PocSimMIN {carat} | R Documentation |

Allocates patients to one of two treatments using Pocock and Simon's method proposed by Pocock S J, Simon R (1975) <doi:10.2307/2529712>.

```
PocSimMIN(data, weight = NULL, p = 0.85)
```

`data` |
a data frame. A row of the dataframe corresponds to the covariate profile of a patient. |

`weight` |
a vector of weights for within-covariate-margin imbalances. It is required that at least one element is larger than 0. If |

`p` |
the biased coin probability. |

Consider `I`

covariates 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 this patient, `j=1,\ldots,n`

. For convenience, `(k_1,\dots,k_I)`

and `(i;k_i)`

denote the stratum and margin, respectively. `D_j(.)`

is the difference between the numbers of patients assigned to treatment `1`

and treatment `2`

at the corresponding levels after `j`

patients have been assigned. The Pocock and Simon's minimization procedure is as follows:

(1) The first patient is assigned to treatment `1`

with probability `1/2`

;

(2) Suppose that `j-1`

patients have been assigned (`1<j\le n`

) and the `j`

th patient falls within `(k_1^*,\dots,k_I^*)`

;

(3) If the `j`

th patient were assigned to treatment `1`

, then the potential within-covariate-margin differences between the two treatments would be

`D_j^{(1)}(i;k_i^*)=D_{j-1}(i,k_i^*)+1`

for margin `(i;k_i^*)`

. Similarly, the potential differences would be obtained in the same way if the `j`

th patient were assigned to treatment `2`

;

(4) An imbalance measure is defined by

`Imb_j^{(l)}=\sum_{i=1}^{I}\omega_{m,i}[D_j^{(l)}(i;k_i^*)]^2,l=1,2;`

(5) Conditional on the assignments of the first (`j-1`

) patients as well as the covariate profiles of the first `j`

patients, assign the `j`

th patient to treatment `1`

with the probability

`P(T_j=1|Z_j,T_1,\dots,T_{j-1})=q`

for `Imb_j^{(1)}>Imb_j^{(2)},`

`P(T_j=1|Z_j,T_1,\dots,T_{j-1})=p`

for `Imb_j^{(1)}<Imb_j^{(2)}`

, and

`P(T_j=1|Z_j,T_1,\dots,T_{j-1})=0.5`

for `Imb_j^{(1)}=Imb_j^{(2)}.`

Details of the procedure can be found in Pocock S J, Simon R (1975).

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, |

`weight` |
a vector giving the weights imposed on each covariate. |

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

`data` |
the data frame. |

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

See `PocSimMIN.sim`

for allocating patients with covariate data generating mechanism.
See `PocSimMIN.ui`

for the command-line user interface.

```
# a simple use
## Real Data
## creat 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)
weight <- c(1, 2, 1)
Res <- PocSimMIN(data = df, weight)
## view the output
Res
## view all patients' profile and assignments
Res$Cov_Assig
## Simulated Data
cov_num = 3
level_num = c(2, 3, 3)
pr = c(0.4, 0.6, 0.3, 0.3, 0.4, 0.4, 0.3, 0.3)
Res.sim <- PocSimMIN.sim(n = 1000, cov_num, level_num, pr)
## view the output
Res.sim
## view the detials of difference
Res.sim$Diff
N <- 5
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))
omega <- c(0.2, 0.2, rep(0.6 / cov_num, times = cov_num))
weight <- c(2, rep(1, times = cov_num - 1))
## generate a container to contain Diff
DH <- matrix(NA, ncol = N, nrow = 1 + prod(level_num) + sum(level_num))
DP <- matrix(NA, ncol = N, nrow = 1 + prod(level_num) + sum(level_num))
for(i in 1 : N){
result <- HuHuCAR.sim(n, cov_num, level_num, pr, omega)
resultP <- PocSimMIN.sim(n, cov_num, level_num, pr, weight)
DH[ , i] <- result$Diff; DP[ , i] <- resultP$Diff
}
## do some analysis
require(dplyr)
## analyze the overall imbalance
Ana_O <- matrix(NA, nrow = 2, ncol = 3)
rownames(Ana_O) <- c("NEW", "PS")
colnames(Ana_O) <- c("mean", "median", "95%quantile")
temp <- DH[1, ] %>% abs
tempP <- DP[1, ] %>% abs
Ana_O[1, ] <- c((temp %>% mean), (temp %>% median),
(temp %>% quantile(0.95)))
Ana_O[2, ] <- c((tempP %>% mean), (tempP %>% median),
(tempP %>% quantile(0.95)))
## analyze the within-stratum imbalances
tempW <- DH[2 : (1 + prod(level_num)), ] %>% abs
tempWP <- DP[2 : 1 + prod(level_num), ] %>% abs
Ana_W <- matrix(NA, nrow = 2, ncol = 3)
rownames(Ana_W) <- c("NEW", "PS")
colnames(Ana_W) <- c("mean", "median", "95%quantile")
Ana_W[1, ] = c((tempW %>% apply(1, mean) %>% mean),
(tempW %>% apply(1, median) %>% mean),
(tempW %>% apply(1, mean) %>% quantile(0.95)))
Ana_W[2, ] = c((tempWP %>% apply(1, mean) %>% mean),
(tempWP %>% apply(1, median) %>% mean),
(tempWP %>% apply(1, mean) %>% quantile(0.95)))
## analyze the marginal imbalance
tempM <- DH[(1 + prod(level_num) + 1) :
(1 + prod(level_num) + sum(level_num)), ] %>% abs
tempMP <- DP[(1 + prod(level_num) + 1) :
(1 + prod(level_num) + sum(level_num)), ] %>% abs
Ana_M <- matrix(NA, nrow = 2, ncol = 3)
rownames(Ana_M) <- c("NEW", "PS")
colnames(Ana_M) <- c("mean", "median", "95%quantile")
Ana_M[1, ] = c((tempM %>% apply(1, mean) %>% mean),
(tempM %>% apply(1, median) %>% mean),
(tempM %>% apply(1, mean) %>% quantile(0.95)))
Ana_M[2, ] = c((tempMP %>% apply(1, mean) %>% mean),
(tempMP %>% apply(1, median) %>% mean),
(tempMP %>% apply(1, mean) %>% quantile(0.95)))
AnaHP <- list(Ana_O, Ana_M, Ana_W)
names(AnaHP) <- c("Overall", "Marginal", "Within-stratum")
AnaHP
```

[Package *carat* version 2.0.2 Index]