Update Section 13.2 in the intial survival analysis example

book/chapters/chapter13/beyond_regression_and_classification.qmd

@@ -128,12 +128,14 @@ By using `po("learner_cv")` for internal resampling and `po("tunethreshold")` to
 ## Survival Analysis {#sec-survival}
 
 `r index("Survival analysis")` is a field of statistics concerned with trying to predict/estimate the time until an event takes place.
-This predictive problem is unique as survival models are trained and tested on data that may include 'censoring', which occurs when the event of interest does *not* take place.
+This predictive problem is unique because survival models are trained and tested on data that may include censoring, which occurs when the exact event time is not observed.
+The most common type of censoring is 'right censoring', which happens when the event of interest has not yet occurred by the time observation ends.
+For the rest of this section, censoring means right censoring unless otherwise stated.
 Survival analysis can be hard to explain in the abstract, so as a working example consider a marathon runner in a race.
 Here the 'survival problem' is trying to predict the time when the marathon runner finishes the race.
-However, if the event of interest does not take place (e.g., the marathon runner gives up and does not finish the race), they are said to be censored.
+However, if the organizers stop recording finish times after a certain point, then any runner still running beyond that time will be censored.
 Instead of throwing away information about censored events, survival analysis datasets include a status variable that provides information about the 'status' of an observation.
-So in our example, we might write the runner's outcome as $(4, 1)$ if they finish the race at four hours, otherwise, if they give up at two hours we would write $(2, 0)$.
+In our example, we might record a runner's outcome as $(3, 1)$ if they finish the race at three hours and we observe it, and as $(4, 0)$ if they are still running at four hours when we stop observing.
 
 The key to modeling in survival analysis is that we assume there exists a hypothetical time the marathon runner would have finished if they had not been censored, it is then the job of a survival learner to estimate what the true survival time would have been for a similar runner, assuming they are *not* censored (see @fig-censoring).
 Mathematically, this is represented by the hypothetical event time, $Y$, the hypothetical censoring time, $C$, the observed outcome time, $T = \min(Y, C)$, the event indicator $\Delta := (T = Y)$, and as usual some features, $X$.