Multilevel alternative to Paired t-test I have a problem where we have N patients, and we measure some property of tumoral lesions for each patient, where the number of lesions varies on each patient (patient A could have 1 lesion, and patient B could have 5).
For each lesion we measure the property using two different methods, so from this point of view we could use a paired t-Test, but, I would like to account on possible differences between patients.
Is there any alternative test to the paired t-test that could account for differences in each patient?
Thanks,
 A: Following on from discussion in the comments, my suggestion would be that, in general, for a case like this mixed-effects regression would be the appropriate approach to take.
Your model would contain two random effects (unless there's others not mentioned): patient, and lesion which would be nested under patient. There would be at least one fixed effect: the method used for measurement.
You would likely want to test both random intercepts and random slops for both patient and lesion.
Now the catch, it sounds like you may have some patients who only have one lesion. For these patients you couldn't estimate distinct random effects for both patient and lesion (because you couldn't tease apart the variance associated with each). Assuming such a model would converge, I'm not sure whether this would have a consequence for the estimates associated with the fixed effect (i.e., assessing whether there's a difference overall difference between methods). Someone else may know.
The alternatives here would be to remove the random effect for lesion (the between lesion variance within a patient would no longer be being accounted for) or to retain the random effect but remove the nesting (between lesion variance would still be accounted for, but the fact that a pair of lesions within a single person may be more similar than a pair of lesions between two people would not). I'm not sure whether either way is better than the other...
Some reading:
https://en.wikipedia.org/wiki/Mixed_model
https://cran.r-project.org/web/packages/lme4/index.html
@book{gelman2007data,
  address =  {New York, NY},
  author =   {A. Gelman and J. Hill},
  publisher = {Cambridge University Press},
  title =    {Data analysis using regression and multilevel/hierarchical models},
  year =     2007
}

