Comparing the performance of various Cox models on a given data set

#1
Hi everyone,

First thread here :)

Was wondering if any survival analysis experts could weigh in on my options here.

I am analyzing a data set of patients who have undergone lung transplant (time 0 = transplant), the outcome is death or retransplantation, and I am looking at post-transplant lung function as the co-variate of interest. Specifically, I am looking at if or when serial lung function deteriorates to cross certain thresholds (<50% of their best lung function, <50% of their predicted lung function, or <30% of their predicted lung function). So for a given threshold, a given patient can either (a) not fall below threshold, and stay in the low risk group or (b) meet criteria at time x and cross into the risk group. Given that, we are analyzing crossing the threshold as a time-varying co-variate.

We therefore have three multivariable models (all adjusted for age, gender and original diagnosis they had the transplant for), so we have model performance metrics for each - log likelihood, AIC, BIC etc. They are not, as far as I can see, nested models.

The analyst I've been working with is concerned that these values can't be directly compared to say which model is "better" - ie. better explains variation in the outcome - because they are essentially based on different data points (not all <50% best patients meet criteria for the other states and vice versa) due to the nature of the time-varying co-variates and the different thresholds we're analyzing. But he admits he's not a survival analysis expert and that he could be wrong.

Does anyone have any experience with this? Is it valid to, say, compare the log likelihoods as metrics of model performance to say one threshold is more useful at predicting the outcome?