PocSimMIN: Pocock and Simon's Method in the Two-Arms Case In carat: Covariate-Adaptive Randomization for Clinical Trials

Description

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>.

Usage

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

Arguments

 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 weight = NULL (default), the within-covariate-margin imbalances are weighted with an equal proportion, 1/cov_num, for each covariate-margin. p the biased coin probability. p should be larger than 1/2 and less than 1. The default is 0.85.

Details

Consider I covariates and m_i levels for the ith covariate, i=1,…,I. T_j is the assignment of the jth 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 jth patient falls within (k_1^*,…,k_I^*);

(3) If the jth 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 jth 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 jth 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).

Value

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 (cov_num + 1) * n matrix containing covariate profiles for all patients and the corresponding assignments. The ith column represents the ith patient. The first cov_num rows include patients' covariate profiles, and the last row contains the assignments. 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, Real or Simulated. 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.

References

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