Description Usage Arguments Details Value References See Also Examples

View source: R/rand_completeData.R

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>.

1 |

`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,…,I*. *T_j* is the assignment of the *j*th patient and *Z_j = (k_1,…,k_I)* indicates the covariate profile of this patient, *j=1,…,n*. For convenience, *(k_1,…,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≤ n*) and the *j*th patient falls within *(k_1^*,…,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)}=∑_{i=1}^{I}ω_{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,…,T_{j-1})=q*

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

*P(T_j=1|Z_j,T_1,…,T_{j-1})=p*

for *Imb_j^{(1)}<Imb_j^{(2)}*, and

*P(T_j=1|Z_j,T_1,…,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.

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# 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
``` |

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