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For my research I am doing an health economic assessment of patients with a renal transplant. For my model I need to know their (yearly) mortality probability. My plan was to extrapolate survival data to determine the mortality probability from the extrapolation. So I did the following steps:

I have survival data for ~6,5 years. Using R I fitted the best distribution (which was a Weibull distribution). I extrapolated this distribution for t = 50 (the patients are now 100). Visual analysis of the extrapolation looked like it made sense.

However: Quit frequently in these type of models we make use of background mortality. But I assumed that in my extrapolation of the mortality this background mortality is included. Just to make sure I did compare the two.

So now my problem: After ~t = 40 my yearly background mortality is higher than my extrapolated yearly mortality. From a clinical point this makes no sense, since patients with a renal transplant are more likely to die, not less likely.

I am unsure how to best address this problem. I have considered that at the intersection point the extrapolation will now follow the background mortality. I have also considered to calculate a constant hazard ratio.

Anyone any experience with doing this or any tips?

Please let me know if you need more information or have any questions.

EDIT:

I have found an article from Jackson et al. (2017) "Extrapolating survival from randomized trials using external data: a review of methods". It highlights several possibilities to use external data (so the background mortality e.g.) for extrapolation. I am currently looking in to all the methods to see how they affect the mortality.

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