Methods in longitudinal analyses with different follow-up times

Hi all,

I am new to this forum, but registered because I am looking for the right method to use in the analyses of two different projects, both longitudinal with different follow-up times for patients. I did some research into the study methods, but wasn't sure and wanted to check on this forum whether I'm going in the right direction.

The first study is a study where a questionnaire was sent by mail to all participants (n > 3000) and reply of the participant was seen as the measure time. Four questionnaires have been sent (after 3, 6, 9, and 12 months) but several reminders had to be sent and therefore the exact response times vary between the individuals and not all individuals have filled out every questionnaire (in fact a great deal is missing for the second questionnaire where something went wrong with the reminder emails). We are interested in the increase or decrease in the costs per patient (which can be calculated through the questionnaire answers) over time and compare these between patients that have different diseases.
After some initial research, I came to the conclusion that we might need to perform an unbalanced repeated measures model and because n is different for each measure point and follow-up varies between patients, I thought it may be best to make use of PROC MIXED in SAS (because this apparently is robust for unbalanced designs) and to possibly include time as a random factor (to account for differences in follow-up).

The second study is a study where we measured bone density over time (continuously) and want to make use of the initial measurement and compare this to the last measurement (again, there are multiple, but we are only interested in the last measurement). We want to test several factors for the difference (in this case an increase) in bone density over time, but the time of follow-up again varies between the patients (ranging from 6 months to several years). I was thinking, because we assume the increase is quite steady over time, we might make us of a general linear model using the increase in bone density over time (e.g. 1 g/cm3 per month), but I'm not sure whether this is the right approach and whether there are better ways of performing this analysis.

All help is very much appreciated!