- 1 generateData(): simulate datasets
- 2 Update_beta(): First round of communication for propensity score estimates update:
- 3 Update_ate(): the second round updates causal log odds ratio of the treatment and the variance for the casual log odds ratio
This is a tutorial for the casual-COLA platform. Causal-COLA is a collaborative platform for institutions to make causal inferences on their sensitive data (such as medical data) without sharing them.
The causal-COLA platform consists of two parts :
- Interactive Interface: a website that serves as secure data-hub for data transmissions between sites. https://github.com/Causal-COLA/Causal-COLA-FrontEnd
- R package causalCOLA: a r package that allows users from different sites to run the analysis on their local computers. Built With R
The tutorial illustrates how to conduct a two-round causal-COLA analysis by walking you through a simulated example involving four hypothetical hospitals.
In a real-world application, each hospital only needs to store their data in their local facility. In this demosntration, we saved each hospital's datasets into separate folders. To begin simulating the datasets, first change your directory to where you want to save the simulated datasets using setwd(). The simulated datasets are saved into four separate folders /Simdata/hospital1,/Simdata/hospital2,/Simdata/hospital3, and /Simdata/hospital4 to mimic the scenario where each local sites stores data at their own facilities. Each dataset includes vectors of incidents(Y), treatment status(A) and covariates(X).
The generateData() method will also save the dataset as a list of local datasets through the r object hospital_data which is automatically saved in the current environment.
devtools::install_github("https://github.com/Causal-COLA/Causal-COLA-R-Package")
library(causalCOLA)
generateData()We use b to denote the site that we currently have access to.
When b = 1 which is the starting site, we can initialize a betahat and a sum2(usually 0).
tempdatadir = getwd()
b = 1
# Load Data so X is supposed to be a covariates vector and y is supposed to be the treatment vector
X<-y<-A<-NULL;
load(paste(tempdatadir,"/Simdata/hospital",b,"/Simdata.RData",sep=""))
#Site 1 specifies the number of covariates p. Here we use 5.
p = dim(X)[2]+1
#Initialize betehat using an empty vector or some other initial value init
betahat = rep(0,p)
#Initialize sum2
sum2<-diag(0,p,p)
output= Update_beta(X,A,betahat,sum2,"binomial")
# The intermediate output from site 1 in round 1 invovles beta coefficient estimates and Hessian matrices
print(output)
#> [[1]]
#> [,1]
#> [1,] -0.28402150
#> [2,] 0.36118110
#> [3,] 0.45555729
#> [4,] -0.05081609
#> [5,] 0.47563415
#> [6,] -0.33163140
#>
#> [[2]]
#> 1 X1_all X2_all X3_all X4_all X5_all
#> 1 20.93789 21.78285 11.553201 23.42310 22.19748 13.064873
#> X1_all 21.78285 43.80061 11.220944 26.56848 20.52154 14.437830
#> X2_all 11.55320 11.22094 11.553201 13.00086 11.82413 7.732463
#> X3_all 23.42310 26.56848 13.000855 44.26446 29.24566 14.690996
#> X4_all 22.19748 20.52154 11.824127 29.24566 43.76209 13.113792
#> X5_all 13.06487 14.43783 7.732463 14.69100 13.11379 13.064873Once site 1 finishes analysis, if we were to use the Interactive Interface, site 1 will would upload the results to its homepage using the pre-assgined username and password. The second hospital will log onto the Interactive Interface using its assigned username and password and download the output uploaded by hospital 1 and proceed the analysis.
Here we directly save the local result from hospital 1 into the local folder /Simdata/hospital2 where the raw data of hospital 2 are stored.
#Site 1 finishes analysis and save the results into where the second hospital has access to
save(output, file = paste(tempdatadir,"/Simdata/hospital",b+1, "/output_r1.RData", sep=""))
#Analysis Start from site 2
b=2
#Site 2 loads output results from site 1
load(paste(tempdatadir,"/Simdata/hospital",b, "/output_r1.RData", sep=""))
#Site 2 prepares its local data
X<-y<-A<-NULL;
load(paste(tempdatadir,"/Simdata/hospital",b,"/Simdata.RData",sep=""))
#Site 2 updates statistics
betahat = output[[1]]
sum2 = output[[2]]
output= Update_beta(X,y,betahat,sum2,"binomial")
#Site 2 finishes analysis and save the results in the designated directory
save(output, file = paste(tempdatadir,"/Simdata/hospital",b+1, "/output_r1.RData", sep=""))Now Site 2 has turn the updated results over to site 3 who also updates the results.
#Analysis Start from site 3
b=3
#Site 3 loads output results from site 1
load(paste(tempdatadir,"/Simdata/hospital",b, "/output_r1.RData", sep=""))
#Site 3 prepares its local data
X<-y<-A<-NULL;
load(paste(tempdatadir,"/Simdata/hospital",b,"/Simdata.RData",sep=""))
#Site 3 updates statistics
betahat = output[[1]]
sum2 = output[[2]]
output= Update_beta(X,y,betahat,sum2,"binomial")
#Site 3 finishes analysis and save the results in the Site 4 directory
save(output, file = paste(tempdatadir,"/Simdata/hospital",b+1, "/output_r1.RData", sep="")) Site 4 receives data from site 3 and finishes the first round update #Site 4 completes first-round update (PS). The output from Site 4 will be uploaded to the interactive interface where Site 1 has access to download. Here, we save the output results from Site 4 to the into the local folder /Simdata/hospital1
load(paste(tempdatadir,"/Simdata/hospital",b, "/output_r1.RData", sep=""))
X<-y<-A<-NULL;
load(paste(tempdatadir,"/Simdata/hospital",b,"/Simdata.RData",sep=""))
betahat = output[[1]]
sum2 = output[[2]]
output= Update_beta(X,y,betahat,sum2,"binomial")
save(output, file = paste(tempdatadir,"/Simdata/hospital",1, "/output_r1.RData", sep="")) Update_ate(): the second round updates causal log odds ratio of the treatment and the variance for the casual log odds ratio
Read in the output data from hospital 4 and hospital 1’s own raw data.
b = 1
load(paste(tempdatadir,"/Simdata/hospital",b, "/output_r1.RData", sep=""))
betahat = output[[1]]
X<-y<-A<-NULL;
load(paste(tempdatadir,"/Simdata/hospital",b,"/Simdata.RData",sep=""))Update_ate() is the function that update causal odds ratio as well as the inferences matrices. There are eight inputs needed for the Update_ate() function.
- The first input is betahat which corresponds to the estimated propensity score estimates.
- The second to fourth arguments correspond to the data.
- The fifth to eighth arguments correspond to the intermediate quantities used in calculating the log odds ratio.
- The last argument “lastsite” is optional and is default to be “FALSE”. When the last site which is hospital 4in our example, does the final update, the “lastsite” will be TRUE.
y_treated_sum=0;y_control_sum = 0 ; n_treated =0; n_control= 0; meat = 0; bread =0
output = Update_ate(betahat,A,y,X,y_treated_sum,y_control_sum,n_treated,n_control,meat,bread)
save(output, file = paste(tempdatadir,"/Simdata/hospital",b+1, "/output_r2.RData", sep=""))
#Analysis continue at site 2
b=2
#Site 2 loads output results from site 1
load(paste(tempdatadir,"/Simdata/hospital",b, "/output_r2.RData", sep=""))
#Site 2 prepares its local data
X<-y<-A<-NULL;
load(paste(tempdatadir,"/Simdata/hospital",b,"/Simdata.RData",sep=""))
#Site 2 updates statistics. The outputs from site 1 are used as input for `Update_ate()`.
betahat = output$beta_ps
y_treated_sum =output$y_treated_sum; y_control_sum=output$y_control_sum; n_treated = output$n_treated;n_control = output$n_control
meat = output$meat; bread =output$bread
output = Update_ate(betahat,A,y,X,y_treated_sum,y_control_sum,n_treated,n_control,meat,bread)
#Site 2 finishes analysis and save the results in the designated directory
save(output, file = paste(tempdatadir,"/Simdata/hospital",b+1, "/output_r2.RData", sep=""))
#Analysis continue at site 3
b=3
#Site 3 loads output results from site 2
load(paste(tempdatadir,"/Simdata/hospital",b, "/output_r2.RData", sep=""))
#Site 3 prepares its local data
X<-y<-A<-NULL;
load(paste(tempdatadir,"/Simdata/hospital",b,"/Simdata.RData",sep=""))
#Site 3 updates statistics. The outputs from site 2 are used as input for `Update_ate()`.
betahat = output$beta_ps
y_treated_sum =output$y_treated_sum; y_control_sum=output$y_control_sum; n_treated = output$n_treated;n_control = output$n_control
meat = output$meat; bread =output$bread
output = Update_ate(betahat,A,y,X,y_treated_sum,y_control_sum,n_treated,n_control,meat,bread)
#Site 3 finishes analysis and save the results in the designated directory
save(output, file = paste(tempdatadir,"/Simdata/hospital",b+1, "/output_r2.RData", sep=""))Hospital 4 finishes the second round of updates and output causal log odds ratio and its inference matrices, and output the final updates to all sites:
When we update causal log odds ratio at hospital 4, we need to make sure that we pass in “lastsite = TRUE” in Update_ate
b=4
#Site 4 loads output results from site 3
load(paste(tempdatadir,"/Simdata/hospital",b, "/output_r2.RData", sep=""))
#Site 4 prepares its local data
X<-y<-A<-NULL;
load(paste(tempdatadir,"/Simdata/hospital",b,"/Simdata.RData",sep=""))
#Site 4 updates statistics. The outputs from site 3 are used as input for `Update_ate()`.
betahat = output$beta_ps
y_treated_sum =output$y_treated_sum; y_control_sum=output$y_control_sum; n_treated = output$n_treated;n_control = output$n_control
meat = output$meat; bread =output$bread
output = Update_ate(betahat,A,y,X,y_treated_sum,y_control_sum,n_treated,n_control,meat,bread,TRUE)
#Site 4 finishes analysis and save the results in the designated directory where every group will have access to.
print(output)
#> ATE var
#> 0.08776381 0.88152685
save(output, file = paste(tempdatadir,"/Simdata/hospital",b, "/finalouput.RData", sep=""))Please see AUTHORS for a list of contributors for this package.