grouprar (version 0.1.0)

dyldDBCD_Cont: Hu and Zhang's Doubly Biased Coin Deisgn with delayed Continuous Response

Description

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

Usage

dyldDBCD_Cont(n0 = 20, theta, k, ssn, ent.param, rspT.dist, rspT.param,
              target.alloc = "Neyman", r = 2, nsim = 2000, mRate = NULL, alpha = 0.05)

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 average response value for the entire trial.

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.

Arguments

n0

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

theta

A numerical vector of length equal to 2k. These values specify the true parameters for each treatment and are used for generating data in simulations. For example, if k=2, you should provide two pairs of parameter values, each consisting of the mean and variance, like: theta = c(13, 4.0^2, 15, 2.5^2).

k

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

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))

target.alloc

Desired allocation proportion. The option for this argument could be one of "Neyman", "ZR", "DaOptimal". The default is "Neyman". The details see Zhang L. and Rosenberger. W (2006).

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 Contiunous 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.

References

Hu, F., & Zhang, L. X. (2004). Asymptotic properties of doubly adaptive biased coin designs for multi-treatment clinical trials. The Annals of Statistics, 32(1), 268-301.

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
theta = c(13, 4.0^2, 15, 2.5^2)
k = 2
ssn = 88

### for enter time and response time simulation
ent.param = 5
rspT.param = rep(10, 2)
rspT.dist = "exponential"

## Arguments for the deisgn
target.alloc = "Neyman"

res = dyldDBCD_Cont(n0 = 10, theta, k, ssn, ent.param, rspT.dist,
                    rspT.param, target.alloc, r = 2, nsim = 200,
                    mRate = 0.2, alpha = 0.05)

# View the output (A list of all results)
res