I am analyzing gene expression data for a repeated measure placebo controlled clinical trial. Example dataset:
df <- data.frame(
subject = c(paste0('Healthy', 1:8), paste0('PID', rep(1:12, 2))),
disease = c(rep(FALSE, 8), rep(TRUE, 24)),
treatment = c(rep('none', 8), rep(c('Placebo', 'Drug'), 12)),
visit = c(rep('BL', 8), rep(c('BL', 'Day3'), each=12)),
score = c(rep(NA,8), rep(c(0,0,30,30,50,50,70,70,90,90,100,100), 2)),
gene = rnorm(32, 5)
)
Variables:
subject
: IDs of either healthy controls or patients (PID prefix).
disease
: is TRUE if subjects have the disease and FALSE if they are healthy controls.
treatment
: 'none' for healthy and either 'Placebo' or 'Drug' for patients that will or did receive the corresponding treatment.
visit
: is 'BL' for samples collected prior to treatment and 'Day3' for patient samples collected three days after treatment.
score
: in an outcome that represents improvement in disease outcome and is measured 15 days after baseline. It could reasonably be modeled as an ordered factor but I decided to treat it as continuous for simplicity. This might not be appropriate as the maximum score is 100? Interpreting the polynomial terms confused me.
gene
: is the expression of a sample gene that I want to ask questions about.
Model and Rationale:
mod <- lmerTest::lmer(gene ~ disease + treatment:visit + score:treatment:visit + (1|subject), data=df)
disease
: I expect disease
to independently affect the expression of gene
(main effect).
treatment:visit
: I expect to see an effect of being in the 'Drug' treated group only after treatment (visit Day3). I have omitted the main effect for treatment
as it merely identifies healthy and randomization to Placebo or Drug groups. I have also omitted the main effect for visit
as I don't expect gene expression to change on Day3 independent of treatment. Do these model specifications reflect my assumptions correctly?
score:treatment:visit
: I am specifically interested in whether the expression of a given gene
at both baseline and 3 days after treatment depends on disease improvement as measured by score
on day 15. So, for example, gene
expression could differ between subjects with disease
before and after treatment in a way that depends on eventual score
. Should the interaction be score:treatment:visit:disease
to capture this?
Questions I want to address:
Does the expression of gene
at baseline differ based on score
at day 15?
Does the change in expression of gene
between baseline and Day3 in subjects receiving the drug differ based on score
at day 15?
Does the expression of gene
at baseline differ between individuals with the disease and those without the disease?
How do I go about asking these questions using the model above (or an alternative specification if the above is incorrect)?
Thank you!