Limit of Agreement (Bland-Altman method)

References

Load packages

library(MethComp)
library(dplyr)
library(ggplot2)

Load data

## Load systolic blood pressure data
data(sbp)

## Summarize
sbp %>%
    dplyr::group_by(meth,repl) %>%
    summarize(mean_y = mean(y))

## Source: local data frame [9 x 3]
## Groups: meth
## 
##   meth repl mean_y
## 1    J    1  128.5
## 2    J    2  127.3
## 3    J    3  126.4
## 4    R    1  128.3
## 5    R    2  127.6
## 6    R    3  126.1
## 7    S    1  144.8
## 8    S    2  142.7
## 9    S    3  141.5

Visualize

## Use rater J, replications 1 and 3
sbp2 <- subset(sbp, meth == "J" & repl %in% c(1,3))

## Plot
ggplot(data = sbp2,
       mapping = aes(x = repl, y = y, group = item)) +
           layer(geom = "line") +
           theme_bw() +
           theme(legend.key = element_blank())

plot of chunk unnamed-chunk-4

Bland-Altman plot

## Using MethComp package
BlandAltman(sbp[sbp$repl == 3,"y"], sbp[sbp$repl == 1,"y"],
            x.name = "sbp3", y.name = "sbp1")

## NOTE:
##  'AB.plot' and 'BlandAltman' are deprecated,
##  and likely to disappear in a not too distant future,
##  use 'BA.plot' instead.

plot of chunk unnamed-chunk-5 

## 
## Limits of agreement:
## sbp3 - sbp1  2.5% limit 97.5% limit    SD(diff) 
##      -2.545     -25.355      20.265      11.405

## Manually
(diffs <- sbp[sbp$repl == 3,"y"] - sbp[sbp$repl == 1,"y"])

##   [1]   7   0   6  -4 -12   2 -14  -2  12  -8   4  14  -2   0  -4  -8   2   2  -2  -6 -12 -14  -8 -24   4   2  -6
##  [28]   2   0 -16  -8   2  -4   8  18   4   4 -10   0  -6 -12 -12  -2 -10   0 -14   8 -16 -12  14  -4 -12   6  -6
##  [55] -10   4  -2  10 -12 -14 -16 -10 -10   2   8  -2  14   0  10  22  26   2  -6   0   6  -2  12   0  -4  -6 -24
##  [82] -22   6  -6 -10  13   2   6  -4 -14   2 -16   0  12  -8   4  12  -4   0  -2  -4  -2   2  -4  -4 -16  -4  -6
## [109] -20   4   2  -8   2   0 -14  -6   6  -4  -6  16   6   4 -12   0  -8 -14 -12  -4 -10   2 -14   8 -14 -14  12
## [136]  -4 -10   8  -4 -12   2   0  12 -10 -14 -18 -12  -8  -2   4   0  14   2  12  22  26  -2  -8  -4   6  -6  14
## [163]   2  -4  -6 -24 -22   8  -4  -8   2   7   3   8 -16  -3 -10   5   3 -15   4   2  -9  -9  -1  -5  11  -5 -26
## [190] -10 -15  -9 -19  10  -4   2   1  -7  -2  -6   3  -7  -7  -1   4  -1  11  -8   5 -15 -11 -12  -8 -21   4  -5
## [217]  -4 -40 -15  12  27  -8   5 -23  -8  12  -2   2  -6 -19 -39  24 -13  -6  21 -21 -49  43  -3  14  20   8 -11
## [244]  -5   3  -7 -14  -8  -7  11 -24  13  12  -3   7

(d_bar <- mean(diffs))

## [1] -2.545

(sd_diff <- sd(diffs))

## [1] 11.41

qnorm(0.975)

## [1] 1.96

d_bar + c(-1,+1) * qnorm(0.975) * sd_diff

## [1] -24.90  19.81

## Plot
plot(density(diffs))
abline(v = d_bar)
abline(v = d_bar + c(-1,+1) * qnorm(0.975) * sd_diff)

plot of chunk unnamed-chunk-5