Readme file

SERIES B
Statistical Methodology

Bounds on causal effects in three-arm trials with non-compliance
J. Cheng and D. S. Small,
Journal of the Royal Statistical Society, Series B, volume 68 (2006), part 5, pages 815 - 836

"3arm_bounds&CI" is to compute bounds and confidence intervals (CIs) for average causal effects within principal strata in three-arm trials with noncompliance.

"3arm_bounds&CI" is run in R. 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 CIs, H-M CIs and B-method CIs 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 to calculate the bounds and 95% CIs, 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
--------------------------------------------------------------

» indicates a line break

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
----------------------------------------

Jing Cheng
Division of Biostatistics
University of Florida College of Medicine
Room 5130
1329 SW 16th Street
PO Box 100177
Gainesville
FL 32610
USA

E-mail: jcheng@biostat.ufl.edu

• Dataset (cheng.zip, size - 5kb)

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Statistical Methodology

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Applied Statistics

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