I know that a cross-over experiment (of any number of treatments/levels) necessarily has a repeated-measures design, but that not all repeated-measures designs are cross-overs. However, I wasn't able to find much information on when exactly it is that a repeated-measures design qualifies as cross-over.
Surely the counter-balancing of the order of treatments given to each subject is not the cross-over 'hallmark', as that is also done in a simple repeated-measures experiment.
Does this hallmark perhaps have to do with the longitudinality of the intervention, i.e. each treatment/level has to last for some number of sessions (for some time), as opposed to being just a one-off measurement? Or perhaps with the fact that after each condition, there needs to be a washout period in the cross-over, so as to avoid the effects of condition A spilling over into condition B, whereas for repeated measures there is no such thing?
How does the Venn diagramm look like for these two designs, i.e. when is one also the other and when is it not?
Best Answer
Let's assume a simple situation, where you have to compare two treatments, A and B.
Repeated measures design
In a repeated measures design, you would randomly assign some of your study subjects to treatment A and some to treatment B. Following assignment, you would repeatedly measure the value of the outcome variable of interest over time until the study concludes. If the study lasts one week, you may measure the outcome variable daily for one week. Each subject in this design takes only one of the two treatments under investigation. Subjects are randomized to treatment.
Cross over design
In a cross over design, you would randomly assign some of your study subjects to the treatment sequence AB and some to the treatment sequence BA. Subjects assigned to the treatment sequence AB would take treatment A for one week, say (Period 1) followed by treatment B for another week (Period 2). Subjects assigned to the treatment sequence BA would take treatment B in Period 1 and treatment A in Period 2. You may decide to have a period of rest between Period 1 and Period 2. On each of those weeks, the outcome of interest may be measured daily for each subject. Each subject in this type of design serves as his/her own control (which means that this type of design generally requires fewer subjects than the repeated measures design) and takes, in sequence, both of the treatments under investigation. Subjects are randomized to treatment sequence.
Repeated measures design versus Cross over design
You can think of the repeated measures design in this simplified example as representing what happens in the first period of the cross over design. However, while the repeated measures design ends after the first week, the cross over design continues for a second week, with subjects switching treatments.
The repeated measures design allows you to investigate changes over time in the outcome value for patients who took treatment A versus those who took treatment B. (The two sets of patients are distinct - patients who took treatment A are distinct from those who took treatment B.)
The cross over design allows you to investigate changes over time in the outcome value for patients who took treatment A and then treatment B, or the other way around. (The same patients took both treatments.)