Randomized Encouragement: When noncompliance may be a feature and not a bug

Many times in a randomized controlled trial (RCT) issues related to non-compliance arise. Subjects assigned to the treatment fail to comply, while in other cases subjects that were supposed to be in the control group actually receive treatment. Other times we may have a new intervention (maybe it is a mobile app or some kind of product, service, or employer or government benefit) that law, contract, or nature implies that it can be accessed by everyone in our population of interest. We know that if we let nature take its course, users, adopters, or engagers are very likely going to be a self selected group that is different from others in a number of important ways. In a situation like this it could be very hard to know if observed outcomes from the new intervention are related to the treatment itself, or explained by other factors related to characteristics of those who choose to engage.

In a 2008 article in the American Journal of Public Health, alternatives to randomized controlled trials are discussed, and for situations like this the authors discuss randomized encouragement:

 "participants may be randomly assigned to an opportunity or an encouragement to receive a specific treatment, but allowed to choose whether to receive the treatment."

In this scenario, less than full compliance is the norm, a feature and not a bug. The idea is to roll out access in conjunction with randomized encouragement. A randomized nudge.

For example, in Developing a Digital Marketplace for Family Planning: Pilot Randomized Encouragement Trial (Green, et. al;  2018) randomized encouragement was used to study the impact of a digital health intervention related to family planning:

“women with an unmet need for family planning in Western Kenya were randomized to receive an encouragement to try an automated investigational digital health intervention that promoted the uptake of family planning”

If you have a user base or population already using a mobile app you could randomize encouragement to utilize new features through the app. In other instances, you could randomize encouragement to use a new product, feature, or treatment through text messaging. Traditional ways this has been done is through mailers or phone calls.

While treatment assignment or encouragement is random, non-compliance or the choice to engage or not engage is not! How exactly do we analyze results from a randomized encouragement trial in a way that allows us to infer causal effects?  While common approaches include intent-to-treat (ITT) or maybe even per-protocol analysis, treatment effects for a randomized encouragement trial can also be estimated based on complier average causal effects or CACE.

CACEs compare outcomes for individuals in the treatment group who complied with treatment (engaged as a result of encouragement) with individuals in the control group who would have complied if given the opportunity to do so.  This is key. If you think this sounds a lot like local average treatment effects in an instrumental variables framework this is exactly what we are talking about.

Angrist and Pishke (2015) discuss how instrumental variables can be used in the context of a randomized controlled trial (RCT) with non-compliance issues:

 "Instrumental variable methods allow us to capture the causal effect of treatment on the treated in spite of the nonrandom compliance decisions made by participants in experiments....Use of randomly assigned intent to treat as an instrumental variable for treatment delivered eliminates this source of selection bias." 

Instrumental varaible analysis gives us an estimation of local average treatment effects (LATE), which are the same as CACE. In simplest terms, LATE is the average treatment effect for the sub-population of compliers in a RCT. Or, the compliers or engagers in a randomized encouragement design.

There are obviously some assumptions involved and more technical details. Please see the references and other links below to read more about the mechanics, assumptions, and details involved as well as some toy examples.

References:

Mastering 'Metrics: The Path from Cause to Effect Joshua D. Angrist and Jörn-Steffen Pischke. 2015.

Connell A. M. (2009). Employing complier average causal effect analytic methods to examine effects of randomized encouragement trials. The American journal of drug and alcohol abuse, 35(4), 253–259. doi:10.1080/00952990903005882

Green EP, Augustine A, Naanyu V, Hess AK, Kiwinda L
Developing a Digital Marketplace for Family Planning: Pilot Randomized Encouragement Trial
J Med Internet Res 2018;20(7):e10756

Stephen G. West, Naihua Duan, Willo Pequegnat, Paul Gaist, Don C. Des Jarlais, David Holtgrave, José Szapocznik, Martin Fishbein, Bruce Rapkin, Michael Clatts, and Patricia Dolan Mullen, 2008:
Alternatives to the Randomized Controlled Trial
American Journal of Public Health 98, 1359_1366, https://doi.org/10.2105/AJPH.2007.124446

See also: 

Intent to Treat, Instrumental Variables and LATE Made Simple(er) 

Instrumental Variables and LATE 

Instrumental Variables vs. Intent to Treat 

Instrumental Explanations of Instrumental Variables

A Toy Instrumental Variable Application

Other posts on instrumental variables...