Compare two survival curves for paired data

I want to compare two different methods for detecting status change in a survival analysis. A group of subjects is being followed for a longer period (many years), and two examination methods have been used to examine whether a status change has occurred; one method was used to examine each subject twice a year and the second method was used to examine each subject once a year. The question is if these two methods differ systematically in their ability to detect a status change.

The test that I came to think of is a log rank test to see if the two method’s Kaplan-Meier curves differ. I wonder if it is a problem that the survival curves are “paired” (i.e. the two methods are used on the same subjects) when performing the log-rank test. Is it a violation of assumption in the log-rank test, or is it perhaps just an inefficient test since it doesn't account for that the two curves are related? Does anyone have a suggestion for an alternative analysis that do accounts for the dependence within the observations?

Maybe this is not a problem, maybe I am over thinking.

Well, I don’t know the true time of status change, only the time points when the methods have detected a status change. One thought I had was to set the survival time to the midpoint of the time interval between the last examination when status change had not been detected and the examination when status change had been detected. That could compensate for the disadvantage of the method that is used for examining the subjects only once a year in contrast to the method that is used twice a year. And then construct the survival curves from these data.

• Of possible interest: A distribution-free procedure for comparing receiver operating characteristic curves from a paired experiment. In this paper the authors present a method for comparing two techniques for diagnosing melanoma. The problem I see in your context is that you have triplets $(x_i,y_i^1,y_i^2)$ and therefore it is not clear what is a fair comparison between the methods. I think you have to provide information about how are you constructing the survival curves. – user10525 Nov 6 '12 at 13:52
• Indeed the Kaplan-Meier curve difference assumes independence, and that is not appropriate. One can look at significance of difference of proportions or construct a correlated test of the same type. – Carl Sep 1 '16 at 4:43
• Hint – Carl Sep 1 '16 at 4:49

1 Answer

If you want to compare the model performance of the two survival models, calculation of the C-statistics (Harrell's C, survival ROC...) might be more reasonable approach. Calculate the C-statistics of the two survival model and compare them (p-value can be obtained).

https://rpubs.com/kaz_yos/survival-auc

The link shows various tool for the C-statistics for survival model.