| Title: | Bayesian Single Arm Sample Size Calculation Software |
|---|---|
| Description: | Bayesian sample size calculation software and examples for EuroSARC clinical trials which utilise Bayesian methodology. These trials rely on binomial based endpoints so the majority of programs found here relate to this sort of endpoint. Developed as part of the EuroSARC FP7 grant. |
| Authors: | Peter Dutton |
| Maintainer: | Peter Dutton <[email protected]> |
| License: | GPL-2 |
| Version: | 1.1 |
| Built: | 2024-11-07 13:35:22 UTC |
| Source: | CRAN |
Bayesian sample size calculation software and examples for Eurosarc clinical trials which utilise Bayesian methodology for binary endpoints (response/no-response). These trials rely on binomial based endpoints so the majority of programs found here relate to this sort of endpoint. Interim analyses are permitted for most designs. Developed as part of the EuroSARC FP7 grant.
| Package: | EurosarcBayes |
| Type: | Package |
| Version: | 1.0 |
| Date: | 2015-11-18 |
| License: | None |
This package contains functions and some corresponding shiny versions of them for a user interface approach to sample size calculation and some examples.
There are both frequentist and Bayesian sample size optimisation programs contained here. Both versions are capable of computing frequentist and Bayesian properties of the given approach. This should allow for easy comparison between approaches.
List of user friendly shiny apps:
shiny_binom_single_onestageshiny_binom_single_twostageshiny_LINES_posterior
function naming convention:
Functions are named in the following way:
freq_ or bayes_ denoting a frequentist or Bayesian designs.
binom_ indicating a binomial endpoint.
one_ or two_ indicating one or two endpoints.
methodname_ indicating the approach used.
onestage, twostage or nstage. Program for the number of stages. If the program is designed for any number of stages this has been ommited.
For example freq_binom_one_simons_twostage is a function for designing a frequentist single endpoint binomial trial using Simons two stage design.
One endpoint designs:freq_binom_one_onestage: Finds the smallest sample size for a frequentist trial given the design parameters.
freq_binom_one_simons_twostage: Returns Simon's two stage designs with frequentist and bayesian properties of the designs. Options to return both the optimal and minmax designs.
freq_binom_one_landemets: Returns designs based on Lan-DeMets alpha spending approach using the O'Brien-Fleming alpha spending function (Lan and DeMets 1995, O'Brien and Fleming 1979).
bayes_binom_one_postprob_onestage: Finds the smallest sample size of a Bayesian trial given the design parameters.
bayes_binom_one_postprob_nstage: Computes frequentist and Bayesian properties for a trial with given sample sizes at each interim analysis. The posterior probability is used to determine the stopping critical values at interim.
bayes_binom_one_postlike_nstage: Computes frequentist and Bayesian properties for a trial with given sample sizes at each interim analysis. The posterior predictive probabilities are used to determine the stopping critical values at interim.
Two endpoint designs:
The two endpoint designs assume that two endpoints are independent.
freq_binom_two_singlestage: Finds the smallest sample size for a frequentist trial with two binary endpoints given the design parameters. Exact errors are computed so there is no issue of multiplicity.
freq_binom_two_bryantday_twostage: Returns Bryant and Day's two-stage designs with frequentist and bayesian properties of the designs. Options to return both the optimal and minmax designs (Bryant and Day 1995).
bayes_binom_two_postprob: Computes frequentist and Bayesian properties for a trial with two binary endpoints and given sample sizes at each interim analysis. Posterior probabilities are used to determine the stopping critical values at interim.
bayes_binom_two_postlike: Computes frequentist and Bayesian properties for a trial with two binary endpoints and given sample sizes at each interim analysis. Posterior predictive probabilities are used to determine the stopping critical values at interim.
bayes_binom_two_loss: Computes frequentist and Bayesian properties for a trial with two binary endpoints and given sample sizes at each interim analysis. A Bayesian loss function approach is used to determine the stopping critical values at all analyses (Chen 2009).
Peter Dutton
Maintainer: Peter Dutton <[email protected]>
Simon R. Optimal two-stage designs for phase II clinical trials. Control Clin Trials 1989; 10: 1-10.
Bryant J, Day R. Incorporating toxicity considerations into the design of two-stage phase II clinical trials. Biometrics 1995; 51: 1372-1383.
DeMets, D. L. and G. Lan (1995). The alpha spending function approach to interim data analyses. Cancer Treat Res 75: 1-27.
O'Brien, P. C. and T. R. Fleming (1979). A Multiple Testing Procedure for Clinical Trials. Biometrics 35(3): 549-556.
Chen Y, Smith BJ. Adaptive group sequential design for phase II clinical trials: a Bayesian decision theoretic approach. Stat Med 2009; 28: 3347-3362.
Generate cut-points given interim analyses at set numbers of patients for Bayesian posterior likelihood approach to stopping early for futility or efficacy
bayes_binom_one_postlike_nstage(reviews, prob.success, prob.failure, eta, zeta, p0, p1, prior.a=1e-6, prior.b=1e-6, round=TRUE, warn=TRUE)bayes_binom_one_postlike_nstage(reviews, prob.success, prob.failure, eta, zeta, p0, p1, prior.a=1e-6, prior.b=1e-6, round=TRUE, warn=TRUE)
reviews |
Vector of sample sizes to perform analysis at |
p0 |
Probability of success under the null hypothesis |
p1 |
Probability of success under the alternative hypothesis |
eta |
The smallest probability that p is less than p1 which is allowed to stop for futility |
zeta |
The smallest probability that p is greater than p0 which is allowed to stop for efficacy |
prob.success, prob.failure
|
The probability of success and failure required to stop early at interim analysis |
prior.a, prior.b
|
The prior parameters for the beta prior distribution |
round |
Optionally round the probability outputs to 3 significant figures |
warn |
Turn off warnings for designs which are not optimal |
Returns an object of class trialDesign_binom_one
bayes_binom_one_postprob_onestage
reviews=c(7,18) prob.success=c(0.9) prob.failure=c(0.9) eta=0.9 zeta=0.9 p0=0.1 p1=0.3 prior.a=1e-6 prior.b=1e-6 bayes_binom_one_postlike_nstage(reviews,prob.success,prob.failure, eta,zeta,p0,p1,prior.a,prior.b)reviews=c(7,18) prob.success=c(0.9) prob.failure=c(0.9) eta=0.9 zeta=0.9 p0=0.1 p1=0.3 prior.a=1e-6 prior.b=1e-6 bayes_binom_one_postlike_nstage(reviews,prob.success,prob.failure, eta,zeta,p0,p1,prior.a,prior.b)
Generate cut-points given interim analyses at set numbers of patients for Bayesian posterior probability approach to stopping early for futility or efficacy
bayes_binom_one_postprob_nstage(reviews, eta, zeta, p0, p1, prior.a=0, prior.b=0, h0=p0, h1=p1, round=TRUE, warn=TRUE)bayes_binom_one_postprob_nstage(reviews, eta, zeta, p0, p1, prior.a=0, prior.b=0, h0=p0, h1=p1, round=TRUE, warn=TRUE)
reviews |
Vector of sample sizes to perform analysis at |
p0 |
Probability of success under the null hypothesis |
p1 |
Probability of success under the alternative hypothesis |
eta |
The smallest probability that p is less than p1 which is allowed to stop for futility |
zeta |
The smallest probability that p is greater than p0 which is allowed to stop for efficacy |
h0, h1
|
Optional values to be used if the properties of the design should be based on hypotheses which do not use the last values of p0 and p1. |
prior.a, prior.b
|
The prior parameters for the beta prior distribution |
round |
Optionally round the probability outputs to 3 significant figures |
warn |
Turn off warnings for designs which are not optimal |
Returns an object of class trialDesign_binom_one
bayes_binom_one_postprob_onestage
reviews=c(7,18) eta=c(0.9,0.9) zeta=c(0.9,0.9) p0=0.1 p1=0.3 prior.a=0 prior.b=0 bayes_binom_one_postprob_nstage(reviews,eta,zeta,p0,p1,prior.a, prior.b)reviews=c(7,18) eta=c(0.9,0.9) zeta=c(0.9,0.9) p0=0.1 p1=0.3 prior.a=0 prior.b=0 bayes_binom_one_postprob_nstage(reviews,eta,zeta,p0,p1,prior.a, prior.b)
Generate minimum sample size for the Bayesian single-endpoint single-arm trial. Also provided a shiny app to evaluate the same thing with both frequentist and Bayesian methods side by side.
bayes_binom_one_postprob_onestage(p0, p1, eta, zeta, prior.a, prior.b, round=TRUE) shiny_binom_single_onestage()bayes_binom_one_postprob_onestage(p0, p1, eta, zeta, prior.a, prior.b, round=TRUE) shiny_binom_single_onestage()
p0 |
Probability of success under the null hypothesis |
p1 |
Probability of success under the alternative hypothesis |
eta |
The smallest probability that p is less than p1 which is allowed to stop for futility |
zeta |
The smallest probability that p is greater than p0 which is allowed to stop for efficacy |
prior.a, prior.b
|
The prior parameters for the beta prior distribution |
round |
Optionally round the probability outputs to 3 significant figures |
Returns an object of class trialDesign_binom_one
bayes_binom_one_postprob_nstage
p0=0.1 p1=0.3 eta=c(0.9) zeta=c(0.9) prior.a=0 prior.b=0 bayes_binom_one_postprob_onestage(p0,p1,eta,zeta,prior.a,prior.b)p0=0.1 p1=0.3 eta=c(0.9) zeta=c(0.9) prior.a=0 prior.b=0 bayes_binom_one_postprob_onestage(p0,p1,eta,zeta,prior.a,prior.b)
Computes the decision rules for a single arm, two endpoint bayesian trial using a region of acceptable designs and loss functions to make decisions. This program assumes that the two endpoints are independent. A number of region spaces are provided. This function has the option of providing pre-existing decision matrices to skip this section if you wish to run additional simulations on an already computed design.
bayes_binom_two_loss(t, r, reviews, pra, prb, pta, ptb, l_alpha_beta, l_alpha_c, stage_after_trial, fun.integrate, efficacy_critical_value, toxicity_critical_value, futility_critical_value, no_toxicity_critical_value, decision=NULL, W=NULL, fun.graph=NULL, ...)bayes_binom_two_loss(t, r, reviews, pra, prb, pta, ptb, l_alpha_beta, l_alpha_c, stage_after_trial, fun.integrate, efficacy_critical_value, toxicity_critical_value, futility_critical_value, no_toxicity_critical_value, decision=NULL, W=NULL, fun.graph=NULL, ...)
t, r
|
A vector of the probability of response and toxicity for the simulation scenarios used to compute frequentist properties. The print function requires the first to be the alternative hypothesis and subsequent entries to be the three null hypotheses. This can be run with any scenario when not using the print method |
reviews |
A vector of the number of patients each interim and final analysis will occur at |
pra, prb, pta, ptb
|
Numeric values for the beta prior distribution to be used |
l_alpha_beta, l_alpha_c
|
The two loss function variables weighting between stopping early for futility or efficacy and continuing the trial |
fun.integrate |
function used to integrate the probability of being in the region of interest given the posterior distributions of the data and prior information |
stage_after_trial |
Optional argument for censored stages after the trial has completed. This is likely to create a region of inclusiveness upon concluding the trial |
futility_critical_value, efficacy_critical_value, toxicity_critical_value, no_toxicity_critical_value
|
Four values, for the critical values to be used as thresholds for the posterior distribution |
decision |
Optional input the decision matrices from a previous run to perform additional frequentist simulations on the design. |
W |
Optional input the posterior probabilities from a previous run to perform additional frequentist simulations on the design. |
fun.graph |
Optional function printing a graph of the region of interest. No region is plotted if this is left blank |
... |
Options passed to the integration function |
Returns an object of S4 class trialDesign_binom_two-class. This has plot and print methods. For comparison between designs saved as trialDesign_binom_two objects there is a print function for the S3 class list_trialDesign_binom_two.
The following region spaces are included in the package: tradeoff_square_integrate tradeoff_square_graph tradeoff_ratio_intercepts tradeoff_linear_graph tradeoff_ratio_integrate tradeoff_ratio_graph tradeoff_ellipse_integrate tradeoff_ellipse_graph
Returns an object of class trialDesign_binom_two
Chen Y, Smith BJ. Adaptive group sequential design for phase II clinical trials: a Bayesian decision theoretic approach. Stat Med 2009; 28: 3347-3362.
bayes_binom_two_postprob, bayes_binom_two_postlike
Integration functions and corresponding graphs:
tradeoff_square_integrate,tradeoff_ellipse_integrate,tradeoff_linear_integrate,tradeoff_ratio_integrate
# modelled toxicity probability t=c(0.1,0.1,0.3,0.3) # modelled response probability r=c(0.35,0.2,0.2,0.35) reviews=c(10,15,20,25,30,35,40) stage_after_trial=40 # uniform prior pra=1;prb=1;pta=1;ptb=1 efficacy_critical_value=0.2 futility_critical_value=0.35 toxicity_critical_value=0.1 no_toxicity_critical_value=0.3 # alpha/beta ratio l_alpha_beta=3 # cost of continuing compared to cost of alpha l_alpha_c=750 efficacy_region_min=0.2 toxicity_region_max=0.3 ######################################## # square region s=bayes_binom_two_loss(t,r,reviews,pra,prb,pta,ptb,l_alpha_beta, l_alpha_c,stage_after_trial,fun.integrate=tradeoff_square_integrate, fun.graph=tradeoff_square_graph,efficacy_critical_value, toxicity_critical_value,futility_critical_value, no_toxicity_critical_value,efficacy_region_min=efficacy_region_min, toxicity_region_max=toxicity_region_max) plot(s) ######################################## # ellipse region efficacy_region_min=0.2 efficacy_region_max=0.35 toxicity_region_min=0.1 toxicity_region_max=0.3 s=bayes_binom_two_loss(t,r,reviews,pra,prb,pta,ptb,l_alpha_beta, l_alpha_c,stage_after_trial,fun.integrate=tradeoff_ellipse_integrate, fun.graph=tradeoff_ellipse_graph,efficacy_critical_value, toxicity_critical_value,futility_critical_value, no_toxicity_critical_value,efficacy_region_min=efficacy_region_min, toxicity_region_max=toxicity_region_max, efficacy_region_max=efficacy_region_max, toxicity_region_min=toxicity_region_min) plot(s)# modelled toxicity probability t=c(0.1,0.1,0.3,0.3) # modelled response probability r=c(0.35,0.2,0.2,0.35) reviews=c(10,15,20,25,30,35,40) stage_after_trial=40 # uniform prior pra=1;prb=1;pta=1;ptb=1 efficacy_critical_value=0.2 futility_critical_value=0.35 toxicity_critical_value=0.1 no_toxicity_critical_value=0.3 # alpha/beta ratio l_alpha_beta=3 # cost of continuing compared to cost of alpha l_alpha_c=750 efficacy_region_min=0.2 toxicity_region_max=0.3 ######################################## # square region s=bayes_binom_two_loss(t,r,reviews,pra,prb,pta,ptb,l_alpha_beta, l_alpha_c,stage_after_trial,fun.integrate=tradeoff_square_integrate, fun.graph=tradeoff_square_graph,efficacy_critical_value, toxicity_critical_value,futility_critical_value, no_toxicity_critical_value,efficacy_region_min=efficacy_region_min, toxicity_region_max=toxicity_region_max) plot(s) ######################################## # ellipse region efficacy_region_min=0.2 efficacy_region_max=0.35 toxicity_region_min=0.1 toxicity_region_max=0.3 s=bayes_binom_two_loss(t,r,reviews,pra,prb,pta,ptb,l_alpha_beta, l_alpha_c,stage_after_trial,fun.integrate=tradeoff_ellipse_integrate, fun.graph=tradeoff_ellipse_graph,efficacy_critical_value, toxicity_critical_value,futility_critical_value, no_toxicity_critical_value,efficacy_region_min=efficacy_region_min, toxicity_region_max=toxicity_region_max, efficacy_region_max=efficacy_region_max, toxicity_region_min=toxicity_region_min) plot(s)
Computes the decision rules for a single arm, two endpoint bayesian trial using the likelihood of success to make decisions. This program assumes that the two endpoints are independent.
bayes_binom_two_postlike(t, r, reviews, pra, prb, pta, ptb, efficacy_critical_value, efficacy_prob_stop, toxicity_critical_value, toxicity_prob_stop, int_combined_prob, int_futility_prob, int_toxicity_prob, int_efficacy_prob, futility_critical_value, no_toxicity_critical_value)bayes_binom_two_postlike(t, r, reviews, pra, prb, pta, ptb, efficacy_critical_value, efficacy_prob_stop, toxicity_critical_value, toxicity_prob_stop, int_combined_prob, int_futility_prob, int_toxicity_prob, int_efficacy_prob, futility_critical_value, no_toxicity_critical_value)
t, r
|
A vector of the probability of response and toxicity for the simulation scenarios used to compute frequentist properties. The print function requires the first to be the alternative hypothesis and subsequent entries to be the three null hypotheses. This can be run with any scenario when not using the print method |
reviews |
A vector of the number of patients each interim and final analysis will occur at |
pra, prb, pta, ptb
|
Numeric values for the beta prior distribution to be used |
futility_critical_value, efficacy_critical_value, toxicity_critical_value, no_toxicity_critical_value
|
Four values, for the critical values to be used as thresholds for the posterior distribution |
int_combined_prob, int_futility_prob, int_toxicity_prob, int_efficacy_prob
|
Probabilities to stop at interim analyses |
efficacy_prob_stop, toxicity_prob_stop
|
Values or vectors of the probability required to stop at this interim analysis. If you do not wish to stop due to a rule set this to 1 at that analysis. If you wish to ignor a rule when stopping set this to 0 at that analysis |
Returns an object of S4 class trialDesign_binom_two-class. This has plot and print methods. For comparison between designs saved as trialDesign_binom_two objects there is a print function for the S3 class list_trialDesign_binom_two.
Returns an object of class trialDesign_binom_two
bayes_binom_two_postprob, bayes_binom_two_postlike,bayes_binom_two_loss
# modelled toxicity probability t=c(0.1,0.1,0.3,0.3) # modelled response probability r=c(0.35,0.2,0.2,0.35) reviews=c(10,15,20,25,30,35,40) # uniform prior pra=1;prb=1;pta=1;ptb=1 # End of trial stopping rules for success efficacy_critical_value=0.2 efficacy_prob_stop=0.9 toxicity_critical_value=0.2 toxicity_prob_stop=0.8 # interim required probability to stop int_combined_prob=0.99 int_futility_prob=1 int_toxicity_prob=1 int_efficacy_prob=0.99 # unused in the design for comparison to previous design futility_critical_value=0.35 no_toxicity_critical_value=0.3 s=bayes_binom_two_postlike(t,r,reviews,pra,prb,pta,ptb, efficacy_critical_value,efficacy_prob_stop,toxicity_critical_value, toxicity_prob_stop,int_combined_prob,int_futility_prob, int_toxicity_prob,int_efficacy_prob,futility_critical_value, no_toxicity_critical_value) s plot(s)# modelled toxicity probability t=c(0.1,0.1,0.3,0.3) # modelled response probability r=c(0.35,0.2,0.2,0.35) reviews=c(10,15,20,25,30,35,40) # uniform prior pra=1;prb=1;pta=1;ptb=1 # End of trial stopping rules for success efficacy_critical_value=0.2 efficacy_prob_stop=0.9 toxicity_critical_value=0.2 toxicity_prob_stop=0.8 # interim required probability to stop int_combined_prob=0.99 int_futility_prob=1 int_toxicity_prob=1 int_efficacy_prob=0.99 # unused in the design for comparison to previous design futility_critical_value=0.35 no_toxicity_critical_value=0.3 s=bayes_binom_two_postlike(t,r,reviews,pra,prb,pta,ptb, efficacy_critical_value,efficacy_prob_stop,toxicity_critical_value, toxicity_prob_stop,int_combined_prob,int_futility_prob, int_toxicity_prob,int_efficacy_prob,futility_critical_value, no_toxicity_critical_value) s plot(s)
Computes the decision rules for a single arm, two endpoint bayesian trial using posterior probabilities to generate the decision rules. This program assumes that the two endpoints are independent.
bayes_binom_two_postprob(t, r, reviews, pra, prb, pta, ptb, futility_critical_value, futility_prob_stop, efficacy_critical_value, efficacy_prob_stop, toxicity_critical_value, toxicity_prob_stop, no_toxicity_critical_value, no_toxicity_prob_stop)bayes_binom_two_postprob(t, r, reviews, pra, prb, pta, ptb, futility_critical_value, futility_prob_stop, efficacy_critical_value, efficacy_prob_stop, toxicity_critical_value, toxicity_prob_stop, no_toxicity_critical_value, no_toxicity_prob_stop)
t, r
|
A vector of the probability of response and toxicity for the simulation scenarios used to compute frequentist properties. The print function requires the first to be the alternative hypothesis and subsequent entries to be the three null hypotheses. This can be run with any scenario when not using the print method |
reviews |
A vector of the number of patients each interim and final analysis will occur at |
pra, prb, pta, ptb
|
Numeric values for the beta prior distribution to be used |
futility_critical_value, efficacy_critical_value, toxicity_critical_value, no_toxicity_critical_value
|
Four values, for the critical values to be used as thresholds for the posterior distribution |
futility_prob_stop, efficacy_prob_stop, toxicity_prob_stop, no_toxicity_prob_stop
|
Values or vectors of the probability required to stop at this interim analysis. If you do not wish to stop due to a rule set this to 1 at that analysis. If you wish to ignor a rule when stopping set this to 0 at that analysis |
Returns an object of S4 class trialDesign_binom_two-class. This has plot and print methods. For comparison between designs saved as trialDesign_binom_two objects there is a print function for the S3 class list_trialDesign_binom_two.
Returns an object of class trialDesign_binom_two
bayes_binom_two_postprob, bayes_binom_two_postlike,bayes_binom_two_loss
# modelled toxicity probability t=c(0.1,0.1,0.3,0.3) # modelled response probability r=c(0.35,0.2,0.2,0.35) reviews=c(10,15,20,25,30,35,40) # uniform prior pra=1;prb=1;pta=1;ptb=1 futility_critical_value=0.35 futility_prob_stop=c(0.95,0.95,0.95,0.95,0.95,0.95,0) efficacy_critical_value=0.2 efficacy_prob_stop=c(1,1,0.95,0.95,0.95,0.95,0.9) toxicity_critical_value=0.1 toxicity_prob_stop=c(0.95,0.95,0.95,0.95,0.95,0.95,0.95) no_toxicity_critical_value=0.3 toxicity_prob_stop=c(0.95,0.95,0.95,0.95,0.95,0.95,0.95) s=bayes_binom_two_postprob(t,r,reviews,pra,prb,pta,ptb, futility_critical_value,futility_prob_stop,efficacy_critical_value, efficacy_prob_stop,toxicity_critical_value,toxicity_prob_stop, no_toxicity_critical_value,toxicity_prob_stop) s plot(s)# modelled toxicity probability t=c(0.1,0.1,0.3,0.3) # modelled response probability r=c(0.35,0.2,0.2,0.35) reviews=c(10,15,20,25,30,35,40) # uniform prior pra=1;prb=1;pta=1;ptb=1 futility_critical_value=0.35 futility_prob_stop=c(0.95,0.95,0.95,0.95,0.95,0.95,0) efficacy_critical_value=0.2 efficacy_prob_stop=c(1,1,0.95,0.95,0.95,0.95,0.9) toxicity_critical_value=0.1 toxicity_prob_stop=c(0.95,0.95,0.95,0.95,0.95,0.95,0.95) no_toxicity_critical_value=0.3 toxicity_prob_stop=c(0.95,0.95,0.95,0.95,0.95,0.95,0.95) s=bayes_binom_two_postprob(t,r,reviews,pra,prb,pta,ptb, futility_critical_value,futility_prob_stop,efficacy_critical_value, efficacy_prob_stop,toxicity_critical_value,toxicity_prob_stop, no_toxicity_critical_value,toxicity_prob_stop) s plot(s)
P-value (alpha) for single arm binomial clinical trials. This is done exactly accounting for all interim analysis prior to stopping the trial.
binom_one_alpha(result.success, result.n, p0, failure, success, n)binom_one_alpha(result.success, result.n, p0, failure, success, n)
result.success |
total successes at the end of the trial |
result.n |
total patients at the end of the trial |
p0 |
Probability of success under H0 |
failure |
A vector of the number of failures required to stop for futility, if not able to stop NA or a character string should be provided |
success |
A vector of the number of successes required to stop for efficacy, if not able to stop NA or a character string should be provided |
n |
A vector of the total number of patients to recruit up to each stage of the trial |
binom_one_power, binom_one_assurance
# Simon's two stage design failure=c(0,3) success=c(NA,4) n=c(7,18) p0=0.1 result.success=4 result.n=18 # without accounting for interim analysis when calculating # the p-value 1-pbinom(result.success-1,result.n,p0) # account for interim analysis binom_one_alpha(result.success,result.n,p0,failure,success,n)# Simon's two stage design failure=c(0,3) success=c(NA,4) n=c(7,18) p0=0.1 result.success=4 result.n=18 # without accounting for interim analysis when calculating # the p-value 1-pbinom(result.success-1,result.n,p0) # account for interim analysis binom_one_alpha(result.success,result.n,p0,failure,success,n)
Computes the assurance of a given trial design given a prior assurance distribution.
binom_one_assurance(failure, success, n, ass.dist, type="continuous", lower=0, upper=1, ...) plot_binomassurance(failure, success, n, ass.dist,type="continuous", ndivisions=1000, xlim=c(0,1), xaxs="i", yaxs="i", ylim=NULL, main="Assurance distribution", col="red", col.fill="green", lwd=2, xlab="Probability of successful treatment", ylab="Prior assurance probability" ,...)binom_one_assurance(failure, success, n, ass.dist, type="continuous", lower=0, upper=1, ...) plot_binomassurance(failure, success, n, ass.dist,type="continuous", ndivisions=1000, xlim=c(0,1), xaxs="i", yaxs="i", ylim=NULL, main="Assurance distribution", col="red", col.fill="green", lwd=2, xlab="Probability of successful treatment", ylab="Prior assurance probability" ,...)
failure |
A vector of the number of failures required to stop for futility, if not able to stop NA or a character string should be provided |
success |
A vector of the number of successes required to stop for efficacy, if not able to stop NA or a character string should be provided |
n |
A vector of the total number of patients to recruit up to each stage of the trial |
ass.dist |
Distribution of prior probability for assurance. May be different to prior information. |
type |
Tells the program you are passing it a continuous distribution ("continuous") or a discrete distribution ("discrete") for the assurance distribution |
ndivisions |
The number of points calculated for the plot |
lower, upper
|
Range of the distribution to use |
col.fill |
Colour of the true positive results in the graph |
xlim, xaxs, yaxs, ylim, main, col, lwd, xlab, ylab
|
Different defaults for plotting parameters |
... |
Additional plotting parameters to pass to plot function |
binom_one_power, binom_one_alpha
# Simon's two stage design failure=c(0,3) success=c(NA,4) n=c(7,18) p0=0.1 p1=0.3 # continuous assurance distribution ass.dist = function(p) dbeta(p,4,18) # assurance binom_one_assurance(failure,success,n,ass.dist) # plot plot_binomassurance(failure,success,n,ass.dist,ndivisions=1000) # discrete assurance distribution ass.dist = matrix(c(0.2,0.3,0.4,0.3,0.4,0.3),ncol=2) # assurance binom_one_assurance(failure,success,n,ass.dist,type="discrete") # plot plot_binomassurance(failure,success,n,ass.dist,type="discrete", ndivisions=1000)# Simon's two stage design failure=c(0,3) success=c(NA,4) n=c(7,18) p0=0.1 p1=0.3 # continuous assurance distribution ass.dist = function(p) dbeta(p,4,18) # assurance binom_one_assurance(failure,success,n,ass.dist) # plot plot_binomassurance(failure,success,n,ass.dist,ndivisions=1000) # discrete assurance distribution ass.dist = matrix(c(0.2,0.3,0.4,0.3,0.4,0.3),ncol=2) # assurance binom_one_assurance(failure,success,n,ass.dist,type="discrete") # plot plot_binomassurance(failure,success,n,ass.dist,type="discrete", ndivisions=1000)
Computes the power of a given trial design given the probability of success of treatment p.
binom_one_power(p,failure,success,n) plot_binom_one_power(failure, success, n, ndivisions=1000, xlim=c(0,1), xaxs="i", yaxs="i", ylim=c(0,1.1), main="Power curve for a single arm binomial trial design", xlab="Probability of successful treatment", ylab="Probability of successful trial", p=NULL, alpha=NULL, power=NULL, col.error="red", ...)binom_one_power(p,failure,success,n) plot_binom_one_power(failure, success, n, ndivisions=1000, xlim=c(0,1), xaxs="i", yaxs="i", ylim=c(0,1.1), main="Power curve for a single arm binomial trial design", xlab="Probability of successful treatment", ylab="Probability of successful trial", p=NULL, alpha=NULL, power=NULL, col.error="red", ...)
p |
Probability of success to compute power for |
failure |
A vector of the number of failures required to stop for futility, if not able to stop NA or a character string should be provided |
success |
A vector of the number of successes required to stop for efficacy, if not able to stop NA or a character string should be provided |
n |
A vector of the total number of patients to recruit up to each stage of the trial |
ndivisions |
The number of points calculated for the plot |
col.error |
Colour of type II errors in the plot |
alpha, power
|
Plotted as lines if provided |
xlim, ylim, xaxs, yaxs, main, xlab, ylab
|
Different defaults for plotting parameters |
... |
Additional plotting parameters to pass to plot function |
binom_one_alpha, binom_one_assurance
# Simon's two stage design failure=c(0,3) success=c(NA,4) n=c(7,18) p0=0.1 p1=0.3 # power binom_one_power(p1,failure,success,n) # type 1 error (alpha) binom_one_power(p0,failure,success,n) # plot plot_binom_one_power(failure,success,n,ndivisions=1000,p=c(p0,p1), alpha=0.1,power=0.8)# Simon's two stage design failure=c(0,3) success=c(NA,4) n=c(7,18) p0=0.1 p1=0.3 # power binom_one_power(p1,failure,success,n) # type 1 error (alpha) binom_one_power(p0,failure,success,n) # plot plot_binom_one_power(failure,success,n,ndivisions=1000,p=c(p0,p1), alpha=0.1,power=0.8)
"binom_two_bryantday"
This is the S4 class for constructing Bryant and Day designs. This can be converted to the standard format using properties.
Objects can be created by calls of the form new("binom_two_bryantday", ...).
optimal:Object of class "data.frame", single row data.frame containing the optimal design under H0
minmax:Object of class "data.frame", Single row data.frame containing the minmax design under H0
all.fit:Object of class "data.frame", A data.frame containing all designs which satisfy the required alpha and power specified for the trial
signature(x = "binom_two_bryantday")(x, t, r, pra, prb,
pta, ptb, futility_critical_value = 0.2,
efficacy_critical_value = 0.35, toxicity_critical_value = 0.3,
no_toxicity_critical_value = 0.1)
Class object which you wish to get properties for
A vector of the probability of response and toxicity for the simulation scenarios used to compute frequentist properties. The print function requires the first to be the alternative hypothesis and subsequent entries to be the three null hypotheses. This can be run with any scenario when not using the print method
A vector of the number of patients each interim and final analysis will occur at
Numeric values for the beta prior distribution to be used
Four values, for the critical values to be used as thresholds for the posterior distribution
Bryant J, Day R. Incorporating toxicity considerations into the design of two-stage phase II clinical trials. Biometrics 1995; 51: 1372-1383.
showClass("binom_two_bryantday")showClass("binom_two_bryantday")
"binom_two_singlestage"
This class is created from the function freq_binom_two_singlestage. This is an intermediate stage to generate an object of class trialDesign_binom_two.
Objects can be created by calls of the form new("binom_two_singlestage", ...).
optimal:Object of class "data.frame", Optimal trial design
output:Object of class "data.frame", list of all acceptable trial designs
signature(x = "binom_two_singlestage")(x, t, r, pra, prb,
pta, ptb, futility_critical_value = 0.2,
efficacy_critical_value = 0.35, toxicity_critical_value = 0.3,
no_toxicity_critical_value = 0.1)
Class object which you wish to get properties for
A vector of the probability of response and toxicity for the simulation scenarios used to compute frequentist properties. The print function requires the first to be the alternative hypothesis and subsequent entries to be the three null hypotheses. This can be run with any scenario when not using the print method
A vector of the number of patients each interim and final analysis will occur at
Numeric values for the beta prior distribution to be used
Four values, for the critical values to be used as thresholds for the posterior distribution
Returns an object of class trialDesign_binom_two.
showClass("binom_two_singlestage")showClass("binom_two_singlestage")
Sample size calculation for single arm, multistage trials using the alpha spending approach to reduce type I and type II error rates. This implimentation uses the O'Brien-Fleming alpha spending function for this purpose.
freq_binom_one_landemets(reviews, p0, p1, r=c(p0,p1), alpha=0.1, beta=0.1, prior.a=0, prior.b=0)freq_binom_one_landemets(reviews, p0, p1, r=c(p0,p1), alpha=0.1, beta=0.1, prior.a=0, prior.b=0)
reviews |
A vector of the number of patients to perform interim analysis at |
p0 |
Probability of success under the H0 |
p1 |
Probability of success under the H1 |
r |
A vector of probabilities used to perform simulations from |
alpha |
The largest allowed value for the frequentist type one error |
beta |
The smallest allowed value for the frequentist type two error |
prior.a, prior.b
|
Prior parameters for the beta prior |
Returns an object of class trialDesign_binom_one
DeMets, D. L. and G. Lan (1995). The alpha spending function approach to interim data analyses. Cancer Treat Res 75: 1-27.
O'Brien, P. C. and T. R. Fleming (1979). A Multiple Testing Procedure for Clinical Trials. Biometrics 35(3): 549-556.
reviews=c(11,22,33,44) p0=0.2 p1=0.35 r=c(0.2,0.35) alpha=0.1 beta=0.2 freq_binom_one_landemets(reviews,p0,p1,r,alpha,beta)reviews=c(11,22,33,44) p0=0.2 p1=0.35 r=c(0.2,0.35) alpha=0.1 beta=0.2 freq_binom_one_landemets(reviews,p0,p1,r,alpha,beta)
Generate minimum sample size for the frequentist single-endpoint single-arm trial. Also provided a shiny app to evaluate the same thing with both frequentist and Bayesian methods side by side.
freq_binom_one_onestage(p0, p1, alpha, power, prior.a=0, prior.b=0, round=TRUE) shiny_binom_single_onestage()freq_binom_one_onestage(p0, p1, alpha, power, prior.a=0, prior.b=0, round=TRUE) shiny_binom_single_onestage()
p0 |
Probability of success under H0 |
p1 |
Probability of success under H1 |
alpha |
The largest allowed value for the frequentist type one error |
power |
The smallest allowed frequentist power |
prior.a, prior.b
|
The prior parameters for the beta prior distribution |
round |
Optionally round the probability outputs to 3 significant figures |
Returns an object of class trialDesign_binom_one
p0=0.1 p1=0.3 alpha=0.1 power=0.8 prior.a=0 prior.b=0 freq_binom_one_onestage(p0,p1,alpha,power,prior.a,prior.b)p0=0.1 p1=0.3 alpha=0.1 power=0.8 prior.a=0 prior.b=0 freq_binom_one_onestage(p0,p1,alpha,power,prior.a,prior.b)
Sample size calculation for single arm, two stage designs (Simon's optimal and minmax designs) where stoping early for futility is permitted. Returns frequentist and Bayesian properties for the designs.
A shiny app is also provided. This is interactive for Simon's two stage design and also describes a number of multistage designs for the same problem.
freq_binom_one_simons_twostage(p0, p1, alpha, power, prior.a=0, prior.b=0, nmax=100, round=TRUE, method="optimal") shiny_binom_single_twostage()freq_binom_one_simons_twostage(p0, p1, alpha, power, prior.a=0, prior.b=0, nmax=100, round=TRUE, method="optimal") shiny_binom_single_twostage()
p0 |
Probability of success under H0 |
p1 |
Probability of success under H1 |
alpha |
The largest allowed value for the frequentist type one error |
power |
The smallest allowed frequentist power |
prior.a, prior.b
|
The prior parameters for the beta prior distribution |
nmax |
The maximum sample size to search up to |
round |
Optionally round the probability outputs to 3 significant figures |
method |
Defining the method of optimisation. Either "optimal" or "minmax" |
freq_binom_one_simons_twostage is a wrapper function. It uses ph2simon from the clinfun package to generate optimal sample sizes for the the frequentist single arm, two stage designs. Frequentist and Bayesian properties are then calculated using properties_binom_one and then optimal and minimax designs are returned.
Returns an object of class trialDesign_binom_one
Simon R. (1989). Optimal Two-Stage Designs for Phase II Clinical Trials. Controlled Clinical Trials 10, 1-10.
p0=0.2 p1=0.35 alpha=0.1 power=0.8 freq_binom_one_simons_twostage(p0,p1,alpha,power)p0=0.2 p1=0.35 alpha=0.1 power=0.8 freq_binom_one_simons_twostage(p0,p1,alpha,power)
This function searches for solutions to a single arm two-stage two-endpoint trial first proposed by Bryant and Day (1995). The two endpoints are assumed independent. A wrapper function to compute the Bayesian properties is also provided.
freq_binom_two_bryantday_twostage(r0=0.2, r1=0.35, t0=0.3, t1=0.1, alpha.r, power, nrange, alpha.t=alpha.r)freq_binom_two_bryantday_twostage(r0=0.2, r1=0.35, t0=0.3, t1=0.1, alpha.r, power, nrange, alpha.t=alpha.r)
r0, r1
|
Probability of success under H0 and H1 |
t0, t1
|
Probability of toxicity under H0 and H1 |
alpha.r |
Probability of a false positive trial if the response H0 is true and toxicity is either H0 or H1 |
alpha.t |
Probability of a false positive trial if the toxicity H0 is true and response is either H0 or H1 |
power |
Probability of true positive trial result assuming H1 is true |
nrange |
A vector of the total number of patients to recruit up to each stage of the trial |
Returns an object of class binom_two_bryantday. This can be transformed into an object of class trialDesign_binom_two using properties (see properties) and supplying the necessary values.
Simon R. Optimal two-stage designs for phase II clinical trials. Control Clin Trials 1989; 10: 1-10.
Bryant J, Day R. Incorporating toxicity considerations into the design of two-stage phase II clinical trials. Biometrics 1995; 51: 1372-1383.
r1=0.3 r0=0.1 t0=0.3 t1=0.1 power=0.8 alpha=0.1 ############################################################### # Bryant and Day, two stage nrange=20:27 out=freq_binom_two_bryantday_twostage(r0,r1,t0,t1,alpha,power,nrange) ############################################################### ## Frequentist simulations # modelled toxicity probability t=c(0.1,0.3,0.1,0.3) # modelled response probability r=c(0.3,0.1,0.1,0.3) ## Bayesian uniform prior pra=1;prb=1;pta=1;ptb=1 ## bayesian cutoffs futility_critical_value=0.3 efficacy_critical_value=0.1 toxicity_critical_value=0.1 no_toxicity_critical_value=0.3 byrant_day_optimal=properties(out,t,r,pra,prb,pta,ptb, futility_critical_value,efficacy_critical_value, toxicity_critical_value,no_toxicity_critical_value, target="optimal") byrant_day_minmax=properties(out,t,r,pra,prb,pta,ptb, futility_critical_value,efficacy_critical_value, toxicity_critical_value,no_toxicity_critical_value, target="minmax") bayes_table=list(byrant_day_optimal=byrant_day_optimal, byrant_day_minmax=byrant_day_minmax) class(bayes_table)=c("list_trialDesign_binom_two",class(bayes_table)) bayes_tabler1=0.3 r0=0.1 t0=0.3 t1=0.1 power=0.8 alpha=0.1 ############################################################### # Bryant and Day, two stage nrange=20:27 out=freq_binom_two_bryantday_twostage(r0,r1,t0,t1,alpha,power,nrange) ############################################################### ## Frequentist simulations # modelled toxicity probability t=c(0.1,0.3,0.1,0.3) # modelled response probability r=c(0.3,0.1,0.1,0.3) ## Bayesian uniform prior pra=1;prb=1;pta=1;ptb=1 ## bayesian cutoffs futility_critical_value=0.3 efficacy_critical_value=0.1 toxicity_critical_value=0.1 no_toxicity_critical_value=0.3 byrant_day_optimal=properties(out,t,r,pra,prb,pta,ptb, futility_critical_value,efficacy_critical_value, toxicity_critical_value,no_toxicity_critical_value, target="optimal") byrant_day_minmax=properties(out,t,r,pra,prb,pta,ptb, futility_critical_value,efficacy_critical_value, toxicity_critical_value,no_toxicity_critical_value, target="minmax") bayes_table=list(byrant_day_optimal=byrant_day_optimal, byrant_day_minmax=byrant_day_minmax) class(bayes_table)=c("list_trialDesign_binom_two",class(bayes_table)) bayes_table
Generate minimum sample size for the frequentist two-endpoint single-arm trial.
freq_binom_two_singlestage(r0, r1, t0, t1, power, alpha.r, nmax = 100, alpha.t = alpha.r, nmin = 1, adjust = TRUE)freq_binom_two_singlestage(r0, r1, t0, t1, power, alpha.r, nmax = 100, alpha.t = alpha.r, nmin = 1, adjust = TRUE)
r0 |
Null hypothesis for the response endpoint |
r1 |
Alternative hypothesis for the response endpoint |
t0 |
Null hypothesis for the toxicity endpoint |
t1 |
Alternative hypothesis for the toxicity endpoint |
power |
Required power for the trial design |
alpha.r |
The maximum size for the type one error for the response endpoint |
nmax |
Maximum sample size to look for solutions. Default 100 |
alpha.t |
The maximum size for the type one error for the toxicity endpoint. Optional |
nmin |
Minimum sample size to look for solution, Default 1 |
adjust |
Boolean about whether to adjust for multiple endpoints or not |
Returns an object of class binom_two_singlestage. This can be transformed into an object of class trialDesign_binom_two using properties (see properties) and supplying the necessary values.
r1=0.35 r0=0.2 t0=0.3 t1=0.1 power=0.8 alpha=0.1 nmax=50 out_single=freq_binom_two_singlestage(r0,r1,t0,t1,power,alpha,nmax,adjust=TRUE) ######################################## # Information for properties ## Frequentist simulations # modelled toxicity probability t=c(0.1,0.3,0.1,0.3) # modelled response probability r=c(0.35,0.2,0.2,0.35) ## Bayesian uniform prior pra=1;prb=1;pta=1;ptb=1 ## bayesian cutoffs futility_critical_value=0.35 efficacy_critical_value=0.2 toxicity_critical_value=0.1 no_toxicity_critical_value=0.3 single_stage=properties(out_single,t,r,pra,prb,pta,ptb,futility_critical_value, efficacy_critical_value,toxicity_critical_value,no_toxicity_critical_value) single_stager1=0.35 r0=0.2 t0=0.3 t1=0.1 power=0.8 alpha=0.1 nmax=50 out_single=freq_binom_two_singlestage(r0,r1,t0,t1,power,alpha,nmax,adjust=TRUE) ######################################## # Information for properties ## Frequentist simulations # modelled toxicity probability t=c(0.1,0.3,0.1,0.3) # modelled response probability r=c(0.35,0.2,0.2,0.35) ## Bayesian uniform prior pra=1;prb=1;pta=1;ptb=1 ## bayesian cutoffs futility_critical_value=0.35 efficacy_critical_value=0.2 toxicity_critical_value=0.1 no_toxicity_critical_value=0.3 single_stage=properties(out_single,t,r,pra,prb,pta,ptb,futility_critical_value, efficacy_critical_value,toxicity_critical_value,no_toxicity_critical_value) single_stage
This class is used to compare designs and methodologies frequentist and bayesian properties. To use it create a list of trial designs of class trialDesign_binom_two and assign the class as list_trialDesign_binom_two (class(x)=c("list_trialDesign_binom_two",class(x))).
## S3 method for class 'list_trialDesign_binom_two' print(x, ...)## S3 method for class 'list_trialDesign_binom_two' print(x, ...)
x |
A list of the S4 class object bayes_binom_two_postprob |
... |
Standard arguments to pass to print |
bayes_binom_two_postprob, bayes_binom_two_postlike,bayes_binom_two_loss,freq_binom_two_bryantday_twostage
## Frequentist simulations # modelled toxicity probability t=c(0.1,0.3,0.1,0.3) # modelled response probability r=c(0.35,0.2,0.2,0.35) ## Bayesian uniform prior pra=1;prb=1;pta=1;ptb=1 ## bayesian cutoffs futility_critical_value=0.35 efficacy_critical_value=0.2 toxicity_critical_value=0.1 no_toxicity_critical_value=0.3 ############################################################### # Frequentist methods ############################################################### # Single stage r1=0.35 r0=0.2 t0=0.3 t1=0.1 power=0.8 alpha=0.1 nmax=50 out_single=freq_binom_two_singlestage(r0,r1,t0,t1,power,alpha,nmax, adjust=TRUE) single_stage=properties(out_single,t,r,pra,prb,pta,ptb, futility_critical_value,efficacy_critical_value, toxicity_critical_value,no_toxicity_critical_value) print(single_stage) ############################################################### # Bayesian posterior probability approach # analysis at reviews=c(44) # Stopping rules at each analysis futility_prob_stop=0.9 efficacy_prob_stop=0.9 toxicity_prob_stop=0.9 no_toxicity_prob_stop=0.9 bayes_prob_single=bayes_binom_two_postprob(t,r,reviews,pra,prb,pta, ptb,futility_critical_value,futility_prob_stop, efficacy_critical_value,efficacy_prob_stop, toxicity_critical_value,toxicity_prob_stop, no_toxicity_critical_value,no_toxicity_prob_stop) bayes_prob_single # analysis at reviews=c(10,17,24,30,37,44) # Stopping rules at each analysis futility_prob_stop=c(0.95,0.95,0.95,0.95,0.95,0.9) efficacy_prob_stop=c(1,1,0.95,0.95,0.95,0.9) toxicity_prob_stop=c(0.95,0.95,0.95,0.95,0.95,0.9) no_toxicity_prob_stop=c(1,1,0.95,0.95,0.95,0.9) bayes_prob_six=bayes_binom_two_postprob(t,r,reviews,pra,prb,pta, ptb,futility_critical_value,futility_prob_stop, efficacy_critical_value,efficacy_prob_stop, toxicity_critical_value,toxicity_prob_stop, no_toxicity_critical_value,no_toxicity_prob_stop) plot(bayes_prob_six) ############################################################### # Bayesian posterior likelihood approach ############################################################### reviews=c(11,17,24,30,37,44) efficacy_prob_stop=0.9 toxicity_prob_stop=0.9 # interim required probability to stop int_combined_prob=0.95 int_futility_prob=1 int_toxicity_prob=1 int_efficacy_prob=0.95 bayes_like_six=bayes_binom_two_postlike(t,r,reviews,pra,prb,pta, ptb,efficacy_critical_value,efficacy_prob_stop, toxicity_critical_value,toxicity_prob_stop,int_combined_prob, int_futility_prob,int_toxicity_prob,int_efficacy_prob, futility_critical_value,no_toxicity_critical_value) plot(bayes_like_six) ############################################################### ## Table of all designs ############################################################### tble=list(single_stage=single_stage,bayes_prob_single=bayes_prob_single, bayes_prob_six=bayes_prob_six,bayes_like_six=bayes_like_six) class(tble)=c("list_trialDesign_binom_two",class(tble)) tble ################################################################# Frequentist simulations # modelled toxicity probability t=c(0.1,0.3,0.1,0.3) # modelled response probability r=c(0.35,0.2,0.2,0.35) ## Bayesian uniform prior pra=1;prb=1;pta=1;ptb=1 ## bayesian cutoffs futility_critical_value=0.35 efficacy_critical_value=0.2 toxicity_critical_value=0.1 no_toxicity_critical_value=0.3 ############################################################### # Frequentist methods ############################################################### # Single stage r1=0.35 r0=0.2 t0=0.3 t1=0.1 power=0.8 alpha=0.1 nmax=50 out_single=freq_binom_two_singlestage(r0,r1,t0,t1,power,alpha,nmax, adjust=TRUE) single_stage=properties(out_single,t,r,pra,prb,pta,ptb, futility_critical_value,efficacy_critical_value, toxicity_critical_value,no_toxicity_critical_value) print(single_stage) ############################################################### # Bayesian posterior probability approach # analysis at reviews=c(44) # Stopping rules at each analysis futility_prob_stop=0.9 efficacy_prob_stop=0.9 toxicity_prob_stop=0.9 no_toxicity_prob_stop=0.9 bayes_prob_single=bayes_binom_two_postprob(t,r,reviews,pra,prb,pta, ptb,futility_critical_value,futility_prob_stop, efficacy_critical_value,efficacy_prob_stop, toxicity_critical_value,toxicity_prob_stop, no_toxicity_critical_value,no_toxicity_prob_stop) bayes_prob_single # analysis at reviews=c(10,17,24,30,37,44) # Stopping rules at each analysis futility_prob_stop=c(0.95,0.95,0.95,0.95,0.95,0.9) efficacy_prob_stop=c(1,1,0.95,0.95,0.95,0.9) toxicity_prob_stop=c(0.95,0.95,0.95,0.95,0.95,0.9) no_toxicity_prob_stop=c(1,1,0.95,0.95,0.95,0.9) bayes_prob_six=bayes_binom_two_postprob(t,r,reviews,pra,prb,pta, ptb,futility_critical_value,futility_prob_stop, efficacy_critical_value,efficacy_prob_stop, toxicity_critical_value,toxicity_prob_stop, no_toxicity_critical_value,no_toxicity_prob_stop) plot(bayes_prob_six) ############################################################### # Bayesian posterior likelihood approach ############################################################### reviews=c(11,17,24,30,37,44) efficacy_prob_stop=0.9 toxicity_prob_stop=0.9 # interim required probability to stop int_combined_prob=0.95 int_futility_prob=1 int_toxicity_prob=1 int_efficacy_prob=0.95 bayes_like_six=bayes_binom_two_postlike(t,r,reviews,pra,prb,pta, ptb,efficacy_critical_value,efficacy_prob_stop, toxicity_critical_value,toxicity_prob_stop,int_combined_prob, int_futility_prob,int_toxicity_prob,int_efficacy_prob, futility_critical_value,no_toxicity_critical_value) plot(bayes_like_six) ############################################################### ## Table of all designs ############################################################### tble=list(single_stage=single_stage,bayes_prob_single=bayes_prob_single, bayes_prob_six=bayes_prob_six,bayes_like_six=bayes_like_six) class(tble)=c("list_trialDesign_binom_two",class(tble)) tble ###############################################################
Get frequentist and Bayesian properties for a single-arm single binomial endpoint trial design.
properties_binom_one(failure = NULL, success = NULL, reviews = NULL, p0, p1, prior.a = 0, prior.b = 0, round = TRUE, cutpoints = NULL)properties_binom_one(failure = NULL, success = NULL, reviews = NULL, p0, p1, prior.a = 0, prior.b = 0, round = TRUE, cutpoints = NULL)
failure |
Vector of failures needed to stop the trial |
success |
Vector of successes needed to stop the trial |
reviews |
Vector of the number of patients at each analysis |
p0 |
probability of success under H0 |
p1 |
probability of success under H1 |
prior.a, prior.b
|
beta prior parameters |
round |
Option whether to round results or not |
cutpoints |
Alternative usage, this replaces failure, success and reviews with a data.frame with columns of the same names |
Returns an object of class trialDesign_binom_one.
properties in Package EurosarcBayes ~~~~ Methods for function properties in package EurosarcBayes ~~
signature(x = "ANY")signature(x = "binom_two_bryantday")signature(x = "binom_two_singlestage")This is a shiny app for the LINES trial. This trial is a dual endpoint design with both response and toxicity used to make informed decisions at interim anaylsis. This app provides an interactive way of updating the posterior distribution, as well as change the prior distributions.
shiny_LINES_posterior()shiny_LINES_posterior()
An integral and graph for an acceptable region for the bayesian loss function approach (see bayes_binom_two_loss)
tradeoff_ellipse_integrate(ar, br, at, bt, efficacy_region_min, toxicity_region_max, efficacy_region_max, toxicity_region_min) tradeoff_ellipse_graph(input)tradeoff_ellipse_integrate(ar, br, at, bt, efficacy_region_min, toxicity_region_max, efficacy_region_max, toxicity_region_min) tradeoff_ellipse_graph(input)
ar, br
|
Parameters for the posterior distribution for response |
at, bt
|
Parameters for the posterior distribution for toxicity |
efficacy_region_min |
Smallest acceptable efficacy |
toxicity_region_max |
Largest acceptable toxicity |
efficacy_region_max |
Point where no more tradeoff occurs for efficacy |
toxicity_region_min |
Point where no more tradeoff occurs for toxicity |
input |
A list values needed for the graph. It is expecting max.patients, efficacy_region_min, toxicity_region_max and will error without |
Returns value of the integration.
Chen Y, Smith BJ. Adaptive group sequential design for phase II clinical trials: a Bayesian decision theoretic approach. Stat Med 2009; 28: 3347-3362.
Integration functions and corresponding graphs:
tradeoff_square_integrate,tradeoff_ellipse_integrate,tradeoff_linear_integrate,tradeoff_ratio_integrate
# modelled toxicity probability t=c(0.1,0.1,0.3,0.3) # modelled response probability r=c(0.35,0.2,0.2,0.35) reviews=c(10,15,20,25,30,35,40) stage_after_trial=40 # uniform prior pra=1;prb=1;pta=1;ptb=1 efficacy_critical_value=0.2 futility_critical_value=0.35 toxicity_critical_value=0.1 no_toxicity_critical_value=0.3 # alpha/beta ratio l_alpha_beta=3 # cost of continuing compared to cost of alpha l_alpha_c=750 efficacy_region_min=0.2 toxicity_region_max=0.3 ######################################## # ellipse region efficacy_region_min=0.2 efficacy_region_max=0.35 toxicity_region_min=0.1 toxicity_region_max=0.3 s=bayes_binom_two_loss(t,r,reviews,pra,prb,pta,ptb,l_alpha_beta, l_alpha_c,stage_after_trial,fun.integrate=tradeoff_ellipse_integrate, fun.graph=tradeoff_ellipse_graph,efficacy_critical_value, toxicity_critical_value,futility_critical_value, no_toxicity_critical_value,efficacy_region_min=efficacy_region_min, toxicity_region_max=toxicity_region_max, efficacy_region_max=efficacy_region_max, toxicity_region_min=toxicity_region_min) plot(s)# modelled toxicity probability t=c(0.1,0.1,0.3,0.3) # modelled response probability r=c(0.35,0.2,0.2,0.35) reviews=c(10,15,20,25,30,35,40) stage_after_trial=40 # uniform prior pra=1;prb=1;pta=1;ptb=1 efficacy_critical_value=0.2 futility_critical_value=0.35 toxicity_critical_value=0.1 no_toxicity_critical_value=0.3 # alpha/beta ratio l_alpha_beta=3 # cost of continuing compared to cost of alpha l_alpha_c=750 efficacy_region_min=0.2 toxicity_region_max=0.3 ######################################## # ellipse region efficacy_region_min=0.2 efficacy_region_max=0.35 toxicity_region_min=0.1 toxicity_region_max=0.3 s=bayes_binom_two_loss(t,r,reviews,pra,prb,pta,ptb,l_alpha_beta, l_alpha_c,stage_after_trial,fun.integrate=tradeoff_ellipse_integrate, fun.graph=tradeoff_ellipse_graph,efficacy_critical_value, toxicity_critical_value,futility_critical_value, no_toxicity_critical_value,efficacy_region_min=efficacy_region_min, toxicity_region_max=toxicity_region_max, efficacy_region_max=efficacy_region_max, toxicity_region_min=toxicity_region_min) plot(s)
An integral and graph for an acceptable region for the bayesian loss function approach (see bayes_binom_two_loss)
tradeoff_linear_integrate(ar, br, at, bt, efficacy_region_min, toxicity_region_max, efficacy_region_max, toxicity_region_min) tradeoff_linear_graph(input)tradeoff_linear_integrate(ar, br, at, bt, efficacy_region_min, toxicity_region_max, efficacy_region_max, toxicity_region_min) tradeoff_linear_graph(input)
ar, br
|
Parameters for the posterior distribution for response |
at, bt
|
Parameters for the posterior distribution for toxicity |
efficacy_region_min |
Smallest acceptable efficacy |
toxicity_region_max |
Largest acceptable toxicity |
efficacy_region_max |
Point where no more tradeoff occurs for efficacy |
toxicity_region_min |
Point where no more tradeoff occurs for toxicity |
input |
A list values needed for the graph. It is expecting max.patients, efficacy_region_min, toxicity_region_max and will error without |
Returns value of the integration.
Chen Y, Smith BJ. Adaptive group sequential design for phase II clinical trials: a Bayesian decision theoretic approach. Stat Med 2009; 28: 3347-3362.
Integration functions and corresponding graphs:
tradeoff_square_integrate,tradeoff_ellipse_integrate,tradeoff_linear_integrate,tradeoff_ratio_integrate
# modelled toxicity probability t=c(0.1,0.1,0.3,0.3) # modelled response probability r=c(0.35,0.2,0.2,0.35) reviews=c(10,15,20,25,30,35,40) stage_after_trial=40 # uniform prior pra=1;prb=1;pta=1;ptb=1 efficacy_critical_value=0.2 futility_critical_value=0.35 toxicity_critical_value=0.1 no_toxicity_critical_value=0.3 # alpha/beta ratio l_alpha_beta=3 # cost of continuing compared to cost of alpha l_alpha_c=750 efficacy_region_min=0.2 toxicity_region_max=0.3 ######################################## # linear region efficacy_region_min=0.2 efficacy_region_max=0.35 toxicity_region_min=0.1 toxicity_region_max=0.3 s=bayes_binom_two_loss(t,r,reviews,pra,prb,pta,ptb,l_alpha_beta, l_alpha_c,stage_after_trial,fun.integrate=tradeoff_linear_integrate, fun.graph=tradeoff_linear_graph,efficacy_critical_value, toxicity_critical_value,futility_critical_value, no_toxicity_critical_value,efficacy_region_min=efficacy_region_min, toxicity_region_max=toxicity_region_max, efficacy_region_max=efficacy_region_max, toxicity_region_min=toxicity_region_min) plot(s)# modelled toxicity probability t=c(0.1,0.1,0.3,0.3) # modelled response probability r=c(0.35,0.2,0.2,0.35) reviews=c(10,15,20,25,30,35,40) stage_after_trial=40 # uniform prior pra=1;prb=1;pta=1;ptb=1 efficacy_critical_value=0.2 futility_critical_value=0.35 toxicity_critical_value=0.1 no_toxicity_critical_value=0.3 # alpha/beta ratio l_alpha_beta=3 # cost of continuing compared to cost of alpha l_alpha_c=750 efficacy_region_min=0.2 toxicity_region_max=0.3 ######################################## # linear region efficacy_region_min=0.2 efficacy_region_max=0.35 toxicity_region_min=0.1 toxicity_region_max=0.3 s=bayes_binom_two_loss(t,r,reviews,pra,prb,pta,ptb,l_alpha_beta, l_alpha_c,stage_after_trial,fun.integrate=tradeoff_linear_integrate, fun.graph=tradeoff_linear_graph,efficacy_critical_value, toxicity_critical_value,futility_critical_value, no_toxicity_critical_value,efficacy_region_min=efficacy_region_min, toxicity_region_max=toxicity_region_max, efficacy_region_max=efficacy_region_max, toxicity_region_min=toxicity_region_min) plot(s)
An integral and graph for an acceptable region for the bayesian loss function approach (see bayes_binom_two_loss). tradeoff_ratio_intercepts computes the intercepts of the odd ratio curve with the limits.
tradeoff_ratio_intercepts(R_min,R_max,T_min,T_max,theta=0) tradeoff_ratio_integrate(ar, br, at, bt, efficacy_region_min, toxicity_region_max, efficacy_region_max, toxicity_region_min, theta, intercepts) tradeoff_ratio_graph(input)tradeoff_ratio_intercepts(R_min,R_max,T_min,T_max,theta=0) tradeoff_ratio_integrate(ar, br, at, bt, efficacy_region_min, toxicity_region_max, efficacy_region_max, toxicity_region_min, theta, intercepts) tradeoff_ratio_graph(input)
R_min, R_max, T_min, T_max
|
Limis for tradeoff region |
theta |
odd ratio for efficacy-toxicity tradeoff |
intercepts |
The values returned from tradeoff_ratio_intercepts |
ar, br
|
Parameters for the posterior distribution for response |
at, bt
|
Parameters for the posterior distribution for toxicity |
efficacy_region_min |
Smallest acceptable efficacy |
toxicity_region_max |
Largest acceptable toxicity |
efficacy_region_max |
Point where no more tradeoff occurs for efficacy |
toxicity_region_min |
Point where no more tradeoff occurs for toxicity |
input |
A list values needed for the graph. It is expecting max.patients, efficacy_region_min, toxicity_region_max and will error without |
Returns value of the integration.
Chen Y, Smith BJ. Adaptive group sequential design for phase II clinical trials: a Bayesian decision theoretic approach. Stat Med 2009; 28: 3347-3362.
Integration functions and corresponding graphs:
tradeoff_square_integrate,tradeoff_ellipse_integrate,tradeoff_linear_integrate,tradeoff_ratio_integrate
# modelled toxicity probability t=c(0.1,0.1,0.3,0.3) # modelled response probability r=c(0.35,0.2,0.2,0.35) reviews=c(10,15,20,25,30,35,40) stage_after_trial=40 # uniform prior pra=1;prb=1;pta=1;ptb=1 efficacy_critical_value=0.2 futility_critical_value=0.35 toxicity_critical_value=0.1 no_toxicity_critical_value=0.3 # alpha/beta ratio l_alpha_beta=3 # cost of continuing compared to cost of alpha l_alpha_c=750 efficacy_region_min=0.2 toxicity_region_max=0.3 ######################################## # odds ratio region efficacy_region_min=0.2 efficacy_region_max=0.35 toxicity_region_min=0.1 toxicity_region_max=0.3 theta= 0.275/0.725 * 0.8/0.2 intercepts=tradeoff_ratio_intercepts(efficacy_region_min, efficacy_region_max,toxicity_region_min,toxicity_region_max,theta) s=bayes_binom_two_loss(t,r,reviews,pra,prb,pta,ptb,l_alpha_beta, l_alpha_c,stage_after_trial,fun.integrate=tradeoff_ratio_integrate, fun.graph=tradeoff_ratio_graph,efficacy_critical_value, toxicity_critical_value,futility_critical_value, no_toxicity_critical_value,efficacy_region_min=efficacy_region_min, toxicity_region_max=toxicity_region_max, efficacy_region_max=efficacy_region_max, toxicity_region_min=toxicity_region_min, theta=theta,intercepts=intercepts) plot(s)# modelled toxicity probability t=c(0.1,0.1,0.3,0.3) # modelled response probability r=c(0.35,0.2,0.2,0.35) reviews=c(10,15,20,25,30,35,40) stage_after_trial=40 # uniform prior pra=1;prb=1;pta=1;ptb=1 efficacy_critical_value=0.2 futility_critical_value=0.35 toxicity_critical_value=0.1 no_toxicity_critical_value=0.3 # alpha/beta ratio l_alpha_beta=3 # cost of continuing compared to cost of alpha l_alpha_c=750 efficacy_region_min=0.2 toxicity_region_max=0.3 ######################################## # odds ratio region efficacy_region_min=0.2 efficacy_region_max=0.35 toxicity_region_min=0.1 toxicity_region_max=0.3 theta= 0.275/0.725 * 0.8/0.2 intercepts=tradeoff_ratio_intercepts(efficacy_region_min, efficacy_region_max,toxicity_region_min,toxicity_region_max,theta) s=bayes_binom_two_loss(t,r,reviews,pra,prb,pta,ptb,l_alpha_beta, l_alpha_c,stage_after_trial,fun.integrate=tradeoff_ratio_integrate, fun.graph=tradeoff_ratio_graph,efficacy_critical_value, toxicity_critical_value,futility_critical_value, no_toxicity_critical_value,efficacy_region_min=efficacy_region_min, toxicity_region_max=toxicity_region_max, efficacy_region_max=efficacy_region_max, toxicity_region_min=toxicity_region_min, theta=theta,intercepts=intercepts) plot(s)
An integral and graph for an acceptable region for the bayesian loss function approach (see bayes_binom_two_loss)
tradeoff_square_integrate(ar, br, at, bt, efficacy_region_min, toxicity_region_max) tradeoff_square_graph(input)tradeoff_square_integrate(ar, br, at, bt, efficacy_region_min, toxicity_region_max) tradeoff_square_graph(input)
ar, br
|
Parameters for the posterior distribution for response |
at, bt
|
Parameters for the posterior distribution for toxicity |
efficacy_region_min |
Smallest acceptable efficacy |
toxicity_region_max |
Largest acceptable toxicity |
input |
A list values needed for the graph. It is expecting max.patients, efficacy_region_min, toxicity_region_max and will error without |
Returns value of the integration.
Chen Y, Smith BJ. Adaptive group sequential design for phase II clinical trials: a Bayesian decision theoretic approach. Stat Med 2009; 28: 3347-3362.
Integration functions and corresponding graphs:
tradeoff_square_integrate,tradeoff_ellipse_integrate,tradeoff_linear_integrate,tradeoff_ratio_integrate
# modelled toxicity probability t=c(0.1,0.1,0.3,0.3) # modelled response probability r=c(0.35,0.2,0.2,0.35) reviews=c(10,15,20,25,30,35,40) stage_after_trial=40 # uniform prior pra=1;prb=1;pta=1;ptb=1 efficacy_critical_value=0.2 futility_critical_value=0.35 toxicity_critical_value=0.1 no_toxicity_critical_value=0.3 # alpha/beta ratio l_alpha_beta=3 # cost of continuing compared to cost of alpha l_alpha_c=750 efficacy_region_min=0.2 toxicity_region_max=0.3 ######################################## # square region s=bayes_binom_two_loss(t,r,reviews,pra,prb,pta,ptb,l_alpha_beta, l_alpha_c,stage_after_trial,fun.integrate=tradeoff_square_integrate, fun.graph=tradeoff_square_graph,efficacy_critical_value, toxicity_critical_value,futility_critical_value, no_toxicity_critical_value,efficacy_region_min=efficacy_region_min, toxicity_region_max=toxicity_region_max) plot(s)# modelled toxicity probability t=c(0.1,0.1,0.3,0.3) # modelled response probability r=c(0.35,0.2,0.2,0.35) reviews=c(10,15,20,25,30,35,40) stage_after_trial=40 # uniform prior pra=1;prb=1;pta=1;ptb=1 efficacy_critical_value=0.2 futility_critical_value=0.35 toxicity_critical_value=0.1 no_toxicity_critical_value=0.3 # alpha/beta ratio l_alpha_beta=3 # cost of continuing compared to cost of alpha l_alpha_c=750 efficacy_region_min=0.2 toxicity_region_max=0.3 ######################################## # square region s=bayes_binom_two_loss(t,r,reviews,pra,prb,pta,ptb,l_alpha_beta, l_alpha_c,stage_after_trial,fun.integrate=tradeoff_square_integrate, fun.graph=tradeoff_square_graph,efficacy_critical_value, toxicity_critical_value,futility_critical_value, no_toxicity_critical_value,efficacy_region_min=efficacy_region_min, toxicity_region_max=toxicity_region_max) plot(s)
"trialDesign_binom_one"
This is the s4 class for Binomial one endpoint designs with frequentist and Bayesian properties.
Objects can be created by calls of the form new("trialDesign_binom_one", ...).
reviews:Object of class "numeric", numeric vector of the number of patients an interim analysis will occur at
success:Object of class "numeric", number of successed needed to stop for efficacy
failure:Object of class "numeric", number of failures needed to stop for futility
eta, zeta:Object of class "numeric", bayesiand properties of the design
alpha, power, exp.p0, exp.p1:Object of class "numeric", frequentist properties of the design including the expected sampel size under H0 and H1
p0, p1:Object of class "numeric", the probabilities used for H0 and H1 respectively
signature(x = "trialDesign_binom_one", y = "ANY"): ...
signature(x = "trialDesign_binom_one"): ...
signature(object = "trialDesign_binom_one"): ...
showClass("trialDesign_binom_one")showClass("trialDesign_binom_one")
"trialDesign_binom_two"
This is the s4 class for Binomial two endpoint designs with frequentist and Bayesian properties.
Objects can be created by calls of the form new("trialDesign_binom_two", ...).
reviews:Object of class "numeric", a vector of the number of patients each interim analysis will occur at
data:Object of class "data.frame", exact simulation values for each scenario
cutpoints:Object of class "data.frame", the most extreme cutpoints when cause the trial to stop on their own (ignoring interaction with the other endpoint)
precision:Object of class "numeric", should be a vector of ones confirming probability is all accounted for
decision:Object of class "list", a list of matrices for the decisions to be made at each interim analysis
post.futility, post.efficacy, post.toxicity, post.no_toxicity:Object of class "numeric", The posterior probabilities of the design
graph:Object of class "list", an optional argument to pass to plot for the ploting of the first graph
Exact simulation values for each scenario
signature(x = "trialDesign_binom_two", y = "ANY"): ...
signature(x = "trialDesign_binom_two"): ...
signature(object = "trialDesign_binom_two"): ...
showClass("trialDesign_binom_two")showClass("trialDesign_binom_two")