Ideally, a generalized linear mixed model (GLMM) would be fit for a binary phenotype; however, fitting a GLMM is much more computationally demanding than fitting an LMM. To provide a compuationally efficient approach to fitting such a model, fitNullMM uses the penalized quasi-likelihood (PQL) approximation to the GLMM (Breslow and Clayton). The implementation of this procedure in GENESIS is the same as in GMMAT (Chen et al.), and more details can be found in that manuscript. If our outcome variable, “pheno”, were binary, then the same R code could be used to fit the null model, but with family = binomial .
The two steroids are really interchangeable, and cypionate is not at all superior. Both are long acting oil-based injectables, which will keep testosterone levels sufficiently elevated for approximately two weeks. Enanthate may be slightly better in terms of testosterone release, as this ester is one carbon atom lighter than cypionate (remember the ester is calculated in the steroids total milligram weight). The difference is so insignificant however that no one can rightly claim it to be noticeable (we are maybe talking a few milligrams per shot).