dyldDBCD_Bin {grouprar}

Hu and Zhang's Doubly Biased Coin Deisgn with delayed Binary Response

Description

Simulating Hu and Zhang's doubly biased coin deisgn with delayed binary response (number of arms \ge 2) in a clinical trial context. (Inference: two-sided hypothesis testing t-test or chi-square test)

Usage

dyldDBCD_Bin(n0 = 20, p, k, ssn, ent.param, rspT.dist,
             rspT.param, theta0 = NULL, target.alloc = "RPW", r = 2,
             nsim = 2000, mRate = NULL, alpha = 0.05)

Arguments

n0

A positive integer. n0 represents the initial patient population assogned through restricted randomization for initial parameter estimation.

p

A positive vector of length equals to k. The values specify the true success rates for the various treatments, and these rates are used to generate data for simulations.

k

A positive integer. The value specifies the number of treatment groups involved in a clinical trial. (k = 2)

ssn

A positive integer. The value specifies the total number of participants involved in each round of the simulation.

ent.param

A positive integer. The value specified the parameter for an expoential distribution which determine the time for each participant enter the trial.

rspT.dist

Distribution Type. Specifies the type of distribution that models the time spent for the availability of patient i under treatment k. Acceptable options for this argument include: "exponential", "normal", and "uniform".

rspT.param

A vector. Specifies the parameters required by the distribution that models the time spent for the availability under each treatment. (eg. If there are 3 treatments groups and each of them follows truncated normal distribution with parameter pair (3, 2), (2, 1), (4, 1), repectively. Then the rspT.param = c(3, 2, 2, 1, 4, 1))

theta0

A vector of length k. Each value in the vector represents a probability used for adjusting parameter estimates. If the argument is not provided, it defaults to a vector of length k, with all values set to 0.5.

target.alloc

Desired allocation proportion. The option for this argument could be one of "Neyman", "RSIHR", "RPW", "WeisUrn". The default is "RPW".

r

A positive number. Parameter for Hu and Zhang's doubly biased coin design and usually take values 2-4. The default value is 2.

nsim

a positive integer. The value specifies the total number of simulations, with a default value of 2000.

mRate

a numerical value between 0 and 1, inclusive, representing the missing rate for the responses. This parameter pertains to missing-at-random data. The default value is NULL, indicating no missing values by default.

alpha

a numerical value between 0 and 1. The value represents the predetermined level of significance that defines the probability threshold for rejecting the null hypothesis, with a default value of 0.05.

Details

Hu and Zhang's Doubly Biased Coin Design with delayed Binary Response employs the following treatment allocation scheme:

(a) Initially, due to limited information about treatment efficacy, the first n0 patients are assigned to K treatments using restricted randomization (as described by Rosenberger and Lachin, 2002).

(b) For m \ge n_0, patient (m+1) is allocated to treatment k with a probability p_{m+1, k}, which depends on the available responses and estimated target allocation via g_k, as proposed by Hu and Zhang (2004).

For a more comprehensive description of the procedure, please refer to the paper titled 'Doubly adaptive biased coin designs with delayed responses' authored by Hu et al. in 2008.

Value

name

The name of procedure.

parameter

The true parameters used to do the simulations.

assignment

The randomization sequence.

propotion

Average allocation porpotion for each of treatment groups.

failRate

The proportion of individuals who do not achieve the expected outcome in each simulation, on average.

pwClac

The probability of the study to detect a significant difference or effect if it truly exists.

k

Number of arms involved in the trial.

References

Hu, F., Zhang, L. X., Cheung, S. H., & Chan, W. S. (2008). Doubly adaptive biased coin designs with delayed responses. Canadian Journal of Statistics, 36(4), 541-559.

Examples

# a simple use
# Define the arguments
## Arguments for generate the simulated data
### For response simulation
p = c(0.6, 0.8)
k = 2
ssn = 100
### for enter time and response time simulation
ent.param = 0.7
rspT.dist = "exponential"
rspT.param = c(1, 1, 3, 1)

## Arguments for the deisgn
n0 = 20
target.alloc = "RSIHR"

dyldDBCD_Bin(n0 = n0, p = p, k = k, ssn = ssn, ent.param, rspT.dist, rspT.param, theta0 = NULL,
             target.alloc, r = 2, nsim = 150, mRate = NULL, alpha = 0.05)