My question pertains to necessary caution/downfalls in adjustment of a binomial mixed effect model with a low number of "success" outcomes (p̂ = .05).
I have a data frame in the form:
data <- data.frame("SubjectID"=1:221, "Group"=sample(gl(8, 28, labels = 280:288), size=221), "Condition"=sample(relevel(gl(2, 130, labels = c("Intervention", "Control")), ref="Control"), size = 221), "Outcome"=rbinom(221, 1, prob=.05))
While in reality, the data has approximately 11 success outcomes (4 to intervention, 7 to control). This data stems from a pilot phase of a GRCT that's being modeled with a binomial mixed effect model (as below) to account for the random effect of group:
require(lme4) binModel <- glmer(Outcome ~ Condition + (1 | Group), data = data, family = binomial, control = glmerControl(optimizer="bobyqa"), nAGQ = 50)
Further, there's a battery of psychometric and socio-demographic variables collected at baseline, tied to each of these these individuals I'd like to integrate a final model. Given the presence of this additional data, I'd like to build a model, inclusive of these variables, in order to better account for these outcomes. Is there any precautions/best practices to take in ensuring that adjustments are compatible with the nature/size of the data?