# How to analyze crossover trial with a scale as outcome variable?

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.

• Some more information on the nature of the scale would help. Are there always 40 points on the scale each day, but in most cases the score is 0? If that's the case, how much do you care about differences among non-0 scores versus differences between 0-score and non-0-score cases? What type of distribution do you expect among the scores when they are non-zero? – EdM Aug 17 '15 at 13:25
• These questions are difficult to answer, but I had a look at some other studies that use this particular scale to get an idea. I would expect that about 90% of scores are 0 and among the non-0-scores, one study reported a mean of about 9 and SD of about 5 (among non-zero scores), perhaps indicating a positively skewed normal distribution? Of course, using a binomial distribution and comparing any non-zero score to zero-scores (meaning an event has occurred vs no event occurred) would be the easiest way, but I do care about the score of each "event"... – JonB Aug 18 '15 at 8:24