AdjBCD {carat} | R Documentation |

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>.

```
AdjBCD(data, a = 3)
```

`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 |

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).

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 |

`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, |

`framework` |
the framework of the used randomization procedure: stratified randomization, or model-based method. |

`data` |
the data frame. |

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.

```
# 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]