Let's say there are two types of treatment, namely treatment A and treatment B.
A subject can be in one of these categories:
- get treatment A and then treatment B.
- get treatment B and then treatment A.
- get only treatment A.
- get only treatment B.
- get no treatment.
There are several ways we can construct the control group. For example, we can:
- construct a pure control group who gets no treatment.
- construct control groups for treatment A and treatment B independently. A portion of the control subjects for treatment A may have gotten treatment B. In other words there can be overlap.
Edit: Note that I only have ability to design and assign control group in the experiment. The treatment order happens naturally in the test group without moderation.
Also the post-experiment analysis to estimate treatment effects get tricky since there are two types of treatment, and they may interact with each other.
Anyone have good pointers for reference I can read on?
Context was requested in the comment section, so I'd like to provide some exemplar cases:
- Treatment A: doing yoga daily
- Treatment B: running 3 miles daily
- Metric: body weight in kg
Button on a web page
- Treatment A: change button's location
- Treatment B: change button's color
- Metric: click-through-rate
Completing online course
- Treatment A: chunking hour-long videos into smaller sessions
- Treatment B: sending reminder emails
- Metric: course completion rate
In general, carrying out multiple experiments to estimate effect of two types of treatment on the same metric requires more time and/or subjects and increases cost. It also ignores potential interaction effect of treatment A and treatment B.