Aggregating Kaplan Meier Curves

[Eduardo Urgesi]

Hi all,
I have multiple Kaplan Meier curves expressed as:

X: (time variable)
Y: Survival probability (0 to 1)
95% Confidence interval for Y
SE for Y

All the KM curves share the same X intervals (i.e. all X variables are either 0, 1, 2, 3, .. etc.

What is the best method to aggregate the survival probabilities of the curves, to construct a singe KM curve with a 95% Confidence interval for Y, at each X,Y co-ordinate? Is it appropriate to use the DerSimonian-Laird Method?

Many thanks

[Leonardo Guizzetti]

I think you’re basically repeating your previous question.

I don’t believe it’s possible to do this because of censoring. You will need to know the full distribution of event and censoring times.

[Eduardo Urgesi]

This user interface (https://www.trialdesign.org/one-page...html#IPDfromKMc) allows you to extract individual patient data, and therefore offers censoring information as:
Survival time (X months) and status (1 or 0) according to study outcome, for each of the patients in the cohort. Given this information, would not it be possible to obtain censoring times?

[Leonardo Guizzetti]

Interesting, tool. I've heard of such "data ripper" software but have never tried it myself. It looks like you will get as output the survival fraction at each point in the curve. Combining this with the starting sample size, you should be able to reconstruct the number of events, timing of events, and number of censoring events within an interval. If you have this in hand, it's reasonable that you can perform, essentially, a meta-analysis of the curves. More accurately, you are reconstructing aggregate failure and event data from which you are slightly approximating the real data (since you'll be forced to assume interval censoring), and so you can generate aggregate-level meta-analyses. I haven't thought about whether the curves can be validly combined or not.

[Eduardo Urgesi]

This is the type of data the software ("ripper") provide me with.

The censoring information can be derived by the columns on the far right. By these means, the numbers at risk and censoring are available for any given Time (X).
For instance, at 4 months, SP is 0.9545 and censoring is 5. The total number of patients in the cohort is 114, therefore the numbers at risk at 4 months is 109.

What is the best approach to combine 2 KMs (provided the above is available for both)? The DerSimonian Leird does not account for censoring. Any suggestions on how to proceed from here?

[Tiago Pereira]

Eduardo, the only approach suitable for your case is to reconstruct individual patient data (IPD), and then generate a simple KM plot. This will be a fixed-effect-like analysis. Since you have IPD, you can fit any suitable model/analysis and account for each individual stratum. Meta-analysis of survival estimates will not provide good estimates, specially around the extremes.

[Tiago Pereira]

Today I came across this paper. It seems to work with survival estimates. Not sure if this approach has been implemented in R or Stata, though.

https://onlinelibrary.wiley.com/doi/10.1002/sim.6111