I am interested in checking how (and if at all) predictive is the position of genetic mutations in a given disease gene on the severity of the disease phenotype (so, I only have affected individuals (N=120). I have about 5 phenotypic measurements (continuous variables) and 5 events (e.g. syncope, death etc - binary variables) that I am interested in including in the model, alongside age (continuous) and gender (binary). I am using R to do this, and I am wondering which would be the correct approach. The way in which I would proceed is the following:
Build one regression model per phenotypic variable / event (so, some binomial and some linear), in the form:
lm(continuous_variable~age+gender+variant_position+ all_other_pheno_or_events, ...)
glm(binary_variable~age+gender+variant_position+ all_other_pheno_or_events, ..., family=binomial)
Perform backward variable selection to check which independent variables have an influence on the predicted phenotype. Here I am not sure whether I should use AIC or BIC. I know the fundamental differences between the two, and maybe I'd go for AIC aiming for "inclusivity" (given it lower penalty for additional predictors), to then:
Check the significance of each predictor retained by the backward variable selection procedure using nested models comparison (by likelihood ratio test) e.g.:
anova(glm(binary_variable~pred+pred+...+pred[N-1]), glm(binary_variable~pred+pred+...+pred[N]), test="LRT")
I suspect this approach may be unnecessarily complex, but I hope for this idea to be correct. I'd really appreciate some advice from others more expert than me in statistics and regression.