"3arm_bounds&CI.R" is to compute bounds and CIs for average causal effects 
within principal strata in three-arm trials with noncompliance discussed in 
Cheng and Small's paper "Bounds on causal effects in three-arm trials with 
non-compliance" to appear in JRSSB.

There are various functions to compute the bounds, CIs and change the output 
formats. 

You just need to input your data by "truedata", define the confidence level 
by "conf" and the number of bootstrap resamplings you want to use by "r". 
The first column of the data should be the outcome "Y", the second column should 
be the treatment-received "D", and the third column should be the randomization 
assignment "Z". 

The outputs will give you the bounds, Bonferroni CI, H-M CI and B-method CI for 
the average causal effects within principal strata. "A_OAB" and "B_OAB" are 
the average causal effects of treatments A and B for OAB stratum under 
assumptions 1-4, respectively. "A_OAO" and "B_OOB" are the average causal 
effects of treatments A and B for strata OAO and OOB under assumptions 1-4, 
respectively. "A_OAB_monot", "A_OAO_monot" , and "B_OAB_monot" are the 
corresponding average causal effects within principal strata under the additional
monotonicity assumption (assumption 5) in addition to assumptions 1-4. 

For the example of the hypothetical data used in the paper, we input the data, 
define the confidence level and the number of bootstrap resamplings as the 
following. 

-----------------------------------------------------------------------------------------
Z<-c(rep(0,400),rep(1,400),rep(2,400))
D<-c(rep(0,400),rep(0,20),rep(1,380),rep(0,80),rep(2,320))
Y<-c(rep(0,220),rep(1,180),rep(0,16),rep(1,4),rep(0,19),rep(1,361),rep(0,60),rep(1,20),rep(0,96),rep(1,224))
truedata<-cbind(Y,D,Z)
conf<-0.95  
r<-1000
------------------------------------------------------------------------------------------

The outputs are as the following.

----------------------------------------
[1] "Bounds"
            Lower Bound Upper Bound
A_OAB         0.4111842   0.5063291
A_OAO         0.3906250   0.7894737
B_OAB         0.1578947   0.2266667
B_OOB        -1.0000000   1.0000000
A_OAB_monot   0.4406250   0.5000000
A_OAO_monot   0.4166667   0.7333333
B_OAB_monot   0.2000000   0.2000000

[1] "Bonferroni CI"
            Lower Limit Upper Limit
A_OAB        0.33121637   0.5720473
A_OAO        0.13507503   0.8965968
B_OAB        0.06280614   0.3122225
B_OOB       -1.00000000   1.0000000
A_OAB_monot  0.36486731   0.5657348
A_OAO_monot  0.14593598   0.8684370
B_OAB_monot  0.11582281   0.2834139

[1] "H-M CI"
            Lower Limit Upper Limit
A_OAB        0.33720960   0.5803037
A_OAO        0.22094727   0.9591514
B_OAB        0.06609786   0.3184635
B_OOB       -1.00000000   1.0000000
A_OAB_monot  0.37153320   0.5690918
A_OAO_monot  0.19791667   0.9520833

[1] "B-method CI"
            Lower Limit Upper Limit
A_OAB        0.33439030   0.5765856
A_OAO        0.19069740   0.9071469
B_OAB        0.06776053   0.3161835
B_OOB       -1.00000000   1.0000000
A_OAB_monot  0.37101515   0.5675152
A_OAO_monot  0.20906792   0.8818657
----------------------------------------