I'm working on a pilot study for a new drug. We will use a crossover design in which half of the patients will be given the drug for the first 6 weeks, then, after a washout period of one week, they will get placebo for 6 weeks. The other half of the patients will get placebo for 7 weeks and then the drug for the remaining 6 weeks. The main outcome measure is the score on a certain instrument consisting of a number of items. This will be measured daily as this makes sense.
I'm thinking that I need to use a mixed model approach with random effects for each patient plus of course a variable on treatment and group (drug first or placebo first) and such. The problem I'm having is what kind of distribution to choose for the mixed model. I don't have the data yet, but I expect that most patients will score zero on instrument for the majority of days, and higher scores occasionally. A linear mixed model is thus not appropriate, and neither are binomial, poisson or negative binomial models since the last two concern counts. What about ordinal regression? Is there any way to use the proportion of points scored on the scale (30 points where 40 points is the maximum = 0.75)?
I use R for statistics.