crit)

Arguments

`p`	true response rate
`vn.int`	vector of sample sizes at the interim analyses
`v.crit`	vector of critical boundaries for futility stopping at the interim analyses (stop for futility if number of successes <= boundary). Choose boundary=-1 if no stopping is allowed.

Examples

pFstop(p=0.3,vn.int=c(3,9,13,18,20),v.crit=c(0,1,2,3,3))
pFstop(p=0.3,vn.int=c(3,9,13,18,20),v.crit=c(0,1,2,3,3))

operating characteristics of a single-arm trial with a binary endpoint with futility stopping and calling efficacy at interim

Description

Determines the operating characteristics of a single-arm trial with a binary endpoint (success - failure) on the basis of analytical derivations. The design allows for futility stopping and evaluates efficacy at interim. Outputs are

probability of calling efficacy (P.effic) at each interim analysis
cumulative probability of calling efficacy up to the interim (P.effic.cum).
probability of futility stopping (P.futil) at each interim analysis
cumulative stopping probability up to the interim (P.futil.cum).

Usage

pFstopEcall(p, vn.int, v.critE, v.critF)
pFstopEcall(p, vn.int, v.critE, v.critF)

Arguments

`p`	true response rate
`vn.int`	vector of sample sizes at the interim analyses
`v.critE`	vector of critical boundaries for calling efficacy at the interim analyses (call efficacy if number of successes >= boundary)
`v.critF`	vector of critical boundaries for futility stopping at the interim analyses (stop for futility if number of successes <= boundary). Choose boundary=-1 if no stopping for futility is allowed.

Examples

pFstopEcall(p=0.3,vn.int=c(3,9,13,18,20),v.critE=4:8, v.critF=c(0,1,2,3,3))
pFstopEcall(p=0.3,vn.int=c(3,9,13,18,20),v.critE=4:8, v.critF=c(0,1,2,3,3))

Operating characteristics of a single-arm trial with a binary endpoint with stopping for futility and stopping for efficacy

Description

Determines the operating characteristics of a single-arm trial with a binary endpoint (success - failure) on the basis of analytical derivations. The design allows for stopping for futility and stopping for efficacy. Outputs are

probability of stopping for efficacy (P.effic) at each interim analysis
cumulative probability of stopping for efficacy up to the interim (P.effic.cum).
probability of futility stopping (P.futil) at each interim analysis
cumulative stopping probability up to the interim (P.futil.cum).

Usage

pFstopEstop(p, vn.int, v.critE, v.critF)
pFstopEstop(p, vn.int, v.critE, v.critF)

Arguments

`p`	true response rate
`vn.int`	vector of sample sizes at the interim analyses
`v.critE`	vector of critical boundaries for calling efficacy at the interim analyses (stop for efficacy if number of successes >= boundary)
`v.critF`	vector of critical boundaries for futility stopping at the interim analyses (stop for futility if number of successes <= boundary). Choose boundary=-1 if no stopping for futility is allowed.

Examples

pFstopEstop(p=0.3,vn.int=c(3,9,13,18,20),v.critE=4:8, v.critF=c(0,1,2,3,3))
pFstopEstop(p=0.3,vn.int=c(3,9,13,18,20),v.critE=4:8, v.critF=c(0,1,2,3,3))

Plot objects returned by plotBDP2()

Description

Plot objects returned by plotBDP2 with arguments x="cE" and either y="PEcall" or y="PEstop" which can computationally be relatively expensive.

Usage

## S3 method for class 'cE_vs_pEcall'
plot(x, ...)
## S3 method for class 'cE_vs_pEstop'
plot(x, ...)
## S3 method for class 'cE_vs_pEcall'
plot(x, ...)
## S3 method for class 'cE_vs_pEstop'
plot(x, ...)

Arguments

`x`	Object returned by `plotBDP2` with arguments `x="cE"` and either `y="PEcall"` or `y="PEstop"`
`...`	arguments passed to `plot.default`

Examples

shape1F=0.3
shape2F=0.7
shape1E=0.12
shape2E=0.88
res=plotBDP2(x="cE",y="PEcall",n=30,interim.at=15,
             pF=0.3,cF=0.01,pE=0.12,cE=seq(.5,1,by=.01),p0=0.3,p1=0.12,
             shape1F=shape1F,shape2F=shape2F,shape1E=shape1E,shape2E=shape2E,
             col=c("green","red"),cex.sub=.8)
plot(res)
shape1F=0.3
shape2F=0.7
shape1E=0.12
shape2E=0.88
res=plotBDP2(x="cE",y="PEcall",n=30,interim.at=15,
             pF=0.3,cF=0.01,pE=0.12,cE=seq(.5,1,by=.01),p0=0.3,p1=0.12,
             shape1F=shape1F,shape2F=shape2F,shape1E=shape1E,shape2E=shape2E,
             col=c("green","red"),cex.sub=.8)
plot(res)

Plots

Description

Output of desired plots

Usage

plotBDP2(x = c("n", "k", "ptrue", "cE", "cF"), 
          y = c("Prob0Successes", "PostProb0or1Successes", "bFbE", 
                "PEcall_p0_p1", "PEstop_p0_p1", 
                "PFstopEcall", "PFstopEstop",
                "PEcall", "PEstop", "PFstop", "PFstopEstop", 
                "ExpectedNumber", 
                "PredictivePower"), 
          n, interim.at, ptrue, 
          pF, cF, pE, cE, p0, p1, Estop=FALSE,
          shape1F, shape2F, shape1E = NULL, shape2E = NULL, 
          col = c("green", "red"), cex.legend=1, add = FALSE, 
          show=TRUE, progress = FALSE, ...)
plotBDP2(x = c("n", "k", "ptrue", "cE", "cF"), 
          y = c("Prob0Successes", "PostProb0or1Successes", "bFbE", 
                "PEcall_p0_p1", "PEstop_p0_p1", 
                "PFstopEcall", "PFstopEstop",
                "PEcall", "PEstop", "PFstop", "PFstopEstop", 
                "ExpectedNumber", 
                "PredictivePower"), 
          n, interim.at, ptrue, 
          pF, cF, pE, cE, p0, p1, Estop=FALSE,
          shape1F, shape2F, shape1E = NULL, shape2E = NULL, 
          col = c("green", "red"), cex.legend=1, add = FALSE, 
          show=TRUE, progress = FALSE, ...)

Arguments

`x`	character string specifying what is given by the x axis "n" for number of patients at final or at first interim, depending on plot "ptrue" for the true response rate "k" number of successes at interim (only for `y=="PredictivePower"`) "cE" for the critical level of posterior probabilities used for declaring efficacy "cF" for the critical level of posterior probabilities used for declaring futility
`y`	character string specifying what is given by the y axis "Prob0Successes" for plot of probability of 0 successes out of n at first interim, i.e. (1-p)^n. Two curves are generated: one for p0 and one for p1. Choose x="n" and set n to a vector of number patients at first interim. "PostProb0or1Successes" generates two curves of posterior probability that reponse rate exceeds cF. One given 0 successes and one given 1 success observed in n, i.e. P(p>pF\| 0 successes out of n) and P(p>pF\| 1 success out of n). Choose x="n" and set n to a vector of number patients at first interim. "bFbE" for plot of boundaries for futility bF and for efficacy bE in terms of number of successes per n number of patients. Futility stop if number of successes <= bF, call efficacy if number of successes >= bE. Choose x="n" and set n to the maximal number of patients (not a vector). "PEcall_p0_p1" for plot of probability to call efficacy at final (i.e. P(p>pE\|Data)>=cE ), evaluated for data generated with control response rate p0 (corresponds to type I error) and for data generated with target response rate p1 (corresponds to power) for varying number of patients at final. Choose x="n" and set n to a vector of number patients at final. "PEstop_p0_p1" as above but with stopping for efficacy instead of calling efficacy "PFstopEcall" for plotting operating characteristics for a given response rate as a function of number of patients at final, n. Shows one curve (default: in red) for the probability of stopping for futility up to final analysis and one curve (default: in green) for the probability of calling efficacy at final analysis. For the setting ptrue=p0, the curves show the probability of true stopping (default: in red) and type I error (default: in green). For the setting ptrue=p1, the curves show the probability of false stopping (default: in red) and power (default: in green). Choose x="n" and set n to a vector of number patients at final. "PFstopEstop" as above but with stopping for efficacy instead of calling efficacy "PEcall" for plot of probability to call efficacy at final (i.e. P(p>pE\|Data)>=cE ). For x="ptrue" then this is the power function. For x="cE" this gives plots of probability to call efficacy at final, evaluated for data generated with control response rate p0 (corresponds to type I error) and for data generated with target response rate p1 (corresponds to power). "PEstop" For x="ptrue" then this is the power function. For x="cE" this gives plots of probability to call efficacy at final, evaluated for data generated with control response rate p0 (corresponds to type I error) and for data generated with target response rate p1 (corresponds to power). "PFstop" for plot of cumulative probability to stop for futility up to final. For x="ptrue" this gives the futility stopping probability as function of ptrue. For x="cF" this gives 2 curves, evaluated for data generated with control response rate p0 (corresponds to true stopping probability, default: in green) and for data generated with target response rate p1 (corresponds to false stopping probability, default: in red). "ExpectedNumber" for expected number of patients in the trial. Choose x= "ptrue". Takes stopping for efficacy into account if `Estop==TRUE` "PredictivePower" for predictive power (only for `x=="k"`)
`n`	sample size at the final analysis, vector if `x=="n"`
`interim.at`	vector of sample sizes at the interim analyses
`ptrue`	true (assumed) response rate used for simulating the trial, vector if `x=="ptrue"`
`pF`	response rate used for the futility criterion P(p>pF\|Data) < cF (may be identical to pE)
`cF`	critical level of posterior probabilities used for declaring futility, vector if `x=="cF"`
`pE`	response rate used for the efficacy criterion P(p>pE\|Data) >= cE
`cE`	critical level of posterior probabilities used for declaring efficacy, vector if `x=="cE"`
`p0`	response rate corresponding to H0
`p1`	response rate corresponding to H1 (p1 > p0)
`shape1F`	first parameter of the Beta prior for futility analysis
`shape2F`	second parameter of the Beta prior for futility analysis
`shape1E`	first parameter of the Beta prior for efficacy analysis
`shape2E`	second parameter of the Beta prior for efficacy analysis
`Estop`	Stop for efficacy? Defaults to `FALSE`. Only relevant if `y=="ExpectedNumber"`.
`col`	line color, for some plots vector of length 2.
`add`	add line to existing plot. Only supported if `x=="ptrue"`
`show`	show plot (otherwise computed objects are invisibly returned)
`progress`	only used by shiny app
`cex.legend`	size of legend text relative to cex
`...`	additional arguments passed to `plot.default()`

References

Examples

# See vignette for more details and examples
pF=0.3
pE=0.12
shape1F=0.3
shape2F=0.7
shape1E=0.12
shape2E=0.88
cF=0.01
cE=0.9
nvec=c(18:40)
interim.at=c(10,20,30)

# Type I error and probability of true stopping for the uninteresting response rate. 
ptrue=0.12
plotBDP2(x="n", y="PFstopEcall",
         n =nvec, interim.at = interim.at,
         pF=pF,cF=cF,pE=pE,cE=cE,ptrue=ptrue,
         shape1F=shape1F,shape2F=shape2F,shape1E=shape1E,shape2E=shape2E)


# Power and probability of false stopping for the target response rate. 
ptrue=0.3
plotBDP2(x="n", y="PFstopEcall",
         n =nvec, interim.at = interim.at,
         pF=pF,cF=cF,pE=pE,cE=cE,ptrue=ptrue,
         shape1F=shape1F,shape2F=shape2F,shape1E=shape1E,shape2E=shape2E)

# See vignette for more details and examples
pF=0.3
pE=0.12
shape1F=0.3
shape2F=0.7
shape1E=0.12
shape2E=0.88
cF=0.01
cE=0.9
nvec=c(18:40)
interim.at=c(10,20,30)

# Type I error and probability of true stopping for the uninteresting response rate. 
ptrue=0.12
plotBDP2(x="n", y="PFstopEcall",
         n =nvec, interim.at = interim.at,
         pF=pF,cF=cF,pE=pE,cE=cE,ptrue=ptrue,
         shape1F=shape1F,shape2F=shape2F,shape1E=shape1E,shape2E=shape2E)


# Power and probability of false stopping for the target response rate. 
ptrue=0.3
plotBDP2(x="n", y="PFstopEcall",
         n =nvec, interim.at = interim.at,
         pF=pF,cF=cF,pE=pE,cE=cE,ptrue=ptrue,
         shape1F=shape1F,shape2F=shape2F,shape1E=shape1E,shape2E=shape2E)

Package 'BDP2'

Help Index

Bayesian Adaptive Designs for Phase II Trials with Binary Endpoint

Description

Details

Author(s)

References

Examples

Operating characteristics of a single-arm trial with a binary endpoint

Description

Usage

Arguments

Details

Decisions based on posterior probabilities

Decisions based on predictive power

References

Examples

Simulated operating characteristics of a single-arm trial with a binary endpoint for different types of futility criteria

Description

Usage

Arguments

Details

Examples

Shiny app for workflow

Description

Usage

Arguments

References

Examples

Calculates CritBoundaries for different types of futility criteria

Description

Usage

Arguments

internal functions

Operating characteristics of a single-arm trial with a binary endpoint with futility stopping

Description

Usage

Arguments

Examples

operating characteristics of a single-arm trial with a binary endpoint with futility stopping and calling efficacy at interim

Description

Usage

Arguments

Examples

Operating characteristics of a single-arm trial with a binary endpoint with stopping for futility and stopping for efficacy

Description

Usage

Arguments

Examples

Plot objects returned by plotBDP2()

Description

Usage

Arguments

Examples

Plots

Description

Usage

Arguments

References

Examples