Discussion of Dynamic Treatment Regimens

1. Discussion of Dynamic Treatment Regimens Dean Follmann NIAID

2. Thoughts • Most clinical trials are 2 arms, maybe 2x2 factorial. • Simple, clear, familiar. • Dynamic Treatment Regimens • Not • DTRs efficiently address treatment strategies for settings where multiple sequential treatment decisions are made • More efficient than multiple separate clinical trials • Randomized design and analysis is best. • Selling DTRs • Randomization quality inference where we efficiently address multiple questions

3. Kidwell

5. Collins Continue Med (SG1) Response Medication Response Enhance (SG2) Enhance (SG5) Non-Response R R Non-Response R Augment (SG3) Augment (SG6) Continue BMOD (SG4) BMOD Med=G1+SG2+SG3 versus BMOD=SG4+SG5+SG6 2 arm trial E=SG2+ SG5 versus A=SG3+SG6 Stratified clinical trial Two strata are 1) Medication NR 2)BMOD NR What is the best overall strategy? Med + E for NR, Med + A for NR BMOD + E for NR, BMOD + A for NR. An Uncovered 4 arm trial!

6. Farm Story • Seed company interested in • Manure versus anhydrous fertilizer • Chemical versus mechanical weeding for weedy fields • In March, randomize fields to 1 of the 4 strategies • March Manure + chemical if weedy in June • March Manure + mechanical if weedy in June • March Anhydrous + chemical if weedy in June • March Anhydrous + mechanical if weedy in June • A standard 2 x 2 factorial clinical trial

7. DeKalb Seed Trial, sequentially No weeding few weeds Manure few weeds Mechanical weeding Mechanical weeding weedy R R weedy R Herbicide Herbicide No weeding Anhydrous March June October

8. Moral of the Story • Factorial trials have a rich literature • Parsimony in analysis: Main effects, low order interactions • ``Two studies for the price of one” • Fractional factorials • If randomize completely in March, factorial analysis of the 4 strategies is very clear.

9. Factorial Analysis Intended Action for Weedy Fields Herbicide Weeding Anhydrous Manure Compare Anhydrous versus Manure using 2 strata: Herbicide & Weeding And vice versa

10. Two Analyses Herbicide Weeding Weedy Fields Anhydrous Manure Compare Anhydrous versus Manure using 2 strata: Herbicide & Weeding Compare Herbicide to Weeding in the weedy fields using 2 strata: Anhydrous weedy fields & Manure weedy fields (it’s legit!)

11. Best Strategy? • Four strategies • Med + Enhancement for Nonresponse • Med + Augment for Nonresponse • BMOD + Enhancement for Nonresponse • BMOD + Augment for Nonresponse • Best way to pick the winner? • Pick the best of the 4 means. • Pick Med/BMOD then Pick Enhancement/Augment • Use factorial methods

12. Best Strategy? • Four strategies • Med + Enhancement for Nonresponse • Med + Augment for Nonresponse • BMOD + Enhancement Method C for Nonresponse • BMOD + Augment Method D for Nonresponse • Best way to pick the winner? • Pick the best of the 4 means. • Pick Med/BMOD then Pick Enhancement/Augment • Use factorial methods

13. DTRs • Seem an exciting, rigorous, & efficient way to address multiple questions when we need to titrate a treatment strategy. • When equivalent to factorial trial, sister literature may be somewhat helpful. • If on the fence fall to a factorial? • Complication can be daunting to collaborators. • Emphasize efficiency of design • Find simple ways to convey results

14. Backup

15. Responders Non-Responders & Augmented Non-Responders & Enhanced ,lwd=3) MED BMOD Post Randomization Subgroups for Responders. Strata for Non-responders

16. Responders Mean response For BMOD+AUGNR Non Responders & Augmented x X NonResponders & Enhanced ,lwd=3) BMOD MED

17. Mean response For BMOD+AUGNR x X BMOD 1st line treatment MED 1st line treatment

18. The uncovered 4 arm trial of strategies 2nd line augmented x X 2nd Line enhanced O O BMOD 1st line treatment MED 1st line treatment

19. Complexity • DTRs can become complicated with multiple trajectories. • Desirable to model mean structure with parsimony e.g. main effects. • Unclear if conventional wisdom about interactions applies here. • But worth exploring • Must fit separate means to uncovered trial if no common treatments.

20. Lynch • Appealing design to efficiently ask several questions. Best initial therapy. Best 2nd therapy for Responders & Non-responders. • Initial analyses respect randomization. • Subsequent analyses extracts randomized trials for 8 strategies. • (1) initial D2 if R then R1 if NR then NR1 • … • (8) initial D2 if R then R2 if NR then NR2 • Can compare the 8 strategies

21. One of 8 strategies

22. Above has D = +1,-1 5 day, not RespTx = +1, -1 NTX ONLY, not NRespTx = +1, -1 CBI+MM+PLA, not Just as we would for an old-school 2x2x2 factorial trial Does RespTX = -1 identify everyone else? i.e. Responders who got NTX+TDM and all Nonresponders?

23. Moodie • Detailed development of strategies to optimize warfarin dosing. • Comes up with suggested combinations that can be tested in clinical trials. • Practicality of algorithms important

24. Kidwell

25. Dynamic Treatment Regimens • Interested in efficiently answering many sequentially appropriate questions. • Subsequent Randomizations can depend on previous responses. • # possible Trajectories is large 2 x 2 x 2 Randomizations Early Randomizations Responses

26. Vanilla 2x2 Factorial Trial in would-be responders D2=R D5=? AND D2=? D5=R

27. 2x2x2 DTR is likeTwo Old School 2x2 Randomized Trials Vanilla 2x2 Factorial in would be D2 or D5 Responders D2 Responders are from Principal Stratum 2 & 4 D5 Responders are from Principal Stratum 3 & 4

28. 2 by 2 Factorial D2 + P D2 R D2 + T R D5 + P D5 R D5 + T R = Randomization

29. Vanilla 2 by 2 Factorial in Would be D2 or D5 responders D2 + P D2 R D2 + T R D5 + P D5 R D5 + T R = Randomization

30. Factorial Studies • How to analyze vanilla 2x2 trials? • Long history. Emphasis on parsimony & main effects • Y = b0 + b1 Z1 + b2 Z2 + b3 Z1 Z2 + e • Z1 = 1 if D2 (0 otherwise) • Z2 = 1 if TDM (0 otherwise) • a

31. Analysis