Prophetic variable in survival analysis - or not?

Problems with using “prophetic” variables in survival analysis are well known. Just to fix concepts, let me quote Terry Therneau:

This particular incorrect analysis is re-discovered every few years in oncology. (Or I should say republished). Like the mythical hydra, it never seems to go away. Group people, at baseline, according to whether they eventually had a complete or partial response to therapy (shrinkage of tumor), and then draw the survival curves. Surprise – responders always do better! Why?

He then goes on to explain that to have response determined at all, you need to live long enough to reach assessment. Finally he gives the well-known recommendation:

Some time-dependent covariates are not predictors of an event as much as they are markers of a failure-in-progress. […] Basic rule: At any time point, the covariates can be anything that you want, as long as they use only information that would have been available on that day, had analysis been done then.

Now, consider the following example (Antonia et al. Lancet Oncol 2019):

At first glance, my impression was “ah, again what Terry was talking about, grouping people according to response”. However, if you look more carefully, you’ll see that the horizontal axis measures time not from the original index time, but rather from 6 months, at the time when response was assessed. So, in these survival plots response is not a prophetic variable as it was determined for everyone, and was known at Time 0 (of this plot), those who had no response assessment were excluded (as described by the footnote).

For some reason I still have some bad feeling about this whole plot, so I thought it worth asking you, if you see any problem with this analysis.


I think the difficulty mainly lies in what this graph tells us and what information you are interested in.

For some more background, normally these analyses are problematic as they determine the responder status at the end (or at some midpoint) of the study and then compare the response groups with regards to survival time or percentage. As individuals need to survive up to that timepoint to be able to be classified as responder, the individuals that end up in the responder group are in a sense ‘immortal’ up to that timepoint (as they would not be in that group if they had died already). When you then compare the survival from baseline (t0) between responder and non-responder groups then the non-responder group by definition has a shorter survival (or lower percentage survival). Hence the name immortal time bias.
In short, you create groups that by definition have a longer/better or shorter/worse survival and then when you compare them you find that they are different with regards to this defining characteristic.

The approach the authors use here is a landmark analysis at 6 months which is one way of dealing with the immortal time bias these analyses introduce. They only take individuals that have survived up till month 6, assess their response status and then determine their survival from the 6 month mark onwards. This ensures that all individuals in your analyses will have lived for at least 6 months (and so all individuals that died/dropped out before the 6 month mark are removed from your analyses). This eliminates the immortal time problem as all individuals in this analysis now have survived the first six months.

Then what the graph itself tells us is basically what the survival looks like in the upcoming period for individuals that have survived for at least 6 months depending on their response status at 6 months. It makes sense of course that responders have a better apparent survival and this will almost always be the case (bit of an open door analysis in a sense but you could still be interested in quantifying the difference). However, you could imagine that maybe some medication only has beneficial short term effects while after 6 months there is no difference between people that responded or not and so then the curves might be much closer to each other than in this example.

Edit: specifically, what this graph does not tell us is the overall survival on this medication or compare the performance against the other medication. For that you would need the other graphs/analyses. Also in Figure 3 they visualize the landmark analysis at 6 months for both nivolumab and docetaxel:

I would however not feel completely comfortable comparing the medication performance based on this graph. As mentioned above, these analyses exclude all individuals that die during the first 6 months. If mortality in both treatment groups is substantially different in this 6 month period, then the performance after the 6 month mark based on response is somewhat difficult to interpret I think.

1 Like

First of all, thank you very much @scboone for your detailed answer!

Thanks! I actually haven’t realized that this is simply a form of “immortal time bias”, but otherwise your description matches that of Therneau which I have quoted.

OK, it seems my “bad feelings” were not warranted, and it is correct… thanks for the confirmation!

Clear! Thanks. Perhaps we could summarize it by saying that this whole analysis is conditional on the patient surviving at least 6 months.

The classification (CR/PR, SD, PD) occurs (or becomes obvious) at t=6. The graph separates the three classes prematurely and exaggerates the differences in survival rates after t=6. The differences in the slopes of the three curves would be easier to evaluate, I believe, were starting point for the comparisons set at t=6 (relabeled as t=0). The time series could begin at t=-6 to show the lead in for each class.