Data set:
- The data is based on a paper by Eliasziw et al., 1994.
- One therapist uses two goniometers (i.e., electro vs. manual) to measure knee joint angles three times.
- Twenty-nine subjects (n=29) were measured three consecutive times (m=3) on each goniometer (t=2) at one joint position (i.e., full passive extension)
The Challenge:
Visualize the data to answer the following questions:
- Inter-goniometer: do the two goniometers agree?
- Intra-goniometer: do the goniometers measure consistently the knee joint angle across the three repeated measurements?
Reference:
Eliasziw M, Young SL, Woodbury MG, Fryday-Field K. Statistical methodology for the concurrent assessment of interrater and intrarater reliability: using goniometric measurements as an example. Phys Ther. 1994 Aug;74(8):777-88. doi: 10.1093/ptj/74.8.777. PMID: 8047565.
A description of the challenge can also be found here.
A recording of the session can be found here.
Example 1. Faceted line plot
Example 2. Visualization by subject
Example 3. Bland-Altman plot
high resolution image
high resolution image
Example 4. Raw data
The html file can be found here.
Example 5. Distribution
The html file can be found here.
Example 6. Distribution adjusted
The html file can be found here.
Example 7. QQ plots
Example 8. BA plot
The html file can be found here.
Example 9. Probability of agreement
Example 10. Accuracy, precision, and reliability
Example 11. BA adjusted
The html file can be found here.
Example 12. Probability of agreement (adj.)
Code
Example 1. Faceted line plot
The SAS file can be found here.
Example 2. Visualization by subject
The Python file can be found here.
Example 3. Bland-Altman plot
library(readxl)
library(dplyr)
library(tidyr)
library(ggplot2)
# Load data
d <- read_excel('Data/2024-12-11-psi-vissig-goniometer.xlsx') |>
mutate(time=as.numeric(time))
# Bland-Altman plot - Inter-goniometer agreement
df<-d |>
pivot_wider(names_from = `rater`, values_from = `y`) |>
mutate(
time = paste("T", time),
diff = manual - electro,
avg = (manual + electro) / 2)
df2 <- df |>
group_by(time) |>
summarise(
g_avg = mean(avg),
g_diff = mean(diff),
sd_diff = sd(diff),
n = n()
)
df2
df <- df |>
left_join(df2)
ggplot(data=df, aes(x = avg, y = diff, col = ifelse(diff>(g_diff+1.96*sd_diff) | diff<(g_diff-1.96*sd_diff), "1", "0"))) +
geom_point() +
geom_rug(col="grey") +
# orange and blue colors do not show legend
scale_color_manual(values = c("black", "red")) +
geom_hline(aes(yintercept = g_diff)) +
geom_hline(aes(yintercept = g_diff+1.96*sd_diff), linetype = "dashed") +
geom_hline(aes(yintercept = g_diff-1.96*sd_diff), linetype = "dashed") +
#geom_smooth(method = "lm", se = F) +
labs(
title = "Bland-Altman plot - Inter-goniometer agreement (electro vs. manual)",
x = "Average",
y = "Difference",
caption = "Solid line represents average of differences. \nDashed lines represent limits of agreement (±1.96xSD). \nData outside 95% limits of agreement are labeled"
) +
facet_wrap(time~.) +
#plot data outside g_diff+1.96*sd_diff
geom_text(data=df, aes(label = ifelse(diff>(g_diff+1.96*sd_diff) | diff<(g_diff-1.96*sd_diff), id, NA), hjust = -0.5)) +
scale_y_continuous(limits = c(-10, 10)) +
theme_bw() +
theme(legend.position = "none")
# save the plot
ggsave("Figures/inter-goniometer-agreement.png", width = 10, height = 5)
# Bland-Altman plot - Intra-goniometer agreement
df<-NULL
for (i in 1:3){
c <- combn(1:3,2)[,i]
d1 <- d |>
filter(time %in% c) |>
pivot_wider(names_from = `time`, values_from = `y`)
names(d1) <- c("id", "goniometer", "A", "B")
d2 <- d1 |>
mutate(
diff = A - B,
avg = (A + B) / 2,
comparison=paste("T",c[1],"vs", "T", c[2]))
df <- rbind(df, d2)
}
df2 <- df |>
group_by(goniometer, comparison) |>
summarise(
g_avg = mean(avg),
g_diff = mean(diff),
sd_diff = sd(diff),
n = n()
)
df <- df |>
left_join(df2)
ggplot(data=df, aes(x = avg, y = diff, col = ifelse(diff>(g_diff+1.96*sd_diff) | diff<(g_diff-1.96*sd_diff), "1", "0"))) +
geom_point() +
geom_rug(col="grey") +
# orange and blue colors do not show legend
scale_color_manual(values = c("black", "red")) +
geom_hline(aes(yintercept = g_diff)) +
geom_hline(aes(yintercept = g_diff+1.96*sd_diff), linetype = "dashed") +
geom_hline(aes(yintercept = g_diff-1.96*sd_diff), linetype = "dashed") +
#geom_smooth(method = "lm", se = F) +
labs(
title = "Bland-Altman plot - Intra-goniometer agreement",
x = "Average",
y = "Difference",
caption = "Solid line represents average of differences. \nDashed lines represent limits of agreement (±1.96xSD). \nData outside 95% limits of agreement are labeled"
) +
# add text to geom_hline
facet_wrap(goniometer~comparison) +
geom_text(aes(label = ifelse(diff>(g_diff+1.96*sd_diff) | diff<(g_diff-1.96*sd_diff), id, NA), hjust = -0.5)) +
theme_bw() +
theme(legend.position = "none")
# save the plot
ggsave("Figures/intra-goniometer-agreement.png", width = 9, height = 6)Examples 4 - 12.
The html file can be found here.