Optimizing the tie-breaker regression discontinuity design

Also known as “how to approve a vaccine and still continue with stage III trials.”  From Art B. Owen and Hal Varian:

Motivated by customer loyalty plans and scholarship programs, we study tie-breaker designs which are hybrids of randomized controlled trials (RCTs) and regression discontinuity designs (RDDs). We quantify the statistical efficiency of a tie-breaker design in which a proportion Δ of observed subjects are in the RCT. In a two line regression, statistical efficiency increases monotonically with Δ, so efficiency is maximized by an RCT. We point to additional advantages of tie-breakers versus RDD: for a nonparametric regression the boundary bias is much less severe and for quadratic regression, the variance is greatly reduced. For a two line model we can quantify the short term value of the treatment allocation and this comparison favors smaller Δ with the RDD being best. We solve for the optimal tradeoff between these exploration and exploitation goals. The usual tie-breaker design applies an RCT on the middle Δ subjects as ranked by the assignment variable. We quantify the efficiency of other designs such as experimenting only in the second decile from the top. We also show that in some general parametric models a Monte Carlo evaluation can be replaced by matrix algebra.

Published version here.  Whether or not you agree with that particular approach, you can view 2020 in the following terms.  Public health experts have told us that:

1. We citizens have to lock down many of our schools and sometimes jobs.

2. We citizens have to significantly change many of our commercial and retail and travel habits.

3. We citizens have to significantly limit or cut off many of our contacts with other human beings.

At the same time, they also are saying that:

4. “We public health experts do not have to come up with a way of approving a vaccine and simultaneously continuing to conduct our other clinical trials.”

And they wonder why people do not have greater faith in science.


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