sim_dabcd_max_power {RARtrials}

Simulate a Trial Using Doubly Adaptive Biased Coin Design with Maximal Power Strategy for Binary Endpoint

Description

sim_dabcd_max_power can be used for doubly adaptive biased coin design with maximal power strategy for binary outcomes, targeting generalized Neyman allocation and generalized RSIHR allocation.

Usage

sim_dabcd_max_power(
  Pats,
  nMax,
  TimeToOutcome,
  enrollrate,
  N1,
  N2,
  armn,
  armlabel,
  h,
  BB,
  type,
  gamma = 2,
  alphaa = 0.025,
  side
)

Arguments

Pats

the number of patients accrued within a certain time frame indicates the count of individuals who have been affected by the disease during that specific period, for example, a month or a day. If this number is 10, it represents that 10 people have got the disease within the specified time frame.

nMax

the assumed maximum accrued number of patients with the disease in the population, this number should be chosen carefully to ensure a sufficient number of patients are simulated, especially when considering the delay mechanism.

TimeToOutcome

the distribution of delayed response times or a fixed delay time for responses. The delayed time could be a month, a week or any other time frame. When the unit changes, the number of TimeToOutcome should also change. It can be in the format of expression(rnorm( length( vStartTime ),30, 3)), representing delayed responses with a normal distribution, where the mean is 30 days and the standard deviation is 3 days.

enrollrate

probability that patients in the population can enroll in the trial. This parameter is related to the number of people who have been affected by the disease in the population, following an exponential distribution.

N1

number of participants with equal randomization in the burn-in period. Recommend using 10 percent of the total sample size.

N2

maximal sample size for the trial.

armn

number of total arms in the trial.

armlabel

a vector of arm labels with an example of c(1, 2), where 1 and 2 describes how each arm is labeled in a two-armed trial.

h

a vector of success probabilities in hypotheses, for example, as c(0.1,0.1) where 0.1 stands for the success probability for both groups. Another example is c(0.1,0.3) where 0.1 and 0.3 stand for the success probabilities for the control and the treatment group, respectively.

BB

the minimal allocation probabilities for each arm, which is within the range of [0,1/armn].

type

allocation type, with choices from 'RSIHR' and 'Neyman'.

gamma

tuning parameter in Hu & Zhang's formula. When dabcd=0, this parameter does not need to be specified. Default value is set to 2.

alphaa

the overall type I error to be controlled for the one-sided test. Default value is set to 0.025.

side

direction of a one-sided test, with values 'upper' or 'lower'.

Details

The function simulates a trial for doubly adaptive biased coin design with maximal power strategy targeting generalized Neyman allocation with 2-5 arms which is provided in (Tymofyeyev et al. 2007) and generalized RSIHR allocation with 2-3 arms which is provided in (Jeon and Feifang 2010), with modifications for typos in (Sabo and Bello 2016). All of those methods are not smoothed. The output of this function is based on Hu \& Zhang's formula (Hu and Zhang 2004). With more than two armd the one-sided nominal level of each test is alphaa divided by arm*(arm-1)/2; a Bonferroni correction. Considering the delay mechanism, Pats (the number of patients accrued within a certain time frame), nMax (the assumed maximum accrued number of patients with the disease in the population) and TimeToOutcome (the distribution of delayed response times or a fixed delay time for responses) are parameters in the functions adapted from https://github.com/kwathen/IntroBayesianSimulation. Refer to the website for more details.

Value

sim_dabcd_max_power returns an object of class "dabcd". An object of class "dabcd" is a list containing final decision based on the Z test statistics with 1 stands for selected and 0 stands for not selected, Z test statistics, the simulated data set and participants accrued for each arm at the time of termination of that group in one trial. The simulated data set includes 5 columns: participant ID number, enrollment time, observed time of results, allocated arm, and participants' result.

References

Hu F, Zhang L (2004). “Asymptotic Properties of Doubly Adaptive Biased Coin Designs for Multitreatment Clinical Trials.” The Annals of Statistics, 32(1), 268–301. Tymofyeyev Y, Rosenberger WF, Hu F (2007). “Implementing Optimal Allocation in Sequential Binary Response Experiments.” Journal of the American Statistical Association, 102(477), 224-234. doi:10.1198/016214506000000906. Jeon Y, Feifang H (2010). “Optimal Adaptive Designs for Binary Response Trials With Three Treatments.” Statistics in Biopharmaceutical Research, 2, 310-318. doi:10.1198/sbr.2009.0056. Sabo R, Bello G (2016). “Optimal and lead-in adaptive allocation for binary outcomes: a comparison of Bayesian methodologies.” Communications in Statistics - Theory and Methods, 46.

Examples

sim_dabcd_max_power(Pats=10,nMax=50000,TimeToOutcome=expression(rnorm(
length( vStartTime ),30, 3)),enrollrate=0.9,N1=30,N2=300,armn=3,
armlabel=c(1,2,3),h=c(0.2,0.3,0.2),BB=0.1,type='Neyman',
side='upper')
sim_dabcd_max_power(Pats=10,nMax=50000,TimeToOutcome=expression(rnorm(
length( vStartTime ),60, 3)),enrollrate=0.1,N1=50,N2=500,armn=3,
armlabel=c(1,2,3),h=c(0.2,0.3,0.3),BB=0.15,type='RSIHR',
side='upper')