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3. Stepped Wedge Design: An RCT for Developmental Growth in Phelan-McDermid Children October 2014 Edwin R. van den Heuvel Professor of Statistics e.r.v.d.heuvel@tue.nl Department of Mathematics and Computer Science Eindhoven University of Technology

4. Content • Introduction • Type of Trial Designs • Statistical Model • Simulation • Parameter Settings • Results • Conclusions

5. Introduction • Children with Phelan-McDermid syndrome develop slower (~70%) than normal children • The syndrome is caused by a deletion of gene 22q13.3 • It is a rare disease (~50 known children in Netherlands) • A pilot study showed that insuline can enhance mental development • An RCT is needed to investigate a possible effect of intranasal insuline versus placebo

6. Introduction • First type of designs that were thought off were • Cross-over design: issues with carry-over? • Parallel group design: possible • Matched-pairs design: possible • Parents were not cooperative to participate if their child would not receive the intervention • In a stepped wedge design all participants will switch during the trial (one-directional cross-over) • We felt it would only be ethical when this design would have similar power than other trials • Expected number of participants was ~20

7. Introduction Stepped wedge designs: • All patients are first treated with the control • Patients or group of patients are changing at different time points • It uses intra- and inter-individual variation of patients to test for treatment effect • It could take longer than parallel group designs • Example: Three groups with four periods 7 SWD-S3 6 7

8. Type of Trial Designs Prerequisites: • Five time moments: 0, 6, 12, 18, and 24 months • More time moments would be to much of a burden • Shorter times affect test-retest variability • Development is measured by Bayley III • Scores are transformed to developmental age • Possible types of designs • Parallel group design (PGD) • Matched-Pairs design (MPD) • Stepped Wedge Designs (SWD) • Delayed Start Design (DSD)

9. Type of Trial Designs 0 6 12 18 24 Parallel Group Design: • At time zero patients are randomly allocated to either placebo or intranasal insuline • Ramdomization is balanced (ratio 1:1) • Dotted line is placebo • Solid line is intranasal insuline • Ratio of total treatment time on bothtreatments is 1:1

10. Type of Trial Designs Matched-Pairs Design: • Patients are treated the first six months at placebo • Developmental growth or change is matched • Per pair placebo or intranasal insuline is randomly allocated • Ratio of total treatment in placebo vs. Insuline: 5:3

11. Type of Trial Designs Stepped wedge designs: • Treatment switches coincide with measurements • Ratio of total treatment in placebo vs. Insuline: • SWD-S2a: 1:1 • SWD-S2b: 3:5 • SWD-S3: 1:1

12. Type of Trial Designs Delayed start designs: • Trial starts as a parallel group design • At a specific time point, (part of) the control group switches to treatment • Common trials for Alzheimer and Parkinson’s disease • The goal is to • Investigate treatment effect • Whether disease progression can be slowed down • The second goal is less important for our RCT

13. Type of Trial Designs Delayed start designs: • Ratio of total treatment in placebo vs. Insuline: • DSD-S1a: 1:3 • Others: 1:1

14. Type of Trial Design Ratio 1:1 Ratio 3:5 Ratio 1:1 Ratio 5:3 Ratio 1:1 Ratio 1:3 Ratio 1:1 Ratio 1:1 Ratio 1:1

15. Statistical Model Linear Mixed Model • Random coefficients model Yij: developmental age of child I at time point j Z0,i: developmental age at baseline for child i Z1,i: developmental growth for child i tij: moments of measurement for child i xij: moments of treatment switch for child i eij: residuals g: treatment effect

16. Statistical Model Model for Stepped Wedge Design g: treatment effect Child 2: Insuline Child 2: Placebo Developmental age g: treatment effect Child 1: Insuline Child 1: Placebo 0 6 12 18 24

17. Statistical Model Analysis of Model • Statistical model can be analyzed with standard software for mixed models • Requires two regression time variables: • One for placebo time = tij • One for the new treatment: time2 = tij-xij when tij > xij time2 = 0 when tij ≤ xij • SAS codes PROC MIXED DATA=SIMULATIONDATA METHOD=REML; CLASS INDIVIDUAL; MODEL Y = TIME TIME2/SOLUTION DDFM=SAT; RANDOM INT TIME/SUBJECT=INDIVIDUAL TYPE=UNR; RUN;

18. Simulation Parameter Settings: • Settingswereselected on the basis of real data and on literature on test-retestvariation of the Bayley III test b0 = 21 b1 = 0.3 s0 = 10 t0 = 45 t1 = 0.1 r= 0.25; 0.50; 0.75 g = 0; 0.15; 0.30; 0.45 • Number of simulations: 50000 • Makesitpossibletodistinguisha difference of 1% in power

19. Simulation Type 1 error: • Type 1 error rates are somewhat inflated • The null-distribution of the Wald test statistic is not perfectly chi-squared distributed • SWD-S2b and DSD-S1a have only limited inflation of type 1 error rates

20. Simulation Power: • SWD-S3 and DSD-S3 seem to perform quite good • MPD-A1 is best for r=0.75 • PGD, SWD-S2b, and DSD-S1a are less powerful designs for testing treatment effect

21. Conclusions • Stepped wedge design is competitive with the more classical designs and delayed start designs • Stepped wedge designs are considered ethical since not participant is withhold the new treatment • The number of steps does not seem to affect the power strongly • Imbalance in total treatment time seem to reduce power • Power values are not very large with only 20 participants