cvcrand() example
Study 1 in (L. M. Dickinson et al. 2015) is about two approaches (interventions) for increasing the “up-to-date” immunization rate in 19- to 35-month-old children. They planned to randomize 16 counties in Colorado 1:1 to either a population-based approach or a practice-based approach. There are several county-level variables. The program will randomize on a subset of these variables. The continuous variable of average income is categorized to illustrate the use of the cvcrand() on multi-category variables. And the percentage in CIIS variable is trancated at 100%.
| county | location | inciis | uptodateonimmunizations | hispanic | incomecat |
|---|---|---|---|---|---|
| 1 | Rural | 94 | 37 | 44 | Low |
| 2 | Rural | 85 | 39 | 23 | High |
| 3 | Rural | 85 | 42 | 12 | Low |
| 4 | Rural | 93 | 39 | 18 | High |
| 5 | Rural | 82 | 31 | 6 | High |
| 6 | Rural | 80 | 27 | 15 | Med |
| 7 | Rural | 94 | 49 | 38 | Low |
| 8 | Rural | 100 | 37 | 39 | Low |
| 9 | Urban | 93 | 51 | 35 | Med |
| 10 | Urban | 89 | 51 | 17 | Med |
| 11 | Urban | 83 | 54 | 7 | High |
| 12 | Urban | 70 | 29 | 13 | Med |
| 13 | Urban | 93 | 50 | 13 | High |
| 14 | Urban | 85 | 36 | 10 | Med |
| 15 | Urban | 82 | 38 | 39 | Low |
| 16 | Urban | 84 | 43 | 28 | Med |
For the constrained randomization, we used the cvcrand() function to randomize 8 out of the 16 counties into the practice-based. For the definition of the whole randomization space, if the total number of all possible schemes is smaller than 50,000, we enumerate all the schemes as the whole randomization space. Otherwise, we simulate 50,000 schemes and choose the unique shemes among them as the whole randomization space. We calculate the balance scores of "L2" metric on three continuous covariates as well as two categorical covariates of location and income category. Location has "Rural" and "Urban". The level of "Rural" was then dropped in cvcrand(). As income category has three levels of "low", "med", and "high", the level of "high" was dropped to create dummy variables according to the alphanumerical order as well. Then we constrained the randomization space to the schemes with "L2" balance scores less than the 0.1 quantile of that in the whole randomization space. Finally, a randomization scheme is sampled from the constrained space.
We saved the constrained randomization space in a CSV file in "dickinson_constrained.csv", the first column of which is an indicator variable of the finally selected scheme (1) or not (0). We also saved the balance scores of the whole randomization space in a CSV file in "dickinson_bscores.csv", and output a histogram displaying the distribution of all balance scores with a red line indicating our selected cutoff (the 0.1 quantile).
Design_result<-cvcrand(id = Dickinson_design$county,
metric = "L2",
x = data.frame(Dickinson_design[, -1]),
n = 16,
ntrt = 8,
categorical = c("location","incomecat"),
savedata = "dickinson_constrained.csv",
savebscores = "dickinson_bscores.csv",
cutoff = 0.1,
seed = 12345)
The we had the following output:
# the metric the user specified
Design_result$metric## [1] "L2" # the selected scheme
Design_result$Allocation## id allocation
## [1,] 1 0
## [2,] 2 0
## [3,] 3 0
## [4,] 4 1
## [5,] 5 1
## [6,] 6 0
## [7,] 7 1
## [8,] 8 0
## [9,] 9 1
## [10,] 10 1
## [11,] 11 0
## [12,] 12 1
## [13,] 13 1
## [14,] 14 0
## [15,] 15 1
## [16,] 16 0 # the cutoff balance score, the balance score of the selected scheme, as well as the histogram of the balance scores of the whole randomization space
Design_result$Bscores## CR-Benchmark Selected Point Mean SD Min 5%
## 7.638463 6.763833 24.000000 15.774661 1.161107 5.826458
## 10% 20% 25% 30% 50% 75%
## 7.638463 10.848749 12.221264 13.839891 20.577839 31.620790
## 95% Max
## 55.486080 116.656181 # the statement about how many clusters to randomize to the intervention and the control arms respectively
Design_result$assignment_message## [1] "You have indicated that you want to assign 8 clusters to treatment and 8 to control" # the statement about how to get the whole space of schemes
Design_result$scheme_message## [1] "Enumerating all the 12870 schemes for 8 clusters in the treatment arm out of 16 clusters in total" # the statement about the benchmark of the constrained space
Design_result$BLcut_message## [1] "By cutoff quantile of 0.1 of L2 , the BL constrained randomization benchmark is 7.638" # the statement about the selected scheme from constrained randomization
Design_result$BLchoice_message## [1] "Balance score of selected scheme by L2 has B score of 6.764" # the matrix containing allocation scheme, the id as well as the original covariates' matrix
Design_result$data_BL## inter id location inciis uptodateonimmunizations hispanic incomecat
## 1 0 1 Rural 94 37 44 Low
## 2 0 2 Rural 85 39 23 High
## 3 0 3 Rural 85 42 12 Low
## 4 1 4 Rural 93 39 18 High
## 5 1 5 Rural 82 31 6 High
## 6 0 6 Rural 80 27 15 Med
## 7 1 7 Rural 94 49 38 Low
## 8 0 8 Rural 100 37 39 Low
## 9 1 9 Urban 93 51 35 Med
## 10 1 10 Urban 89 51 17 Med
## 11 0 11 Urban 83 54 7 High
## 12 1 12 Urban 70 29 13 Med
## 13 1 13 Urban 93 50 13 High
## 14 0 14 Urban 85 36 10 Med
## 15 1 15 Urban 82 38 39 Low
## 16 0 16 Urban 84 43 28 Med # the descriptive statistics for all the variables in the original covariates' matrix in the two arms from constrained randomization
Design_result$BL_result## Stratified by inter
## 0 1 p test
## n 8 8
## location = Urban (%) 3 (37.5) 5 (62.5) 0.617
## inciis (mean (sd)) 87.00 (6.59) 87.00 (8.45) 1.000
## uptodateonimmunizations (mean (sd)) 39.38 (7.65) 42.25 (9.18) 0.507
## hispanic (mean (sd)) 22.25 (13.77) 22.38 (12.94) 0.985
## incomecat (%) 0.819
## High 2 (25.0) 3 (37.5)
## Low 3 (37.5) 2 (25.0)
## Med 3 (37.5) 3 (37.5)From the output of Design_result$BL_result, the selected scheme is able to properly balance the baseline values of the covariates. And the selected scheme is shown in Design_result$Allocation.