Thank you for the informative responses. My turn!
1. Because of the censoring and because the body condition covariates are time-varying, I'm not seeing how a good binary GLMM can be constructed. The resume values don't switch back and forth across periods between N and Y depending on body conditions; a resume value is N until it (possibly) becomes Y. Looks like event data to me.
2 and 3. Your approach to variable selection is arguably treacherous. But I concur that you have too many predictor variables for your sample size. Even with this process of down-sizing to 7 variables, you still need to assess multicollinearity among them. A quick Google of "multicollinearity detection" generates a lot of useful links. Multicollinearity is a property of the predictor variables, so you can read about multicollinearity in regression texts that deal with normal-distribution response and use multicollinearity statistics generated by regression software (like REG).
4. If body conditions are largely a consequence of intervention, then it would be appropriate to drop intervention.
5. By default, if an observation contains a missing value for one or more predictor variables, the software will drop that observation in the model fitting; this is true for most (if not all) software packages. So, you need to deal with those missing values in some fashion, or you'll lose those observations.
6 and 7. I commend you for not blinding using stat software! This forum is usually good to help with code when you provide enough detail to identify an appropriate model for a corresponding dataset. In this case, as you can tell, I don't believe a binary GLMM is appropriate so I cannot help with syntax for that model (or should not, but see below). If you switch to a time-to-event model, this website which I linked to earlier http://www.ats.ucla.edu/stat/r/examples/alda/ has SAS code examples, and the forum could help with code if you hit snags.
In the interest of your ongoing education, I will add that if I liked your approach, which I don't, I would start with
proc glimmix data=resumption method=laplace;
class period id;
model resume = wt bmi perbf fm fmi lmi lpct tpct tlpctr apct gpct agpctr period /
link=logit dist=binomial or solution;
random int / subject=id;
random period / subject=id type=ar(1);
run;
This sort of model almost always requires some twiddling, even beyond that needed to identify a good covariance structure type. Including "type=ar(1)" and "residual" on the first random statement is wrong. Including both random statements as here identifies an AR(1)+RE covariance structure. Omitting the first random statement and retaining only the second identifies an AR(1) covariance structure. See Littell et al. http://onlinelibrary.wiley.com/doi/10.1002/1097-0258(20000715)19:13%3C1793::AID-SIM482%3E3.0.CO;2-Q/... or Stroup (2013) Generalized Linear Mixed Models for details about the distinction between AR(1)+RE and AR(1). If you had enough subjects and enough periods and more complete longitudinal data, you could consider a model with random slopes, specified as
random wt bmi perbf fm fmi lmi lpct tpct tlpctr apct gpct agpctr / subject=id type=vc;
but this is way too complex for what you have to work with.
