Approach of a Golden Standard Measurement with questionnaire data

Question

I am a bit lost on the correct approach to this Statistical problem. Let me explain the context of this problem: I have a cohort population with longitudinal measurements during a period of several years and in this population, a subsample of its, has been wearing an accelerometer to measure Physical Activity (considered as the gold standard) and all of the other subjects have been answering a questionnaire regarding Physical Activity.

My goal is to predict or set a rule to approach the accelerometer using the questionnaire data and the set of predictors (like socio-economical variables, etc...) of each participant.

The outcome variable is a score of Physical Activity derived from both Accelerometer or Questionnaire. Any ideas on how to assess this problem in a cross sectional or longitudinal form?

I was thinking about Multivariant linear mixed models, but I feel like some option of training with data and validating with the Accelerometer could be a good option also.

Anything will be very welcome!

Answer 1

It's not clear to me exactly what you are trying to do.

You need to define the gold standard so that you can compare some other measure to it.

You mention longitudinal data - does that mean that the gold standard is change in the activity or the level of activity? If it's change, that's unusual, but OK. If it's level, I'm not sure why having longitudinal data matters.

What's the effect of socieconomic predictors? If they predict activity they probably shouldn't be part of the gold standard, that's asking for bias.

Typically, you're aiming for accuracy. You want a (relatively) simple measure of agreement that tells you how close your measurement is (likely to be) to the gold standard. I don't see how linear mixed models would help with that. (But I might have misunderstood your problem.)