1. Regression Discontinuity for the Replication of Randomized Controlled Trial Results: An Application to the Mycotic Ulcer Treatment Trials
Catherine Oldenburg, ScD MPH
University of California, San Francisco
May 9, 2017

2. Regression Discontinuity
Takes advantage of exogenous source of variation in treatment assignment
Same family of study designs as instrumental variable analysis
CD4 Count-Based Eligibility for Treatment
ART Initiation
Mortality
General Health Status
SES
etc

3. Threshold Rules
Continuous measures (assignment variable) that determine treatment assignment at a certain number
Most compelling are assignment variables measured with error
Examples of clinical applications:
CD4 count
Blood pressure
IOP

4. Conceptualizing RCTs as RD Designs
Randomly select number 1-10 from uniform distribution
Threshold Rule (1:1 randomization):  5: Treatment; > 5: Placebo
Assignment Variable: Uniform distribution from 1-10
Treatment
Placebo 1 2 3 4 5 6 7 8 9 10

5. Conceptualizing RCTs as RD Designs
Randomly select number 1-10 from uniform distribution
Threshold Rule (1:1 randomization):  5: Treatment; > 5: Placebo
Assignment Variable: Uniform distribution from 1-10
Treatment
Placebo 1 2 3 4 5 6 7 8 9 10
How do RCT estimates compare to RD estimates?

6. Mycotic Ulcer Treatment Trials (MUTT)
Two RCTs designed to estimate efficacy of treatment strategies for fungal keratitis
MUTT I: topical natamycin versus topical voriconazole
MUTT II: topical voriconazole plus oral placebo versus topical voriconazole plus oral voriconazole
Assignment to MUTT I or MUTT II depended on baseline visual acuity

7. Fungal keratitis Natamycin Voriconazole Baseline Three Weeks
Three Months

8. Assessed for Eligibility for MUTT I or MUTT II
Is visual acuity worse than 20/400? NO
YES
MUTT I
Randomize to: A: Topical Natamycin
B: Topical Voriconazole
MUTT II
Randomize to: C: Topical Voriconazole + Placebo
D: Topical Voriconazole + Oral Voriconazole
Regression Discontinuity Comparison: MUTT I: Topical Natamycin versus MUTT II: Topical Voriconazole + Placebo

9. RD Baseline Characteristics
MUTT I
Natamycin (<20/400)
N=162
MUTT II
Voriconazole (>20/400)
N=54
Age (median, IQR)
48 (39 to 58)
51.5 (45 to 65)
Female sex
73 (45.1%)
20 (37.0%)
Occupation
Agriculture
Non-agriculture
80 (49.4%)
82 (50.6%)
26 (48.2%)
28 (51.9%)
Duration of symptoms (median, IQR), days
5 (3 to 9)
8.5 (6 to 14)
Baseline BSCVA
0.66 (0.38 to 0.92)
1.70 (1.30 to 1.80)
Baseline infiltrate/scar size
3.09 (2.45 to 3.99)
5.41 (4.69 to 6.69)

10. Continuity in Baseline Characteristics
Age
Sex

11. Regression Discontinuity Methods
Assess the effect of natamycin versus voriconazole (plus placebo) in RD design
Baseline visual acuity is the assignment variable
Outcomes include three—month visual acuity and probability of perforation and/or TPK

12. Visual Acuity Outcome
Natamycin
Voriconazole

13. Visual Acuity Outcome
Natamycin
Voriconazole

14. Probability of Perforation/TPK
Natamycin
Voriconazole

15. Probability of Perforation/TPK
Natamycin
Voriconazole

16. Regression Discontinuity Randomized Controlled Trial
RD versus RCT
Regression Discontinuity
Randomized Controlled Trial
3-month BSCVA (mean logMAR difference, 95% CI)
-0.39 (-0.61 to -0.17)
-0.18 (-0.30 to -0.05)
Perforation/TPK (OR, 95% CI)
0.31 (0.12 to 0.77)
0.42 (0.22 to 0.80)

17. Voriconazole versus Voriconazole
Check the assumptions of regression discontinuity
Expect no difference between two groups
Overall Sample
Fusarium spp Only
3-month BSCVA
(mean difference, 95% CI)
-0.21 (-0.47 to 0.05)
-0.59 (-1.19 to 0.02)
Perforation/TPK (OR, 95% CI)
0.48 (0.19 to 1.20)
0.35 (0.05 to 2.37)

18. Limitations
Sample size
Use of placebo in MUTT II

19. Conclusions
Regression discontinuity is a potentially useful tool when randomization is not possible
Results were broadly similar between RD and RCT, although the RD was an overestimate of effects
Ideally, presenting results of observational studies using methods with different assumptions for causal inference will improve confidence in results

20. Thank you! UCSF: Aravind Eye Hospitals: N. Venkatesh Prajna
Tiruvengada Krishnan
Revathi Rajaraman
Muthiah Srinivasan
UCSF:
Kathryn J. Ray
Kieran O’Brien
Travis C. Porco
Nisha R. Acharya
Jennifer Rose-Nussbaumer
Thomas M. Lietman
Contact: