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In order to find an optimal time for initiation of treatment post surgery (oncologic patients) I created a ROC curve with death defined as event. The AUC was not significant. However, I decided to use the time that provided the best specificity and sensitivity in cox regression as a binary variable. The Cox parameter was significant. I was wondering whether I am committing a sin using data from ROC curve with p-value > 0.05 and by using the data obtained from exploratory analysis to analyse the same training data. I would be very interested in hearing feedback and suggestions (maybe for validation?)

Thanks in advance, Liran

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I can't see how you could find the optimal time without using utilities and incorporating uncertainty.

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If you define a binary variable based in the "best" cutpoint (best sens. and spec.) is not surprising you have a Cox regression with a significant P-value, but the issue this test is not correct now. The selection of the best cutpoint is a similar idea to analysis the máximum of all the statistics over all possible cutpoints. A suggestion is test the significance by permutations, where the censored label and survival times are permuted and the whole analysis is repeated ( search of the best cutpoint and Cox regression with the binary variable )

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