AdjBCD: 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)

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 $i$th column represents the $i$th 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.

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 $i$th covariate, $i=1,\ldots,I$. $T_j$ is the assignment of the $j$th patient and $Z_j = (k_1,\dots,k_I)$ indicates the covariate profile of the $j$th 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).

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.

Ma W, Ye X, Tu F, Hu F. carat: Covariate-Adaptive Randomization for Clinical Trials[J]. Journal of Statistical Software, 2023, 107(2): 1-47.

Examples

Run this code

# 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
# \donttest{
  ## 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)
# \donttest{
  # 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
  # }

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