I am trying to compare 4 different (but correlated) parameters (biomarkers of a disease with continuous values) to identify which parameters would detect more deteriorating subjects and in a shorter period. My data consists of more than 100 subjects, with measurements every 6 months for 2-6 years. Subjects have different follow-up lengths and the data is right-censored.
I am using a time-to-event approach. To define the events (significant change from baseline, first study measurement), I am using 95% repeatability estimates of each parameter. If the difference between a follow-up measurement and the baseline is more than the expected 95% repeatability, that is being considered an event. To compare the Kaplan-Meyer survival curves between the parameters, I intend to use pair-wise log-rank or Cox regression comparisons. (At the moment, I am not concerned to use pair-wise comparisons between 4 parameters)
I see two issues with this approach:
1 - The descriptions of log-rank or Cox regression that I find always describe comparisons between two groups. I imagine that comparing two parameters in the same subjects may violate some assumptions, given their correlation (I don't know how strong the correlation is). Reading this "Which model should I use for Cox proportional hazards with paired data?" and this "How to conduct conditional Cox regression for matched case-control study?", I am planning to use a frailty random coefficient for the subject level. Would it be adequate and sufficient?
2 - My event definition gives a 5% chance of false-positive, i.e. considering a amount of change in a parameter significant (and therefore an event), when it occurred by chance due to measurement variability. Subjects with longer follow-up and more measurements would have a higher chance of having any false-positive during the study. How can I account for this? I am aware of familywise error rate and false discovery rate procedures, but I am not sure if and how they apply in a time-to-event approach.
I would imagine this scenario happen frequently in biomedical research, yet I didn't find clear solutions searching Google, Pubmed or this forum. I would appreciate any solutions or guidance about where to look for them. Thanks!
