From: Nutter, Benjamin <NutterB_at_ccf.org>

Date: Mon, 07 Jul 2008 08:41:49 -0400

*#* 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

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https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Mon 07 Jul 2008 - 12:44:47 GMT

Date: Mon, 07 Jul 2008 08:41:49 -0400

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,...){

#**********************************************************************

#* 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)[[3]][1] # Degrees of Freedom MSW <- anova(model)[[3]][2] # 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

o.fr

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