DoptBCD {carat} R Documentation

## Atkinson's D_A-optimal Biased Coin Design

### Description

Allocates patients to one of two treatments based on the D_A-optimal biased coin design in the presence of the prognostic factors proposed by Atkinson A C (1982) <doi:10.2307/2335853>.

### Usage

DoptBCD(data)


### Arguments

 data a data frame. A row of the dataframe corresponds to the covariate profile of a patient.

### Details

Consider an experiment involving n patients. Assuming a linear model between response and covariates, Atkinson's D_A-optimal biased coin design sequentially assigns patients to minimize the variance of estimated treatment effects. Supposing j patients have been assigned, the probability of assigning the (j+1)th patient to treatment 1 is

\frac{[1 - (1; \bold{x}^t_{j+1})(\bold{F}^t_j\bold{F}_j)^{-1}\bold{b}_j]^2}{[1-(1; \bold{x}^t_{j+1})(\bold{F}_j^t\bold{F}_j)^{-1}\bold{b}_j]^2+[1 + (1; \bold{x}_{j+1}^t)(\bold{F}_j^t\bold{F}_j)^{-1}\bold{b}_j]^2},

where \bold{X} = (\bold{x_i}, i = 1, \dots, j) and \bold{x}_i = (x_{i1}, \dots, x_{ij}) denote the covariate profile of the ith patient; and \bold{F}_j = [\bold{1}_j; \bold{X}] is the information matrix; and \bold{b}_j^T=(2\bold{T}_j-\bold{1}_j)^T\bold{F}_j, \bold{T}_j = (T_1, \dots, T_j) is a sequence containing the first j patients' allocations.

Details of the procedure can be found in A.C.Atkinson (1982).

### Value

It returns an object of class "carandom".

An object of class "carandom" is a list containing the following components:

 datanumeric a bool indicating whether the data is a numeric data frame. covariates a character string giving the name(s) of the included covariates. strt_num the number of strata. cov_num the number of covariates. level_num a vector of level numbers for each covariate. n the number of patients. Cov_Assig a (cov_num + 1) * n matrix containing covariate profiles for all patients and the corresponding assignments. The ith column represents the ith patient. The first cov_num rows include patients' covariate profiles, and the last row contains the assignments. assignments the randomization sequence. All strata a matrix containing all strata involved. Diff a matrix with only one column. There are final differences at the overall, within-stratum, and within-covariate-margin levels. method a character string describing the randomization procedure to be used. Data Type a character string giving the data type, Real or Simulated. framework the framework of the used randomization procedure: stratified randomization, or model-based method. data the data frame.

### References

Atkinson A C. Optimum biased coin designs for sequential clinical trials with prognostic factors[J]. Biometrika, 1982, 69(1): 61-67.

See DoptBCD.sim for allocating patients with covariate data generating mechanism. See DoptBCD.ui for the command-line user interface.

### Examples

# a simple use
## Real Data
df <- data.frame("gender" = sample(c("female", "male"), 100, TRUE, c(1 / 3, 2 / 3)),
"age" = sample(c("0-30", "30-50", ">50"), 100, TRUE),
"jobs" = sample(c("stu.", "teac.", "others"), 100, TRUE),
stringsAsFactors = TRUE)
Res <- DoptBCD(df)
## view the output
Res

## view all patients' profile and assignments
## Res$Cov_Assig ## Simulated Data n <- 1000 cov_num <- 2 level_num <- c(2, 5) # Set pr to follow two tips: #(1) length of pr should be sum(level_num); #(2)sum of probabilities for each margin should be 1. pr <- c(0.4, 0.6, rep(0.2, times = 5)) Res.sim <- DoptBCD.sim(n, cov_num, level_num, pr) ## view the output Res.sim ## view the difference between treatment 1 and treatment 2 ## at overall, within-strt. and overall levels Res.sim$Diff

N <- 5
n <- 100
cov_num <- 2
level_num <- c(3, 5) # << adjust to your CPU and the length should correspond to cov_num
## Set pr to follow two tips:
## (1) length of pr should be sum(level_num);
## (2)sum of probabilities for each margin should be 1
pr <- c(0.3, 0.4, 0.3, rep(0.2, times = 5))
omega <- c(0.2, 0.2, rep(0.6 / cov_num, times = cov_num))

## generate a container to contain Diff
DH <- matrix(NA, ncol = N, nrow = 1 + prod(level_num) + sum(level_num))
DA <- matrix(NA, ncol = N, nrow = 1 + prod(level_num) + sum(level_num))
for(i in 1 : N){
result <- HuHuCAR.sim(n, cov_num, level_num, pr, omega)
resultA <- StrBCD.sim(n, cov_num, level_num, pr)
DH[ , i] <- result$Diff; DA[ , i] <- resultA$Diff
}
## do some analysis
require(dplyr)

## analyze the overall imbalance
Ana_O <- matrix(NA, nrow = 2, ncol = 3)
rownames(Ana_O) <- c("HuHuCAR", "DoptBCD")
colnames(Ana_O) <- c("mean", "median", "95%quantile")
temp <- DH[1, ] %>% abs
tempA <- DA[1, ] %>% abs
Ana_O[1, ] <- c((temp %>% mean), (temp %>% median),
(temp %>% quantile(0.95)))
Ana_O[2, ] <- c((tempA %>% mean), (tempA %>% median),
(tempA %>% quantile(0.95)))

## analyze the within-stratum imbalances
tempW <- DH[2 : (1 + prod(level_num)), ] %>% abs
tempWA <- DA[2 : 1 + prod(level_num), ] %>% abs
Ana_W <- matrix(NA, nrow = 2, ncol = 3)
rownames(Ana_W) <- c("HuHuCAR", "DoptBCD")
colnames(Ana_W) <- c("mean", "median", "95%quantile")
Ana_W[1, ] = c((tempW %>% apply(1, mean) %>% mean),
(tempW %>% apply(1, median) %>% mean),
(tempW %>% apply(1, mean) %>% quantile(0.95)))
Ana_W[2, ] = c((tempWA %>% apply(1, mean) %>% mean),
(tempWA %>% apply(1, median) %>% mean),
(tempWA %>% apply(1, mean) %>% quantile(0.95)))

## analyze the marginal imbalance
tempM <- DH[(1 + prod(level_num) + 1) :
(1 + prod(level_num) + sum(level_num)), ] %>% abs
tempMA <- DA[(1 + prod(level_num) + 1) :
(1 + prod(level_num) + sum(level_num)), ] %>% abs
Ana_M <- matrix(NA, nrow = 2, ncol = 3)
rownames(Ana_M) <- c("HuHuCAR", "DoptBCD")
colnames(Ana_M) <- c("mean", "median", "95%quantile")
Ana_M[1, ] = c((tempM %>% apply(1, mean) %>% mean),
(tempM %>% apply(1, median) %>% mean),
(tempM %>% apply(1, mean) %>% quantile(0.95)))
Ana_M[2, ] = c((tempMA %>% apply(1, mean) %>% mean),
(tempMA %>% apply(1, median) %>% mean),
(tempMA %>% apply(1, mean) %>% quantile(0.95)))

AnaHP <- list(Ana_O, Ana_M, Ana_W)
names(AnaHP) <- c("Overall", "Marginal", "Within-stratum")

AnaHP


[Package carat version 2.0.2 Index]