DataSHIELD Training Part 6: Modelling


 Click here for page contents...

Prerequisites

It is recommended that you familiarise yourself with R first by sitting our Introduction to R tutorial.

It also requires that you have the DataSHIELD training environment installed on your machine, see our Installation Instructions for Linux, Windows, or Mac.

Help

DataSHIELD support is freely available in the DataSHIELD forum by the DataSHIELD community. Please use this as the first port of call for any problems you may be having, it is monitored closely for new threads.

DataSHIELD bespoke user support and also user training classes are offered on a fee-paying basis. Please enquire at datashield@newcastle.ac.uk for current prices. 

Introduction

This is the sixth and final page of a 6-part DataSHIELD tutorial series. Well done!

The other parts in this DataSHIELD tutorial series are:

Quick reminder for logging in:

 Click here to expand...

Recall from the installation instructions, the Opal web interface is a simple check to tell if the VMs have started. Load the following urls, waiting at least 1 minute after starting the training VMs.

Start R/RStudio

Load Packages

#load libraries
library(DSI)
library(DSOpal)
library(dsBaseClient)

Build your login dataframe 

Build your login dataframe
builder <- DSI::newDSLoginBuilder()
builder$append(server = "study1",  url = "http://192.168.56.100:8080/",
               user = "administrator", password = "datashield_test&",
               table = "CNSIM.CNSIM1", driver = "OpalDriver")
builder$append(server = "study2", url = "http://192.168.56.101:8080/",
               user = "administrator", password = "datashield_test&",
               table = "CNSIM.CNSIM2", driver = "OpalDriver")

logindata <- builder$build()

connections <- DSI::datashield.login(logins = logindata, assign = TRUE, symbol = "D")
  • Command to logout:
DSI::datashield.logout(connections)



Modelling

Horizontal DataSHIELD allows the fitting of generalised linear models (GLM). In Generalised Linear Modelling, the outcome can be modelled as continuous, or categorical (binomial or discrete). The error to use in the model can follow a range of distributions including Gaussian, binomial, gamma and Poisson. In this section only one example will be shown, for more examples please see the manual help page for the function.

This section will make more sense with an understanding of Generalised Linear Modelling theory and techniques. More information can always be found online, for example this Colorado University publication.


Basic 1-covariate Gaussian GLM

We want to examine the relationship between BMI (a continuous variable) and Triglycerides (another continuous variable). Because the response variable here, BMI, is continuous, this indicates that there should be a Gaussian underlying distribution.

A correlation command will establish how closely linked these two variables might be:

ds.cor(x='D$PM_BMI_CONTINUOUS', y='D$LAB_TRIG')

Let's visualise with a scatterplot:

ds.scatterPlot(x='D$PM_BMI_CONTINUOUS', y='D$LAB_TRIG')

Regress Triglycerides with BMI using the Individual Partition Data (IPD) approach:

The method for this (ds.glm) is a "pooled analysis"- equivalent to placing the individual-level data from all sources in one warehouse.

Important to note that the link function is by default the canonical link function for each family. So binomial <-> logistic link, poisson <-> log link, gaussian <-> identity link.

ds.glm(formula = "D$LAB_TRIG~D$PM_BMI_CONTINUOUS", family="gaussian", datasources = connections)

Regress Triglycerides with BMI using the Study-Level Meta-Analysis (SLMA) approach:

ds.glmSLMA(formula = "D$LAB_TRIG~D$PM_BMI_CONTINUOUS", family="gaussian", newobj = "workshop.obj", datasources = connections)

For the SLMA approach we can assign the predicted values at each study:

ds.glmPredict(glmname = "workshop.obj", newobj = "workshop.prediction.obj", datasources = connections)
ds.length("workshop.prediction.obj$fit", datasources=connections)
ds.length("D$LAB_TRIG", datasources=connections)

Filter out the incomplete cases, using "ds.completeCases()" sub-setting command:

ds.cbind(c('D$LAB_TRIG', 'D$PM_BMI_CONTINUOUS'), newobj='vars')
ds.completeCases('vars', newobj='vars.complete')
ds.dim('vars.complete')

Then plot the resultant data as a best linear fit on a scatter plot:

df1 <- ds.scatterPlot('D$PM_BMI_CONTINUOUS', "D$LAB_TRIG", datasources = connections, return.coords = TRUE)
df2 <- ds.scatterPlot('vars.complete$PM_BMI_CONTINUOUS', "workshop.prediction.obj$fit", datasources = connections, return.coords = TRUE)
# then in native R
par(mfrow=c(2,2))
plot(as.data.frame(df1[[1]][[1]])$x,as.data.frame(df1[[1]][[1]])$y, xlab='Body Mass Index', ylab='Triglycerides', main='Study 1')
lines(as.data.frame(df2[[1]][[1]])$x,as.data.frame(df2[[1]][[1]])$y, col='red')
plot(as.data.frame(df1[[1]][[2]])$x,as.data.frame(df1[[1]][[2]])$y, xlab='Body Mass Index', ylab='Triglycerides', main='Study 2')
lines(as.data.frame(df2[[1]][[2]])$x,as.data.frame(df2[[1]][[2]])$y, col='red')
plot(as.data.frame(df1[[1]][[3]])$x,as.data.frame(df1[[1]][[3]])$y, xlab='Body Mass Index', ylab='Triglycerides', main='Study 3')
lines(as.data.frame(df2[[1]][[3]])$x,as.data.frame(df2[[1]][[3]])$y, col='red')

1-covariate Binomial GLM

Say we want to regress Cholesterol against Diabetes status. This is not as simple a matter as above, where a simple (& familiar!) Gaussian linear model is fitted. The response data takes values of 0 and 1, the binary measure of whether a person does (=1) or doesn't (=0) have the diabetes diagnosis. Because of this, we want a different type of linear model, to make sense.

Here we will use the ds.glmSLMA command as we are about to calculate predicted values again, which only work with the SLMA version of the function. We will only use the 3rd connected study as we are interested in conducting an analysis and producing the graph for that study site alone.

ds.glmSLMA(formula = "D$DIS_DIAB~D$LAB_HDL", family="binomial", newobj = "workshop.obj", datasources = connections[3])

So, with this formula, family and new object established, this is the rest of the code:

ds.length("workshop.prediction.obj$fit", datasources = connections[3])
ds.length('D$LAB_HDL', datasources = connections[3])
ds.numNA('D$LAB_HDL', datasources = connections[3])
ds.completeCases('D$LAB_HDL', 'hdl.complete', datasources = connections[3])  # FAILED
ds.cbind(c('D$LAB_HDL','D$LAB_HDL'), newobj='D2', datasources = connections[3])
ds.completeCases('D2', 'D2.complete', datasources = connections[3]) #doesnt' fail because input object is dataframe
ds.dim('D2', datasources = connections[3])
ds.dim('D2.complete', datasources = connections[3])

ds.asNumeric('D$DIS_DIAB', newobj='DIAB.n', datasources = connections[3])
df1 <- ds.scatterPlot('D$LAB_HDL', "DIAB.n", datasources = connections[3], return.coords = TRUE)
df2 <- ds.scatterPlot('D2.complete$LAB_HDL', "workshop.prediction.obj$fit", datasources = connections[3], return.coords = TRUE)

plot(as.data.frame(df1[[1]][[1]])$x,as.data.frame(df1[[1]][[1]])$y, xlab='LAB_HDL', ylab='DIS_DIAB')
lines(as.data.frame(df2[[1]][[1]])$x,as.data.frame(df2[[1]][[1]])$y,col='red')

mod <- ds.glm(formula = "D$DIS_DIAB~D$LAB_HDL", family="binomial", datasources = connections[3])
mod$coefficients
modSLMA$output.summary$study1$coefficients


X <- seq(from=-0.5, to=3, by=0.01)
Y <- (exp(mod$coefficients[1,1]+mod$coefficients[2,1]*X))/(1+exp(mod$coefficients[1,1]+mod$coefficients[2,1]*X))
plot(X,Y)

X <- seq(from=-10, to=3, by=0.01)
Y <- (exp(mod$coefficients[1,1]+mod$coefficients[2,1]*X))/(1+exp(mod$coefficients[1,1]+mod$coefficients[2,1]*X))
plot(X,Y)

plot(as.data.frame(df1[[1]][[1]])$x,as.data.frame(df1[[1]][[1]])$y, xlab='LAB_HDL', ylab='DIS_DIAB', xlim=c(-10,3))
lines(X,Y, col='red')

Multi-covariate GLM

  • The function ds.glm is used to analyse the outcome variable DIS_DIAB (diabetes status) and the covariates PM_BMI_CONTINUOUS (continuous BMI), LAB_HDL (HDL cholesterol) and GENDER (gender), with an interaction between the latter two. In R this model is represented as:
D$DIS_DIAB ~ D$PM_BMI_CONTINUOUS+D$LAB_HDL*D$GENDER
  • Since v6.0, the intermediate results are printed by default, (in red when viewing in RStudio):


ds.glm(formula=D$DIS_DIAB~D$PM_BMI_CONTINUOUS+D$LAB_HDL*D$GENDER, family='binomial')
  Aggregated (glmDS1(D$DIS_DIAB ~ D$PM_BMI_CONTINUOUS + D$LAB_HDL * D$GENDER, ) [========] 100% / 0s
Iteration 1...
  Aggregated (glmDS2(D$DIS_DIAB ~ D$PM_BMI_CONTINUOUS + D$LAB_HDL * D$GENDER, ) [========] 100% / 0s
CURRENT DEVIANCE:      5772.52971970323
Iteration 2...
  Aggregated (glmDS2(D$DIS_DIAB ~ D$PM_BMI_CONTINUOUS + D$LAB_HDL * D$GENDER, ) [========] 100% / 0s
CURRENT DEVIANCE:      1316.46958534192
Iteration 3...
  Aggregated (glmDS2(D$DIS_DIAB ~ D$PM_BMI_CONTINUOUS + D$LAB_HDL * D$GENDER, ) [========] 100% / 0s
CURRENT DEVIANCE:      725.530885478793
Iteration 4...
  Aggregated (glmDS2(D$DIS_DIAB ~ D$PM_BMI_CONTINUOUS + D$LAB_HDL * D$GENDER, ) [========] 100% / 0s
CURRENT DEVIANCE:      574.04091649261
Iteration 5...
  Aggregated (glmDS2(D$DIS_DIAB ~ D$PM_BMI_CONTINUOUS + D$LAB_HDL * D$GENDER, ) [========] 100% / 0s
CURRENT DEVIANCE:      539.36484363672
Iteration 6...
  Aggregated (glmDS2(D$DIS_DIAB ~ D$PM_BMI_CONTINUOUS + D$LAB_HDL * D$GENDER, ) [========] 100% / 0s
CURRENT DEVIANCE:      534.529367269197
Iteration 7...
  Aggregated (glmDS2(D$DIS_DIAB ~ D$PM_BMI_CONTINUOUS + D$LAB_HDL * D$GENDER, ) [========] 100% / 0s
CURRENT DEVIANCE:      534.369349024873
Iteration 8...
  Aggregated (glmDS2(D$DIS_DIAB ~ D$PM_BMI_CONTINUOUS + D$LAB_HDL * D$GENDER, ) [========] 100% / 0s
CURRENT DEVIANCE:      534.369101005548
Iteration 9...
  Aggregated (glmDS2(D$DIS_DIAB ~ D$PM_BMI_CONTINUOUS + D$LAB_HDL * D$GENDER, ) [========] 100% / 0s
CURRENT DEVIANCE:      534.369101004809
SUMMARY OF MODEL STATE after iteration 9
Current deviance 534.369101004809 on 4159 degrees of freedom
Convergence criterion TRUE (1.38325209879068e-12)

beta: -6.90641416691308 0.142256253558181 -0.967440739752358 -1.40945273343359 0.646007073975

Information matrix overall:
                    (Intercept) D$PM_BMI_CONTINUOUS  D$LAB_HDL D$GENDER1 D$LAB_HDL:D$GENDER1
(Intercept)            52.47803           1624.8945   71.78440  16.77192            25.91140
D$PM_BMI_CONTINUOUS  1624.89450          51515.6450 2204.90085 503.20484           774.18028
D$LAB_HDL              71.78440           2204.9008  109.48855  25.91140            42.87626
D$GENDER1              16.77192            503.2048   25.91140  16.77192            25.91140
D$LAB_HDL:D$GENDER1    25.91140            774.1803   42.87626  25.91140            42.87626

Score vector overall:
                             [,1]
(Intercept)         -3.618013e-10
D$PM_BMI_CONTINUOUS -9.890691e-09
D$LAB_HDL           -6.317578e-10
D$GENDER1           -2.913176e-10
D$LAB_HDL:D$GENDER1 -5.343783e-10

Current deviance: 534.369101004809
  •  Then, the rest of the results  are printed in black:

$Nvalid
[1] 4164

$Nmissing
[1] 1087

$Ntotal
[1] 5251

$disclosure.risk
       RISK OF DISCLOSURE
study1                  0
study2                  0

$errorMessage
       ERROR MESSAGES
study1 "No errors"   
study2 "No errors"   

$nsubs
[1] 4164

$iter
[1] 9

$family

Family: binomial 
Link function: logit 


$formula
[1] "D$DIS_DIAB ~ D$PM_BMI_CONTINUOUS + D$LAB_HDL * D$GENDER"

$coefficients
                      Estimate Std. Error    z-value      p-value low0.95CI.LP high0.95CI.LP       P_OR
(Intercept)         -6.9064142 1.08980103 -6.3373166 2.338013e-10  -9.04238494    -4.7704434 0.00100034
D$PM_BMI_CONTINUOUS  0.1422563 0.02932171  4.8515676 1.224894e-06   0.08478676     0.1997257 1.15287204
D$LAB_HDL           -0.9674407 0.36306348 -2.6646601 7.706618e-03  -1.67903208    -0.2558494 0.38005445
D$GENDER1           -1.4094527 1.06921103 -1.3182175 1.874308e-01  -3.50506784     0.6861624 0.24427693
D$LAB_HDL:D$GENDER1  0.6460071 0.69410419  0.9307062 3.520056e-01  -0.71441214     2.0064263 1.90790747
                    low0.95CI.P_OR high0.95CI.P_OR
(Intercept)           0.0001182744     0.008405372
D$PM_BMI_CONTINUOUS   1.0884849336     1.221067831
D$LAB_HDL             0.1865544594     0.774258560
D$GENDER1             0.0300447352     1.986079051
D$LAB_HDL:D$GENDER1   0.4894797709     7.436693232

$dev
[1] 534.3691

$df
[1] 4159

$output.information
[1] "SEE TOP OF OUTPUT FOR INFORMATION ON MISSING DATA AND ERROR MESSAGES"


How ds.glm works

After every iteration in the glm, each study returns non disclosive summaries (a score vector and an information matrix) that are combined on the client R session. The model is fitted again with the updated beta coefficients, this iterative process continues until convergence or the maximum number of iterations is reached. The output of ds.glm returns the final pooled score vector and information along with some information about the convergence and the final pooled beta coefficients.

Conclusion

You have now completed our basic DataSHIELD training.

Some extended practicals will be coming soon.

Also remember you can:

You can get back to the training homepage by clicking here.