# stepped wedge and additive intervention effects

Let's say we want to randomize 400 caregivers to a parenting intervention or a wait-list control group. But we also want to look at a program variation for a sub-sample of caregivers of children with identified conduct problems (e.g., a more intense version of the program adds home visits to the standard program components).

We could use a factorial, fractional factorial, or additive design, but we don't want to use the resources to conduct the more intense version of the program with everyone, including caregivers of children without identified conduct problems. Essentially, we want to look at the effect of our selected prevention parenting intervention for all caregivers and the effect of an indicated prevention parenting intervention for caregivers of children with known conduct problems.

So we conduct a baseline survey, identify children who exceed some conduct cutoff, and then block randomize with each group (low and high conduct) to treatment or wait-list control.

Then within the treatment group (n=200), we conduct a second randomization among the 80 caregivers of children who exceeded the conduct cutoff score. We randomize these 80 caregivers to receive the standard treatment that they are scheduled to receive OR an enhanced version of the program that includes everything in the standard version plus home visits to reinforce skills.

So far so good. This seems doable.

Now let's assume we need to randomize communities, not individual caregivers, to treatment or control. But to detect our desired treatment effect, we need more communities (clusters) than we can afford or manage.

So we look to the stepped-wedge design (pdf). Because of repeated measurement, the number of communities required to detect our desired treatment effect becomes more manageable, though we are concerned with the number of observations. [For instance, conducting 5 intervention rounds with 15 communities (14 caregivers per community) means we have 6 observation rounds, or 15 * 6 * 14 = 1260 surveys.]

This is OK, but we also want to estimate the effect of an enhanced program (standard + home visit) among caregivers of children who meet our criteria for conduct problems.

Here is my proposed approach:

1. Double the number of caregivers per community from 14 to 28.
2. Save half of the slots in each community (14) for caregivers of children who screen positive for conduct problems.
3. Randomize caregivers of children who screen positive for conduct problems (14) to the standard program (7) or the enhanced program (7; standard + home visits).

If my power calculation is correct, and I need to deliver the program to 15 communities over 5 rounds with 14 caregivers per community to detect my desired treatment effect, is it correct to assume that I can just double the number of caregivers per community to also look at the effect of the enhanced program (vs standard program)?