AdjBCD {carat} R Documentation

## Covariate-adjusted Biased Coin Design

### Description

Allocates patients to one of two treatments based on covariate-adjusted biased coin design as proposed by Baldi Antognini A, Zagoraiou M (2011) <doi:10.1093/biomet/asr021>.

### Usage

AdjBCD(data, a = 3)


### Arguments

 data a data frame. A row of the dataframe corresponds to the covariate profile of a patient. a a design parameter governing the degree of randomness. The default is 3.

### Details

Consider I covaraites and m_i levels for the ith covariate, i=1,\ldots,I. T_j is the assignment of the jth patient and Z_j = (k_1,\dots,k_I) indicates the covariate profile of the jth patient, j=1,\ldots,n. For convenience, (k_1,\dots,k_I) and (i;k_i) denote stratum and margin, respectively. D_j(.) is the difference between numbers of patients assigned to treatment 1 and treatment 2 at the corresponding level after j patients have been assigned.

Let F^a be a decreasing and symmetric function of D_j(.), which depends on a design parameter a\ge 0. Then, the probability of allocating the (j+1)th patient to treatment 1 is F^a(D_j(.)), where

F^a(x)=\frac{1}{x^a + 1},

for x\ge 1,

F^a(x)=1 / 2,

for  x = 0, and

F^a(x)=\frac{|x|^a}{|x|^a + 1},

for x\le -1. As a goes to \infty, the design becomes more deteministic.

Details of the procedure can be found in Baldi Antognini and M. Zagoraiou (2011).

### 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

Baldi Antognini A, Zagoraiou M. The covariate-adaptive biased coin design for balancing clinical trials in the presence of prognostic factors[J]. Biometrika, 2011, 98(3): 519-535.

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

### Examples

# a simple use
## Real Data
## create a dataframe
df <- data.frame("gender" = sample(c("female", "male"), 1000, TRUE, c(1 / 3, 2 / 3)),
"age" = sample(c("0-30", "30-50", ">50"), 1000, TRUE),
"jobs" = sample(c("stu.", "teac.", "others"), 1000, TRUE),
stringsAsFactors = TRUE)
Res <- AdjBCD(df, a = 2)
## view the output
Res

## view all patients' profile and assignments
Res$Cov_Assig ## Simulated Data n <- 1000 cov_num <- 3 level_num <- c(2, 3, 5) # Set pr to follow two tips: #(1) length of pr should be sum(level_num); #(2) sum of probabilities for each margin should be 1. pr <- c(0.4, 0.6, 0.3, 0.4, 0.3, rep(0.2, times = 5)) # set the design parameter a <- 1.8 # obtain result Res.sim <- AdjBCD.sim(n, cov_num, level_num, pr, a) # view the assignments of patients Res.sim$Cov_Assig[cov_num + 1, ]
# view the differences between treatment 1 and treatment 2 at all levels
Res.sim\$Diff



[Package carat version 2.0.2 Index]