# Visualizing longitudinal data with binary outcome

For longitudinal data with a numeric outcome, I can use spaghetti plots to visualize the data. For example something like this (taken from the UCLA Stats site):

tolerance<-read.table("http://www.ats.ucla.edu/stat/r/faq/tolpp.csv",sep=",", header=T)
interaction.plot(tolerance$time, tolerance$id, tolerance$tolerance, xlab="time", ylab="Tolerance", legend=F)  But what if my outcome is binary 0 or 1? For example, in the "ohio" data in R the binary "resp" Variable indicates the presence of a respiratory disease: library(geepack) ohio2 <- ohio[2049:2148,] head(ohio2, n=12) resp id age smoke 2049 1 512 -2 1 2050 0 512 -1 1 2051 0 512 0 1 2052 0 512 1 1 2053 1 513 -2 1 2054 0 513 -1 1 2055 0 513 0 1 2056 1 513 1 1 2057 1 514 -2 1 2058 0 514 -1 1 2059 0 514 0 1 2060 1 514 1 1 interaction.plot(ohio2$age+9, ohio2$id, ohio2$resp,
xlab="age", ylab="Wheeze status", legend=F)


The spaghetti plot gives a nice figure, but is not very informative and does not tell me much. What would be a suitable way to visualize this kind of data? Maybe something that includes a probability-value on the y-axis?

• Plotting the average of response versus age is where I'd start. Next level might be showing the fractions of transitions 00, 01, 10, 11 at each age. Nov 13, 2013 at 12:44
• My current version of R does not have the ohio data (2.15) (at least not as part of base). Is it in a newer version or via some other library? This would be an interesting application for a heat-map with individuals on the Y axis and outcomes on the X axis, then plot 1 responses as black and 0 responses as white. Sorting the matrix will then provide an overview of how prevalent different patterns are. Nov 13, 2013 at 15:21
• @Andy I had to scout around... turned out it's inside the geepack package. Nov 13, 2013 at 15:28
• Yes, sorry about that. I modified my posting above. Nov 13, 2013 at 15:29
• please look at article "Dynamics from Multivariable Longitudinal Data" (specifically for binary data) doi:10.1155/2014/901838.
– user46436
May 30, 2014 at 10:26

There are quite a few ways to work around it.

Jittering the variables mildly to smear the lines apart

First, since both age and the outcome are nicely discrete, we can afford to mildly jitter them in order to show some trends. The trick is to use transparency in the line color so that it's easier to discern the magnitude of overlapping.

library(geepack)
set.seed(6277)

ohio2 <- ohio[2049:2148,]

jitteredResp <- ohio2$resp + rnorm(100,0,0.02) #$
jitteredAge  <- ohio2$age+9 + rnorm(100,0,0.02) #$
age          <- ohio2$age+9 #$
id           <- ohio2$id #$
wheeze       <- ohio2$resp #$

#### Variation 1 ####
plot(jitteredAge, jitteredResp, type="n", axes=F,
xlab="Age to the nearest year, jittered",
ylab="Wheeze status, jittered")
for (i in id){
par(new=T)
lines(age[id==i], jitteredResp[id==i], col="#FF000008", lwd=2)
}
axis(side=1, at=seq(7,10))
axis(side=2, at=c(0,1),  label=c("No", "Yes"))


Getting fancy

It's also possible to use this kind of curves to show the flow of the subjects. It's just like a modification of the above chart, but using the width of the line to represent frequency rather using overlapping.

Show the fate of each case

This may sound counter-intuitive, but if you lay the cases out in a systematic manner, it works just as fine to tell the aggregated story. Here the outcome of each case is shown along a grey color reference line. I didn't add a legend there but using legend command it can be added quite easily. Blue is "resp = 0" and Red is "resp = 1". Time (age) is spread out on the x-axis. Your data are conveniently presorted by outcome pattern, so I didn't have to do anything. If they are not presorted, you'd have to use command like dcast in package reshape2 to massage the data a bit.

#### Variation 2 ####
my.col             <- vector()
my.col[wheeze ==1] <- "#D7191C"
my.col[wheeze ==0] <- "#2C7BB6"

plot(age, id, type="n", frame=F, xlab="Age, year", ylab="", axes=F, xlim=c(7,10))
abline(h=id, col="#CCCCCC")
axis(side=1, at=seq(7,10))
mtext(side=2, line=1, "Individual cases")
points(age, id, col=my.col, pch=16)


Tabulation

Visualization is not the only way out. Since there would only be, at most, 16 different patterns, you can also tabulate them. Use + and - to create patterns like + + + + and + - - -, and then for each of these patterns, attach the counts and percentage. This can show the information equally effectively.