compRand {carat} | R Documentation |

Compares randomization procedures based on several different quantities of imbalances. Among all included randomization procedures of class `"careval"`

, two or more procedures can be compared in this function.

```
compRand(...)
```

`...` |
objects of class |

The primary goal of using covariate-adaptive randomization in practice is to achieve balance with respect to the key covariates. We choose four rules to measure the absolute imbalances at overall, within-covariate-margin, and within-stratum levels, which are maximal, 95%quantile, median and mean of the absolute imbalances at different aspects. The Monte Carlo method is used to calculate the four types of imbalances. Let `D_{n,i}(\cdot)`

be the final difference at the corresponding level for `i`

th iteration, `i=1,\ldots`

, `N`

, and `N`

is the number of iterations.

(1) Maximal

`\max_{i = 1, \dots, N}|D_{n,i}(\cdot)|.`

(2) 95% quantile

`|D_{n,\lceil0.95N\rceil}(\cdot)|.`

(3) Median

`|D_{n,(N+1)/2}(\cdot)|`

for `N`

is odd, and

`\frac{1}{2}(|D_{(N/2)}(\cdot)|+|D_{(N/2+1)}(\cdot)|)`

for `N`

is even.

(4) Mean

`\frac{1}{N}\sum_{i = 1}^{N}|D_{n, i}(\cdot)|.`

It returns an object of `class`

`"carcomp"`

.

An object of class `"carcomp"`

is a list containing the following components:

`Overall Imbalances` |
a matrix containing the maximum, 95%-quantile, median, and mean of the absolute overall imbalances for the randomization method(s) to be evaluated. |

`Within-covariate-margin Imbalances Imbalances` |
a matrix containing the maximum, 95%-quantile, median, and mean of the absolute within-covariate-margin imbalances for the randomization method(s) to be evaluated. |

`Within-stratum Imbalances` |
a matrix containing the maximum, 95%-quantile, median, and mean of the absolute within-stratum imbalances for the randomization method(s) to be evaluated. |

`dfmm` |
a data frame containing the mean absolute imbalances at the overall, within-stratum, and within-covariate-margin levels for the randomization method(s) to be evaluated. |

`df_abm` |
a data frame containing the absolute imbalances at the overall, within-stratum, and within-covariate-margin levels. |

`mechanism` |
a character string giving the randomization method(s) to be evaluated. |

`n` |
the number of patients. |

`iteration` |
the number of iterations. |

`cov_num` |
the number of covariates. |

`level_num` |
a vector of level numbers for each covariate. |

`Data Type` |
a character string giving the data type, |

`DataGeneration` |
a bool vector indicating whether the data used for all the iterations is the same for the randomization method(s) to be evaluated. |

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 `evalRand`

or `evalRand.sim`

to evaluate a specific randomization procedure.

```
## Compare stratified permuted block randomization and Hu and Hu's general CAR
cov_num <- 2
level_num <- c(2, 2)
pr <- rep(0.5, 4)
n <- 500
N <- 20 # <<adjust according to CPU
bsize <- 4
# set weight for Hu and Hu's method, it satisfies
# (1)Length should equal to cov_num
omega <- c(1, 2, 1, 1)
# Assess Hu and Hu's general CAR
Obj1 <- evalRand.sim(n = n, N = N, Replace = FALSE, cov_num = cov_num,
level_num = level_num, pr = pr, method = "HuHuCAR",
omega, p = 0.85)
# Assess stratified permuted block randomization
Obj2 <- evalRand.sim(n = n, N = N, Replace = FALSE, cov_num = cov_num,
level_num = level_num, pr = pr, method = "StrPBR",
bsize)
RES <- compRand(Obj1, Obj2)
```

[Package *carat* version 2.0.2 Index]