Regression Discontinuity Desgin

							Regression Discontinuity
        Design
        William Shadish
 University of California, Merced
  Regression Discontinuity Design
• Units are assigned to conditions based on a
  cutoff score on a measured covariate,
• For example, communities that exceed a certain
  cutoff on arrests for drunk driving for young
  drivers per 100,000 receive treatment, and
  communities below that cutoff are in the
  comparison condition.
• The effect is measured as the discontinuity
  between treatment and control regression lines
  at the cutoff (it is not the group mean difference).
             Advantages

• When properly implemented and
  analyzed, RD yields an unbiased estimate
  of treatment effect (see Rubin, 1977).
• Communities are assigned to treatment
  based on their need for treatment,
  consistent with how many policies are
  implemented.
            Disadvantages
• Statistical power is considerably less than
  a randomized experiment of the same
  size. Careful attention to power is crucial.
• Effects are unbiased only if the functional
  form of the relationship between the
  assignment variable and the outcome
  variable is correctly modeled, including:
  – Nonlinear Relationships
  – Interactions
 Citations to Med/PH Examples
Cullen, K.W., Koehly, L.M., Anderson, C., Baranowski, T., Prokhorov,
A., Basen-Engquist, K., Wetter, D., & Hergenroeder, A. (1999).
Gender differences in chronic disease risk behaviors through the
transition out of high school. American Journal of Preventive Medicine,
17, 1-7.
 Finkelstein, M.O., Levin, B., & Robbins, H. (1996a). Clinical and
prophylactic trials with assured new treatment for those at greater risk:
I. A design proposal. American Journal of Public Health, 86, 691-695.
 Finkelstein, M.O., Levin, B., & Robbins, H. (1996b). Clinical and
prophylactic trials with assured new treatment for those at greater risk:
II. Examples. American Journal of Public Health, 86, 696-705.
                                            4.9

                                            4.8

Visits with physician per person per year   4.7

                                            4.6

                                            4.5

                                            4.4

                                            4.3

                                            4.2

                                            4.1

                                             4
                                                  Under    $3,000    $5,000     $7,000    $10,000    $15,000
                                                  $3,000   -$4,999   -$6,999    -$9,999   -$14,999   or more

                                                                     Income Level
   Improvements to the Design
• Modeling of functional form is improved if it
  can be observed prior to implementation of
  treatment (e.g., if archival data is used).
• Using all the standard methods to improve
  power (e.g., add covariates).
• Combining randomized and
  nonrandomized designs
Using Regression Discontinuity
     as a Design Element
 • For those who are cut out of the
   experiment based on quantitative
   eligibility, continue to measure their
   outcome, and they can be added to the
   design to increase power.
 • For those falling below a cutoff on a
   measure of outcome, or of receipt of
   treatment, give a booster and reanalyze
   that part of the data as an RDD.
                Summary
• Of the designs being considered for this
  intervention, RD is the only one that yields
  an unbiased estimate.
• RD can be used with both archival data
  and original data.
• But there is question about whether it can
  be implemented with sufficient power in
  this case.