Is the best way to find the median survival time from a survival plot just to draw a horizontal line from $p = 0.5$ to the curve and project down to the x-axis?
Solved – Finding median survival time from survival function
survival
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There must be many ways to make follow-up time plots with interval censored data, although a quick Google search only found this image in an overview of censoring, which looks a bit busy to my eye.
Just to give another perspective, here's an approach using the ggplot2 package.
require(ggplot2)
# Your example data
dat <- structure(list(ID = 1:5, eventA = c(0L, 1L, 1L, 0L, 1L),
eventB = c(1L, 0L, 0L, 1L, 0L), t1 = c(7, 5, 10, 4.5, 2), t2 = c(7, 5, 10, 4.5,
8), censored = c(0, 0, 0, 0, 1)), .Names = c("ID", "eventA",
"eventB", "t1", "t2", "censored"), class = "data.frame", row.names = c(NA, -5L))
# Create event variable
dat$event <- with(dat, ifelse(eventA, "A", "B"))
# Create id.ordered, which is a factor that is ordered by t2
# This will allow the plot to be ordered by increasing t2, if desired
dat$id.ordered <- factor(x = dat$ID, levels = order(dat$t2, decreasing = T))
# Use ggplot to plot data from dat object
ggplot(dat, aes(x = id.ordered)) +
# Plot solid line representing non-interval censored time from 0 to t1
geom_linerange(aes(ymin = 0, ymax = t1)) +
# Plot line (dotted for censored time) representing time from t1 to t2
geom_linerange(aes(ymin = t1, ymax = t2, linetype = as.factor(censored))) +
# Plot points representing event
# The ifelse() function moves censored marker to middle of interval
geom_point(aes(y = ifelse(censored, t1 + (t2 - t1) / 2, t2), shape = event),
size = 4) +
# Flip coordinates
coord_flip() +
# Add custom name to linetype scale,
# otherwise it will default to "as.factor(censored))"
scale_linetype_manual(name = "Censoring", values = c(1, 2),
labels = c("Not censored", "Interval censored")) +
# Add custom shape scale. Change the values to get different shapes.
scale_shape_manual(name = "Event", values = c(19, 15)) +
# Add main title and axis labels
opts(title = "Patient follow-up") + xlab("Patient ID") + ylab("Days") +
# I think the bw theme looks better for this graph,
# but leave it out if you prefer the default theme
theme_bw()
And the result:
When making graphs with line-type, color, size, etc. conditional on data, I find ggplot2 more intuitive than base graphics and even trellis, although trellis is much faster when plotting bigger data.
I'm not sure if it is preferred to place the event marker in the middle of the censored interval or at the end. I chose the middle here, to emphasize that the event did not necessarily occur near the end of follow-up.
Addendum
Once you decide on a standard plot, and if you find yourself making these plots often, it can be convenient to wrap it up in a function and use R's S3 object system to dispatch the plotting method with a call to the plot() generic. The following does not relate directly to the original question, but for the sake of other readers interested in adding methods to the plot() generic I'll include it here. First, wrap up the ggplot call into a plot method function:
plot.interval.censored <- function(x, title = "Patient follow-up",
xlab = "Patient ID", ylab = "Days",
linetype.values = c(1, 2), shape.values = c(19, 15))
{
x$event <- with(dat, ifelse(eventA, "A", "B"))
x$id.ordered <- factor(x = dat$ID, levels = order(dat$t2, decreasing = T))
out <- ggplot(x, aes(x = id.ordered)) +
geom_linerange(aes(ymin = 0, ymax = t1)) +
geom_linerange(aes(ymin = t1, ymax = t2, linetype = as.factor(censored))) +
geom_point(aes(y = ifelse(censored, t1 + (t2 - t1) / 2, t2), shape = event),
size = 4) +
coord_flip() +
scale_linetype_manual(name = "Censoring", values = linetype.values,
labels = c("Not censored", "Interval censored")) +
scale_shape_manual(name = "Event", values = shape.values) +
opts(title = title) + xlab(xlab) + ylab(ylab) +
theme_bw()
return(out)
}
Then, add internal.censored to the class of your data object:
class(dat) <- c("interval.censored", class(dat))
Now, the plot can be produced simply by calling:
plot(dat)
You can either put plot.interval.censored() into a package, or add it to your .Rprofile, in which case it will always be available to you when you start R on your machine. Publishing a package might be preferred, as it is easier to share with others or install when you are not on your own machine. However, editing .Rprofile might be simpler. Hadley has a great overview of the S3 object system.
The median survival time, $t_{\textrm{med}}$, is the solution of $S(t) = \frac{1}{2}$; in this case, $t_{\textrm{med}} = \exp(\mu)$. This is because $\Phi(0) = \frac{1}{2}$ when $\Phi$ denotes the cumulative distribution function of a standard normal random variable.
When $\mu = 3$, the median survival time is around $20.1$ as depicted in the picture below.
Best Answer
Assuming your survival curve is the basic Kaplan-Meier type survival curve, this is a way to obtain the median survival time. From Machin et al. Survival Analysis: A Practical Approach:
This can either be done, as you suggested, using a graphical technique with your curve, or using the survival function estimates used to construct said curve.