randomized crossover design: one condition repeated twice, need to collapse into one condition

[hyunjeehale]

I am trying to figure out the appropriate method of collapsing two of four session conditions for a randomized crossover trial. 

We had four session conditions (a, b, c, d) and unfortunately discovered that the same condition was provided twice and we technically only have three unique session conditions (a, b, c/d). For the two session conditions that are the same (c and d), we want to collapse them to create a single session condition (c/d). However, the order each participant/dyad received session conditions in was random i.e. participant 1 could have received treatments in this order: a, c, d, b and participant 2 could have received treatments in this order: c, b, d, a. 

My initial thought was to take the results from the two session conditions that were the same (c and d) and calculate the average, but I feel that is not the most appropriate method. We essentially have a session condition that was repeated and two session conditions that were not. 

Appreciate any advice!

[PGStats]

I'm no expert in randomized trials, but consider this:

In a double blind trial, you could be given 4 treatments, not knowing what they are. You are only told after initial analysis that treatments c and d were in fact the same. Knowing this you could then test the differences a - (c+d)/2 and b - (c+d)/2, after fitting your model, without having to manipulate your data or change your model.

hth