sim_Aa_optimal_known_var {RARtrials}

Simulate a Trial Using Aa-Optimal Allocation for Continuous Endpoint with Known Variances

Description

sim_Aa_optimal_known_var simulates a trial for continuous endpoints with known variances, and the allocation probabilities are fixed.

Usage

sim_Aa_optimal_known_var(
  Pats,
  nMax,
  TimeToOutcome,
  enrollrate,
  N2,
  armn,
  mean,
  sd,
  alphaa = 0.025,
  armlabel,
  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.

N2

maximal sample size for the trial.

armn

number of total arms in the trial.

mean

a vector of hypotheses of mean for all arms in the trial, with the first one serving as the control group.

sd

a vector of hypotheses of standard deviation for allarms in the trial, with the first one serving as the control group.

alphaa

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

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.

side

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

Details

This function aims to minimize the criteria tr[A^TM^{-1}(\rho)A] and minimize the overall variance of pairwise comparisons. It is analogous to Neyman allocation, favoring a higher allocation ratio to the control group. With more than two treatment groups 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_Aa_optimal_known_var returns an object of class "Aaoptimal". An object of class "Aaoptimal" 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

Sverdlov O, Rosenberger W (2013). “On Recent Advances in Optimal Allocation Designs in Clinical Trials.” Journal of Statistical Theory and Practice, 7, 753-773. doi:10.1080/15598608.2013.783726.

Examples

#Run the function with delayed responses follow a normal distribution with
#a mean of 30 days and a standard deviation of 3 days under null hypothesis
#in a two-armed trial
sim_Aa_optimal_known_var(Pats=10,nMax=50000,TimeToOutcome=expression(
rnorm(length( vStartTime ),30, 3)),enrollrate=0.9,N2=88,armn=2,
mean=c(9.1/100,9.1/100),sd=c(0.009,0.009),alphaa=0.025,armlabel = c(1,2),side='lower')

#Run the function with delayed responses follow a normal distribution with
#a mean of 30 days and a standard deviation of 3 days under alternative hypothesis
#in a two-armed trial
sim_Aa_optimal_known_var(Pats=10,nMax=50000,TimeToOutcome=expression(
rnorm(length( vStartTime ),30, 3)),enrollrate=0.9,N2=88,armn=2,
mean=c(9.1/100,8.47/100),sd=c(0.009,0.009),alphaa=0.025,armlabel = c(1,2),side='lower')