# Rolling out trial in phases, but not stepped wedge

Update (Sept 10, 2013): I believe it would be more correct to say that increasing baseline or endline measurements are ways to decrease the design effect, thereby making the SW design efficient, rather than stating that the maximum number of measurements is necessary. Woertman et al. (2013).

The stepped wedge design (pdf) is a nice alternative to parallel-group designs when, for logistical reasons, the intervention must be rolled-out in stages. A potential downside of this design, however, can be the number of measurement rounds. Even though SW designs can have increased power (thus reducing required sample size to detect the same effect), every unit is observed/measured before and after every treatment round (step). If you have five steps, there are six measurement rounds, including the initial measurement round when all units are in the control group. So if you have n=1000, this is 1000 x 6 = 6000 observations/measurements.

I'm writing to ask about a possible alternative (see pic below):

1. Stratifying by community (let's say 5 communities overall; increase to N = 1500 because design has less power than SW)
2. Randomize strata (communities) to order of intervention (first, second, third, fourth, fifth)
3. Within the first community strata, Community A, conduct baseline surveys with all n=300 and then randomize units to treatment or control
4. Deliver the intervention to n/2 units randomized to treatment
5. Conduct endline survey with all n=300 in Community A (treatment and wait-list control)
6. Conduct baseline survey with all n=300 in Community B (could be at same time as #5) and then randomize units to treatment or control
7. Deliver the intervention to n/2 units in Community B randomized to treatment AND n/2 wait-list control units from Community A (optional, but this is what we would do)
8. Repeat.

In the alternative design, every unit is surveyed twice, just at different times. With a total sample of n=1500, this is 1500 x 2 = 3000 surveys. Compared to the SW design, this is 6000 - 3000 = 3000 fewer surveys, which has big cost implications.

SW works because we observe every unit before and after every step and then model time.

In the alternative design, we only have 2 measurements (baseline and endline) for every unit assigned to treatment (n=750) and wait-list control (n=750).

In alternative:

• Baseline for Community A conducted in month 1
• Endline for Community A conducted in month 3
• Baseline for Community B conducted in month 3
• Endline for Community B conducted in month 6
• Baseline for Community C conducted in month 6
• Endline for Community C conducted in month 9
• Baseline for Community D conducted in month 9
• Endline for Community D conducted in month 12
• Baseline for Community E conducted in month 12
• Endline for Community E conducted in month 15
• (would not measure post-treatment for Community E wait-list control; just deliver program)

In the alternative design, can we account for the fact that the observations are made at different times? In SW, every unit is measured before and after every round, which makes it easier to model time effects.

Could we regress endline DVs on assignment to treatment (0/1), a vector of baseline controls, dummy variables for community strata, and month of endline measurement? Better alternatives?

Assuming there is a solution, how to think through the implications for power?

Alternative design:

• Just a quick thought: It seems to me that you loose control over time factors in the design you sketched. For example, if the effect differs between cluster A and B, is this natural variation or due to history effects?? – hplieninger Aug 29 '13 at 7:32
• This effect would be balanced across treatment and control since there is a randomization at each round, but you are hitting on the essence of my question: how to best account for the fact that endpoints are measured at different times. – Eric Green Aug 29 '13 at 21:20

## 1 Answer

1. Assuming your inferential focus is the treatment-control contrast, the solution you propose is a multicentre parallel randomised controlled trial design, where the centres are the communities, and there is no clear need to account for measurement times.
2. A particular feature of the design you propose is that all participants from one cluster are accrued at the same time. Another feature is that the accrual times are pre-set and randomised. This step is not necessary for bias control, since period-specific effects will be equally balanced between the two arms. The randomisation of the accrual times may however help control bias under more complex time-community-intervention interactions.
3. In all communities your primary endpoint is at three months (from randomisation). There is no need to account for the fact that endpoints are measured at different calendar times, similarly to a single-center parallel RCT design that may accrue participants over several years. The power implications of your design are those of a multicentre parallel RCT.

4. (This addresses a statement in your post.) The clustered stepped wedge design does not require a measurement at each time interval for every participant. Every participant would usually be assessed at baseline, and then at any later time point set for a primary or secondary endpoint. The related analytical feature of the stepped wedge design is that the time period at which the participant is recruited into the study enters the analysis as a fixed or random effect (see Hussey & Hughes, 2007, section 3.1 & Discussion). This is to alleviate potential confounding with time, as might typically occur with a simple pre-post design. Such confounding will not arise in your design.

• Thanks, @Alain. Maybe I have misunderstood the stepped wedge design. I interpreted this slide by Jim Hughes full deck to mean that must measure each unit at each step. – Eric Green Sep 3 '13 at 11:09
• I am accepting your answer for points 1-3. Much appreciated. On 4, I think you are right to say "does not require", but it is my understanding that increasing the number of baseline or endline measurements decreases the design effect and is therefore part of what makes the SW design efficient. Thoughts? – Eric Green Sep 10 '13 at 11:43