randomized crossover design: combining session conditions

#1
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!
 

hlsmith

Not a robit
#2
Can you please define what you mean by session conditions (exposures)? This will help in understanding how many combinations you have. Also, how many crossovers were there? Lastly, you may be able to better frame this inquiry by using actual content information. What are we talking about here, animal or cell and what were these a, b, c, d variables.

Thanks.
 
#3
Can you please define what you mean by session conditions (exposures)? This will help in understanding how many combinations you have. Also, how many crossovers were there? Lastly, you may be able to better frame this inquiry by using actual content information. What are we talking about here, animal or cell and what were these a, b, c, d variables.

Thanks.
Session conditions are the different products that were given at each session for participants to sample. We had four periods and four treatments with a washout period between each time period. There were 20 product sequences that a participant was randomly assigned to. Our primary outcomes are scores of enjoying the product, liking the product and willingness to use the product again.

A = sweet, flavored tea
B = sweet, non-flavored tea
C = unsweet, flavored tea
D = unsweet, non-flavor tea

Time 1 --> washout --> Time 2 --> washout --> Time 3 --> washout --> Time 4

Unfortunately, we found out later after testing the flavoring and sweetness in the products, that C and D were identical and we did not receive the correct product from the manufacturer.

We are trying to determine if we should combine the results from the C and D products and take an average of the participant results.

Instead of having a 4 period, 4 treatment crossover design, we ended up having a 4 period, 3 treatment crossover design.

I've never ran into a situation where this has happened before in a study, so I'm not sure the correct method to use.