# [R] Bland-Altman method to measure agreement with repeated measures

Nutter, Benjamin NutterB at ccf.org
Mon Jul 7 14:41:49 CEST 2008

```The function given below is one I've written to handle repeated
measures.  I've also included the Help File.  If you happen to see any
potential improvements, I would be open to suggestions.

###
### Function Code
###

'Bland.Altman' <- function(x,y,alpha=.05,rep.meas=FALSE,subject,...){
#**********************************************************************
#* Construct a Bland Altman Plot
#* 1. Set a few constants
#* 2. Calculate mean difference
#* 3. Calculate difference standard deviation
#* 4. Calculate upper and lower confidence limits
#* 5. Make Plot
#**********************************************************************

#*** 1. Set a few constants
z <- qnorm(1-alpha/2)  ## value of z corresponding to alpha
d <- x-y               ## pair-wise differences
m <- (x+y)/2           ## pair-wise means

#*** 2. Calculate mean difference
d.mn <- mean(d,na.rm=TRUE)

#*** 3. Calculate difference standard deviation
if(rep.meas==FALSE){ d.sd=sqrt(var(d,na.rm=TRUE)) }
else{

#*** 3a. Ensure subject is a factor variable
if(!is.factor(subject)) subject <- as.factor(subject)

#*** 3b. Extract model information
n <- length(levels(subject))      # Number of subjects
model <- aov(d~subject)           # One way analysis of variance
MSB <- anova(model)[]       # Degrees of Freedom
MSW <- anova(model)[]       # Sums of Squares

#*** 3c. Calculate number of complete pairs for each subject
pairs <- NULL
for(i in 1:length(levels(as.factor(subject)))){
pairs[i] <- sum(is.na(d[subject==levels(subject)[i]])==FALSE)
}
Sig.dl <- (MSB-MSW)/((sum(pairs)^2-sum(pairs^2))/((n-1)*sum(pairs)))
d.sd <- sqrt(Sig.dl+MSW)
}

#*** 4. Calculate lower and upper confidence limits
ucl <- d.mn+z*d.sd
lcl <- d.mn-z*d.sd

#*** 5. Make Plot
plot(m, d,abline(h=c(d.mn,ucl,lcl)),  ...)
values <- round(cbind(lcl,d.mn,ucl),4)
colnames(values) <- c("LCL","Mean","UCL")
if(rep.meas==FALSE) Output <- list(limits=values,Var=d.sd^2)
else Output <- list(limits=values,Var=Sig.dl)
return(Output)
}

###
### Help File
###

Bland Altman Plots

Description:

Constructs a Bland-Altman Plot.

Usage:

Bland.Altman(x,y,alpha=.05,rep.meas=FALSE,subject,...)

Arguments:

x,y: vectors of values to be compared.

alpha: Significance level for determining confidence limits.
Defaults to 0.05

rep.meas: Toggles if data provided should be considered as repeated
measures.  Defaults to 'FALSE'

subject: Required if 'rep.meas=TRUE'.  A vector of the same length of
'x' and 'y' that  denotes which subject/group the measurement
belongs to.

...: Other arguments to be passed to the 'plot' method.

Details:

When 'rep.meas=TRUE', the confidence limits are calculated using a
method proposed by Bland and Altman. These limits are slightly
wider, allowing for the correlation within subjects/factors.  The
standard deviation used to compute these limits is:

sigma^2[d] = sigma^2[dI] + sigma^2[dw]

where  sigma^2[d]  is the variance of the differences, sigma^2[dI]
is the variance of the subjects and methods interaction, and
sigma^2[dw]  is the within subject variation. Estimates of these
values can be found with

s^2[dw] = MSw

s^2[dI] = (MSb - MSw) / ((sum(m[i])^2 - sum(m[i]^2)) /
((n-1)*sum(m[i]))

)

Where MSb and MSw are the between and within subject variance of
the one way analysis of  variance and m[i] is the number of pairs
for the ith subject.  The sum of these two estimates provides the
estimate for  s^2[d]  .

Value:

limits: A vector containing the Mean Bias and confidence limits.

Var.dl: The Variance of the Bias.  If 'rep.meas=TRUE', this is

s^2[dI]

.

Author(s):

Benjamin Nutter nutterb at ccf.org

Created:  December 2007

References:

J Martin Bland and Douglass G Altman, "Measuring Agreement in
Method Comparison Studies", _Statistical Methods in Medical
Research_, 1999; 8: 135 - 160.

J Martin Bland and Doublas G. Altman, "Agreement Between Methods
of Measurement with Multiple Observations per Individual" _Journal
of Biopharmaceutical Statistics_ 17:571-582, 2007. (Corrects the
formula  given in the 1999 paper).

Burdick RK, Graybill FA. _Confidence Intervals on Variance
Components_. New York: Dekker, 1992.

Examples:

observer1=rnorm(500,5,2)
observer2=rnorm(500,10,4)
ID=rep(1:50,10)

Bland.Altman(observer1,observer2)

Bland.Altman(observer1,observer2,rep.meas=TRUE,subject=ID)

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On Behalf Of kende jan
Sent: Saturday, July 05, 2008 4:18 AM
To: R-help at r-project.org
Subject: [Possible SPAM] [R] Bland-Altman method to measure agreement
with repeated measures

Dear all,

I want to use the Bland-Altman method to measure agreement with repeated
measures collected over period of time (seven periods).

How can I do this with R

Many thanks

________________________________________________________________________
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o.fr
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