carat (version 1.1)

evalRand: Evaluation of Randomization Procedures

Description

Evaluates a specific randomization procedure based on several different quantities of imbalances.

Usage

# S3 method for careval
evalRand(data, method = "HuHuCAR", N = 500, ...)

Arguments

data

a dataframe. A row of the dataframe contains the covariate profile of a patient.

N

the iteration number.

method

the randomization method to be used in allocating patients. The default randomization “HuHuCAR” uses Hu and Hu's general covariate-adaptive randomization; the alternatives are “PocSimMIN”, “StrBCD”, “StrPBR”, “DoptBCD”, and “AdjBCD”.

…

arguments to be passed to methods. These depend on the method and the following arguments are accepted:

omega

the vector of weights at the overall, within-stratum, and marginal levels. It is required that at least one element is larger than 0. Note that omega is only needed when HuHuCAR is to be assessed.

weight

the vector of weights for all involved margins. It is required that at least one element is NOT 0 and length(weight) = cov_num. Note that weight is only needed when PocSimMIN is to be assessed.

p

the probability of assigning one patinet to treatment 1. p should be larger than 1/2 to obtain balance. Note that p is only needed when "HuHuCAR", "PocSimMIN" and "StrBCD" are to be assessed.

a

a design parameter. As a goes to \(\infty\), the design becomes more deteministic. Note that a is only needed when "AdjBCD" is to be assessed.

bsize

the block size for stratified permuted block randomization. It is required to be a multiple of 2. Note that bsize is only needed when "StrPBR" is to be assessed.

Value

It returns an object of class "careval".

The function print is used to obtain results. The generic accessor functions Assig, Diff, data, All strata and others extract various useful features of the value returned by evalRand.

An object of class "careval" is a list containing at least the following components:

N

the number of patients.

Assig

a n*N matrix containing assignments for each patient for N iterations.

Imb

a matrix containing maximum, 95%-quantile, median, and mean of absolute imbalances at overall, each within-stratum and each marginal levels.

SNUM

a matrix with N colunms containing number of patients at overall, each marginal and each within-stratum levels for each iteration.

Data Type

the data type. Real or Simulated.

Details

The data is designed for N times using method.

References

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

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.

Hu Y, Hu F. Asymptotic properties of covariate-adaptive randomization[J]. The Annals of Statistics, 2012, 40(3): 1794-1815.

Pocock S J, Simon R. Sequential treatment assignment with balancing for prognostic factors in the controlled clinical trial[J]. Biometrics, 1975: 103-115.

Shao J, Yu X, Zhong B. A theory for testing hypotheses under covariate-adaptive randomization[J]. Biometrika, 2010, 97(2): 347-360.

Zelen M. The randomization and stratification of patients to clinical trials[J]. Journal of chronic diseases, 1974, 27(7): 365-375.

See Also

See evalRand.sim to evaluate a randomization procedure with covariate data generating mechanism.

Examples

# NOT RUN {
# a simple use
## Access by 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 <- evalRand(data = df, method = "HuHuCAR", N = 500, 
                omega = c(1, 2, rep(1, ncol(df))), p = 0.85)
## view the output
Res
# }
# NOT RUN {
  ## view all patients' assignments
  Res$Assig
# }
# NOT RUN {
## Assess by simulated data
cov_num <- 3
level_num <- c(2, 3, 5)
pr <- c(0.35, 0.65, 0.25, 0.35, 0.4, 0.25, 0.15, 0.2, 0.15, 0.25)
n <- 1000
N <- 50
omega = c(1, 2, 1, 1, 2)
# assess Hu and Hu's procedure with the same group of patients
Res.sim <- evalRand.sim(n = n, N = N, Replace = FALSE, cov_num = cov_num, 
                        level_num = level_num, pr = pr, method = "HuHuCAR", 
                        omega, p = 0.85)
# }
# NOT RUN {
  ## Compare four procedures
  cov_num <- 3
  level_num <- c(2, 10, 2)
  pr <- c(rep(0.5, times = 2), rep(0.1, times = 10), rep(0.5, times = 2))
  n <- 100
  N <- 200 # <<adjust according to CPU
  bsize <- 4
  ## set weights for HuHuCAR
  omega <- c(1, 2, rep(1, cov_num)); 
  ## set weights for PocSimMIN
  weight = rep(1, cov_num); 
  ## set biased probability
  p = 0.80
  # assess Hu and Hu's procedure
  RH <- evalRand.sim(n = n, N = N, Replace = FALSE, cov_num = cov_num, 
                     level_num = level_num, pr = pr, method = "HuHuCAR", 
                     omega = omega, p = p)
  # assess Pocock and Simon's method
  RPS <- evalRand.sim(n = n, N = N, Replace = FALSE, cov_num = cov_num, 
                      level_num = level_num, pr = pr, method = "PocSimMIN", 
                      weight, p = p)
  # assess Shao's procedure
  RS <- evalRand.sim(n = n, N = N, Replace = FALSE, cov_num = cov_num, 
                     level_num = level_num, pr = pr, method = "StrBCD", 
                     p = p)
  # assess stratified randomization
  RSR <- evalRand.sim(n = n, N = N, Replace = FALSE, cov_num = cov_num, 
                      level_num = level_num, pr = pr, method = "StrPBR", 
                      bsize)
  
  # create containers
  C_M = C_O = C_WS = matrix(NA, nrow = 4, ncol = 4)
  colnames(C_M) = colnames(C_O) = colnames(C_WS) = 
    c("max", "95%quan", "med", "mean")
  rownames(C_M) = rownames(C_O) = rownames(C_WS) = 
    c("HH", "PocSim", "Shao", "StraRand")
  
  # assess the overall imbalance
  C_O[1, ] = RH$Imb[1, ]
  C_O[2, ] = RPS$Imb[1, ]
  C_O[3, ] = RS$Imb[1, ]
  C_O[4, ] = RSR$Imb[1, ]
  # view the result
  C_O
  
  # assess the marginal imbalances
  C_M[1, ] = apply(RH$Imb[(1 + RH$strt_num) : (1 + RH$strt_num + sum(level_num)), ], 2, mean)
  C_M[2, ] = apply(RPS$Imb[(1 + RPS$strt_num) : (1 + RPS$strt_num + sum(level_num)), ], 2, mean)
  C_M[3, ] = apply(RS$Imb[(1 + RS$strt_num) : (1 + RS$strt_num + sum(level_num)), ], 2, mean)
  C_M[4, ] = apply(RSR$Imb[(1 + RSR$strt_num) : (1 + RSR$strt_num + sum(level_num)), ], 2, mean)
  # view the result
  C_M
  
  # assess the within-stratum imbalances
  C_WS[1, ] = apply(RH$Imb[2 : (1 + RH$strt_num), ], 2, mean)
  C_WS[2, ] = apply(RPS$Imb[2 : (1 + RPS$strt_num), ], 2, mean)
  C_WS[3, ] = apply(RS$Imb[2 : (1 + RS$strt_num), ], 2, mean)
  C_WS[4, ] = apply(RSR$Imb[2 : (1 + RSR$strt_num), ], 2, mean)
  # view the result
  C_WS
  
  # Compare the four procedures through plots
  meth = rep(c("Hu", "PS", "Shao", "STR"), times = 3)
  shape <- rep(1 : 4, times = 3)
  crt <- rep(1 : 3, each = 4)
  crt_c <- rep(c("O", "M", "WS"), each = 4)
  mean <- c(C_O[, 4], C_M[, 4], C_WS[, 4])
  df_1 <- data.frame(meth, shape, crt, crt_c, mean, 
                     stringsAsFactors = TRUE)
  
  require(ggplot2)
  p1 <- ggplot(df_1, aes(x = meth, y = mean, color = crt_c, group = crt,
                         linetype = crt_c, shape = crt_c)) +
    geom_line(size = 1) +
    geom_point(size = 2) +
    xlab("method") +
    ylab("absolute mean") +
    theme(plot.title = element_text(hjust = 0.5))
  p1
# }