Progression free survival

[May Blake]

I have a very simply survival data that I would like to model. I have modeled overall survival very easily. Next, I want to conduct a progression free survival (PFS). I have 3 patients who are alive that also progressed. But all of my 40 deceased patients also progressed. Does this mean I can't model PFS?

[Carlo Lazzaro]

May:
are you referring to parameters to populate a decision (say, Markov) model?
if this were the case, PFS and Death are considered different health states.
Therefore, you should calculate the transition probability of moving from each health state to the other one (and to remain in the same state with no transition).
At the end of the model time horizon (if lifetime), most of the hypothetical cohort of patients has reached the absorption state (Death).

[Clyde Schechter]

To model progression-free survival you must have a variable with the date at which progression occurred, or a date at which they were last known to be progression-free. This applies whether the patient ultimately died or not. You just change your -stset- command so that the time variable is the date of progression/last known progression-free, and the -failure- variable indicates that progression occurred at that date.

If your data has a date of progression variable, but it has only missing values for the people who died, then replace the missing values of the progression date variable by the last date at which they were followed-up in the study but were still progression-free, and have them censored as of that date in your analysis.

How do you know all of your deceased patients progressed? In almost every study like this there will be some people who die of causes unrelated to the disease under study. (For some cancers that will even be the majority of the deaths in the study. For example, most breast cancer patients die of other causes, heart disease being the commonest.)

[Daniel Schaefer]

I could be mistaken, but I think May is suggesting a survival analysis to model the expected time until a disease progresses (rather than patient death) using regression methods rather than a discrete Markov or hidden Markov model. I think the answer to the question depends to a large extent on what you want to model precisely and how you define "progression". If you define progression very broadly as any kind of "state change" (whether that be death or some other advancement of illness), then you can use regression style techniques to model the time to progression. If you think the kind of progression really matters, that could be tricky.

Just to be more concrete, if, say, you want to model progression from stage 1 cancer to stage 2 cancer and no one in your sample goes straight from state 1 cancer to some other state (like death), then you should be okay to model the transition from state1 to stage 2 cancer, even if some of your patients later die after transitioning to stage 2. All the better if you have theoretical reason to think no one should die from stage 1 cancer, nor should they progress straight from stage 1 to stage 2. The key here is that if you want to model progression from stage 1 to stage 2, and everyone goes from stage 1 through stage 2, then there shouldn't be any problem modeling the duration from stage 1 to stage 2 regardless of the downstream outcomes. Likewise, if there are many possible outcomes but you don't care about the distinctions (you just want to model time to progression broadly) that should be okay too. If you consider transitioning from stage 1 cancer to stage 2 cancer and from stage 1 cancer to death as progression and don't care to model the distinction, then the statistics will support that. If you really care about modeling the different paths a patent might go down, then a Markov model or hidden Markov model (as suggested in #2) might be most appropriate, but keep in mind that modeling time/duration in that context is tricky.

Regardless, the answer is rarely that you simply can't do whichever kind of analysis you want to do. Usually you really just want to be careful and thoughtful about how you model things. A lot of this depends on your study design, the details of what you are modeling, and what your data can support.

Edit: Crossed with #3.

[May Blake]

Hi Carlo, thank you. See below for my data example. From my understanding, to conduct the PFS analyses, I need to create a new variable and censor all the patients who haven't progressed during the mortality analysis so essentially set these to 0 for the 0/1 failure variable. So I am unsure how to do that when all of my deceased patients also progressed so if I set all those values to 0, then I won't have any deceased patients. I have three dates in my data (Death date, progression date and censor date). All the progression dates occur before the death dates.
----------------------- copy starting from the next line -----------------------

* Example generated by -dataex-. For more info, type help dataex
clear
input byte(studytime died drug age _st _d _t _t0) float(progress PFS)
 1 1 1 61 1 1  1 0 1 0
 1 1 1 65 1 1  1 0 1 0
 2 1 1 59 1 1  2 0 1 0
 3 1 1 52 1 1  3 0 1 0
 4 1 1 56 1 1  4 0 1 0
 4 1 1 67 1 1  4 0 1 0
 5 1 1 63 1 1  5 0 1 0
 5 1 1 58 1 1  5 0 1 0
 8 1 1 56 1 1  8 0 1 0
 8 0 1 58 1 0  8 0 1 0
 8 1 1 52 1 1  8 0 1 0
 8 1 1 49 1 1  8 0 1 0
11 1 1 50 1 1 11 0 1 0
11 1 1 55 1 1 11 0 1 0
12 1 1 49 1 1 12 0 1 0
12 1 1 62 1 1 12 0 1 0
15 1 1 51 1 1 15 0 1 0
17 1 1 49 1 1 17 0 1 0
22 1 1 57 1 1 22 0 1 0
23 1 1 52 1 1 23 0 1 0
 6 1 2 67 1 1  6 0 1 0
 6 0 2 65 1 0  6 0 0 0
 7 1 2 58 1 1  7 0 1 0
 9 0 2 56 1 0  9 0 1 0
10 0 2 49 1 0 10 0 0 0
11 0 2 61 1 0 11 0 0 0
13 1 2 62 1 1 13 0 1 0
15 0 2 50 1 0 15 0 0 0
16 1 2 67 1 1 16 0 1 0
19 0 2 50 1 0 19 0 0 0
20 0 2 55 1 0 20 0 0 0
22 1 2 58 1 1 22 0 1 0
23 1 2 47 1 1 23 0 1 0
32 0 2 52 1 0 32 0 0 0
 6 1 3 55 1 1  6 0 1 0
10 1 3 54 1 1 10 0 1 0
17 0 3 60 1 0 17 0 0 0
19 0 3 49 1 0 19 0 0 0
24 1 3 58 1 1 24 0 1 0
25 0 3 50 1 0 25 0 0 0
25 1 3 55 1 1 25 0 1 0
28 1 3 57 1 1 28 0 1 0
28 0 3 48 1 0 28 0 0 0
32 0 3 56 1 0 32 0 0 0
33 1 3 60 1 1 33 0 1 0
34 0 3 62 1 0 34 0 0 0
35 0 3 48 1 0 35 0 1 0
39 0 3 52 1 0 39 0 0 0
end
label values died diedlbl
label def diedlbl 0 "No", modify
label def diedlbl 1 "Yes", modify
label values drug type
label def type 1 "Placebo", modify
label def type 2 "Other", modify
label def type 3 "NA", modify

------------------ copy up to and including the previous line ------------------

Listed 48 out of 48 observations

[Carlo Lazzaro]

May:
have you considered competing risks regression (the two failures being PFS and Death)?

[May Blake]

Carlo, I haven't but this sounds interesting. The other analyses I have considered is combined risk of progression/death and that was easy to model. Would I use the Fine's and grays for competing risks? The stcrreg command?

[Carlo Lazzaro]

May:
exactly.

[May Blake]

Thank you so much!

[Paul Dickman]

In studies of cancer patients, the commonly accepted definition of progression-free survival is

Progression-free survival refers to the time from randomisation or initiation of treatment to the occurrence of disease progression or death. https://www.thelancet.com/journals/l...015-8/abstract

See also the US FDA's Clinical Trial Endpoints for the Approval of Cancer Drugs and Biologics.

That definition is sometimes also used in other areas. I'm guessing that's what you did with the analysis of "combined risk of progression/death". As has been mentioned, there are other measures that can be estimated but I would advice caution with some of these (e.g., competing risks analysis) because you don't appear to have complete data on time-to-progression among individuals who die. You mentioned "all of my 40 deceased patients also progressed" so then your two competing outcomes would be "progression" and "death due to disease with progression but without recorded date of progression". I'm not sure how clinically relevant that would be. If you have patients who have died of other causes, without progression, then things get difficult.