Analysis on repeated measurements with only one follow-up outcome I would like to analyze the association between dietary intake and a specific health outcome. Now suppose I have 100 subjects, each having 10 repeated measurements of dietary intake collected from the following 10 weeks (i.e. the data shape is 100*10). And in the 11th week, I have acquired the follow-up outcome of the health status (diseased/not diseased) for each subject. Then, how can I achieve my goal for the analysis?
I am thinking of some simple regression models, but perhaps it would be better to make the best use of the repeated measurements of dietary intake. This seems like a longitudinal design, but I only have one outcome variable at one time point. Is it okay for just calculating the average intake across the ten time points and regressing the average intake on the binary outcome using logistic regression? Or maybe is there a better choice to construct a one-dimension indicator from the repeated measurements, so that I can include it in a regression model?
 A: It's probably best not to think of the health status as an outcome, because you have no information about its value prior to the study. Since diet-related health status typically changes very slowly, it seems likely (to me, at least) that the pre-study and post-study status will be the same in most cases. You certainly can't make any arguments that the dietary intake caused the final health status, at that might have been the status throughout the study.
You can say something like "participants with this health status at the end of the study had this dietary intake over the prior 10 weeks." For that you can use a regression model but with the order reversed from what you are considering.
The final health status would be the "independent" variable, presumably representing the status throughout the study. That's probably just 2 categories, from what you describe.
The dietary intake values would be the "dependent" variables. You should model the intake with a method that takes into account the repeated measurements for each participant and the associated internal correlations of values. That could be structured as a true "multivariate" (multiple-"outcome") regression, depending on the nature of your dietary intake values. This document is one brief introduction to how that's a set of individual regressions (effectively t-tests, in your case with only a binary "independent" variable) evaluated together with a variance structure that recognizes the within-participant correlations.
If you think that there might be some important trend over time, you could model week directly as a predictor and account for within-participant correlations with generalized least squares. Frank Harrell's course notes and book illustrate that approach in Chapter 7.
You also could include week as a (continuous or categorical) predictor and account for within-participant correlations with a mixed-effect model, treating participants as random effects.
However your proceed, the results will be difficult to interpret as you don't know the health status at the start of the 10-week period. My suggestions assume that the health status was unchanged throughout, so that the final health status is a reliable way to group the participants. If that's not the case, I'm not sure what can be done.
