A n Analytic Road Map for Incomplete Longitudinal Clinical Trial Data

1. Craig Mallinckrodt Graybill Conference June 12, 2008Fort Collins, CO An Analytic Road Map for Incomplete Longitudinal Clinical Trial Data

2. Acknowledgements PhRMA Expert Team on Missing Data Peter Lane GSK Craig Mallinckrodt Lilly James Mancuso Pfizer Yahong Peng Merck Dan Schnell P&G Geert Molenberghs Ray Carroll Many Lilly colleagues

3. Outline • Why do we care • What do we know • Theory • Application • What we should do

4. Medical Needs • Every hour we expect 195 deaths due to cancer 1950 new diagnoses of anxiety disorders 15 new diagnoses of schizophrenia 30 osteoporosis related hip fractures 1500 surgeries requiring pain treatment 70 deaths due to cardiovascular disease Alan Breier – Nov 2006

5. Need for More Effective Medicines There is an efficacygap in terms of customer expectations and the drugs we prescribe • Therapeutic AreaEfficacy rate(%) • Alzheimer’s 30 • Analgesic’s (Cox-2) 80 • Asthma 60 • Cardiac Arrhythmias 60 • Depression (SSRI) 62 • Diabetes 57 • HCV 47 • Incontinence 40 • Migraine (acute) 52 • Migraine (prophylaxis) 50 • Oncology 25 • Osteoporosis 48 • Rheumatoid arthritis 50 • Schizophrenia 60 Trends in Molecular Medicine 7(5):201-204, 2001

6. Industry R&D Expense($ Billions) Annual NMEApprovals R&D Investment NME & Biologics Approvals R&D Productivity Decreasing Source:PhRMA, FDA, Lehman Brothers; [Dr. Robert Ruffolo]

7. Outline • Why do we care • What do we know • Theory • Application • What we should do

8. Starting Point • No universally best method for analyzing longitudinal data • Analysis must be tailored to the specific situation at hand • Consider the hypothesis to be tested, desired attributes of the analysis, and the characteristics of the data

9. Missing Data Mechanisms • MCAR - missing completely at random • Conditional on the independent variables in the model, neither observed or unobserved outcomes of the dependent variable explain dropout • MAR - missing at random • Conditional on the independent variables in the model, observed outcomes of the dependent variable explain dropout, but unobserved outcomes do not

10. Missing Data Mechanisms • MNAR - missing not at random • Conditional on the independent variables in the model and the observed outcomes of the dependent variable, the unobserved outcomes of the dependent variable explain dropout

11. Consequences • Missing data mechanism is a characteristic of the data AND the model • Differential dropout by treatment indicates covariate dependence, not mechanism • Mechanism can vary from one outcome to another in the same dataset

12. Missing Data in Clinical Trials • Efficacy data in clinical trials are seldom MCAR because the observed outcomes typically influence dropout (DC for lack of efficacy) • Trials are designed to observe all the relevant information, which minimizes MNAR data • Hence in the highly controlled scenario of clinical trials missing data may be mostly MAR • MNAR can never be ruled out

13. Implications • All analyses rely on missing data assumptions • Any options in the trial design to minimize dropout should be strongly considered

14. Assumptions • ANOVA with BOCF / LOCF assumes • MCAR & constant profile • MAR always more plausible than MCAR • MAR methods will be valid in every case where BOCF/ LOCF is valid • BOCF / LOCF will not be valid in every scenario where MAR methods are valid

15. Research Showing MAR Is Useful And / Or Better Than LOCF • Arch. Gen. Psych. 50: 739-750. • Arch. Gen. Psych. 61: 310-317. • Biol. Psychiatry. 53: 754-760. • Biol. Psychiatry. 59: 1001-1005. • Biometrics. 52: 1324-1333. • Biometrics. 57: 43-50. • Biostatistics. 5:445-464. • BMC Psychiatry. 4: 26-31. • Clinical Trials. 1: 477–489. • Computational Statistics and Data Analysis. 37: 93-113. • Drug Information J. 35: 1215-1225. • J. Biopharm. Stat. 8: 545-563. • J. BioPharm. Stat. 11: 9-21.

16. Research Showing MAR Is Useful And / Or Better Than LOCF • J. Biopharm. Stat. 12: 207-212. • J. Biopharm. Stat. 13:179-190. • J. Biopharm. Stat. 16: 365-384. • Neuropsychopharmacol. 6: 39-48. • Obesity Reviews. 4:175-184. • Pharmaceutical Statistics. 3:161-170. • Pharmaceutical Statistics. 3:171-186. • Pharmaceutical Statistics. 4:267-285. • Pharmaceutical Statistics (2007 early view) DOI: 10.1002/pst.267 • Statist. Med. 11: 2043-2061. • Statist. Med. 14: 1913-1925. • Statist. Med. 22: 2429-2441.

17. Why Is LOCF Still Popular • LOCF perceived to be conservative • Concern over how MAR methods perform under MNAR • More explicit modeling choices needed in MAR methods • LOCF thought to measure something more valuable

18. Conservatism Of LOCF • Bias in LOCF has been shown analytically and empirically to be influenced by many factors • Direction and magnitude of bias highly situation dependent and difficult to anticipate • Summary of recent NDA showed LOCF yielded lower p value than MMRM in 34% of analyses Biostatistics. 5:445-464. BMC Psychiatry. 4: 26-31.

19. Performance Of MAR With MNAR Data • Studies showing MAR methods provide better control of Type I and Type II error than LOCF • Arch. Gen. Psych. 61: 310-317. • Clinical Trials. 1: 477–489. • Drug Information J. 35: 1215-1225. • J. BioPharm. Stat. 11: 9-21. • J. Biopharm. Stat. 12: 207-212. • Pharmaceutical Statistics (2007 early view) DOI: 10.1002/pst.267 • JSM Proceedings. 2006. pp. 668-676. 2006.

20. More Explicit Modeling Choices Needed • MMRM 6 lines of code, LOCF 5 lines of code • Convergence and choice of correlation not difficult in MMRM Clinical Trials. 1: 477–489.

21. LOCF Thought To Measure Something More Valuable • LOCF is “effectiveness”, MAR is “efficacy” • LOCF is what is actually observed • MAR is what is estimated to happen if patients stayed on study • Non longitudinal interpretation of LOCF • LO, LAV • Dropout is an outcome

22. Non-longitudinal Interpretation Of LOCF • An LOCF result can be interpreted as an index of rate of change times duration on study drug - a composite of efficacy, safety, tolerability • An index with unknown weightings • The same estimate of mean change via LOCF can imply different clinical profiles • The LOCF penalty is not necessarily proportional to the risk • Result can be manipulated by design

23. Completion Rates in Depression Trials Drug Placebo

24. Placebo Dropout Rates Influenced by Design In a Recent MDD NDA % % Trial DC-AE Dropout 1 4.3 34.3 2 6.7 41.3 3 3.3 31 4 9.0 42 5 3.2196 1.097 2.5 29.5 8 4.3 35.3 Trials 5 and 6 had titration dosing and extension phases Lillytrials.com

25. Outline • Why do we care • What do we know • Theory • Application • What we should do

26. Modeling Philosophies • Restrictive modeling • Simple models with few independent variables • Often include only the design factors of the experiment Psychological Methods, 6, 330-351.

27. Modeling Philosophies • Inclusive modeling • Auxiliary variables included to improve performance of the missing data procedure – expand the scope of MAR • Baseline covariates • Time varying post-baseline covariates: Must be careful to not dilute treatment effect. Can be dangerous to include time varying postbaseline covariates in analysis model, may be better to use via imputation (or propensity scoring or weighted analyses) Psychological Methods, 6, 330-351.

28. Rationale For Inclusive Modeling • MAR: conditional on the dependent and independent variables in the analysis, unobserved values of the dependent variable are independent of dropout • Hence adding more variables that explain dropout can make missingness MAR that would otherwise be MNAR

29. Analytic Road Map • MAR with restrictive modeling as primary • Use MAR with inclusive modeling and MNAR methods as sensitivity analyses • Use local influence to investigate impact ofinfluential patients Pharmaceutical Statistics. 4: 267–285.J. Biopharm. Stat. 16: 365-384.

30. Why Not MNAR As Primary • Can do better than MAR only via assumptions • Assumptions untestable • Sensitivity to violations of assumptions and model misspecification more severe in MNAR • MNAR methods lack some desired attributes of a primary analysis in a confirmatory trial • No standard software • Complex

31. Implementing The Road Map: Example From A Depression Trial • 259 patients, randomized 1:1 ratio to drug and placebo • Response: Change of HAMD17 score from baseline • 6 post-baseline visits (Weeks 1,2,3,5,7,9) • Primary objective: test the difference of mean change in HAMD17 total score between drug and placebo at the endpoint • Primary analysis: LB-MEM

32. Patient Disposition • Drug Placebo • Protocol complete 60.9% 64.7% • Adverse event 12.5% 4.3% • Lack of efficacy 5.5% 13.7% • Differential rates, timing, and/or reasons for dropout do not necessarily distinguish between MCAR, MAR, MNAR

33. Primary Analysis: LB-MEM proc mixed; class subject treatment time site; model Y = baseline treatment time site treatment*time ; repeated time / sub = subject type = un; lsmeans treatment*time / cl diff; run; This is a full multivariate model, with unstructured modeling of time and correlation. More parsimonious approaches may be useful in other scenarios Treatment contrast 2.17, p = .024

34. Inclusive Modeling in MI:Including Auxiliary AE Data • Imputation Models • *Yih = µ +1 Yi1 +…+ h-1 Yi(h-1) + ih • Yih = µ + 1 Yi1 +…+ h-1 Yi(h-1) + 1 AEi1 +…+ h-1 AEi(h-1) + ih • Yih= µ + 1 Yi1 +…+ h-1 Yi(h-1) + 1 AEi1 +…+ h-1 AEi(h-1) +11 (Yi1 *AEi1 ) + …+i(h-1) (Yi(h-1) * AEi(h-1) ) + ih • Analysis Model • MMRM as previously described

35. Result • MI results were not sensitive to the different imputation models Endpoint contrastMMRM 2.2MI Y+AE 2.3MI Y+AE+Y*AE 2.1 • Including AE data might be important in other scenarios. Many ways to define AE

36. MNAR Modeling • Implement a selection model • Had to simplify model: modeled time as linear + quadratic, and used ar(1) correlation • Compare results from assuming MAR, MNAR • Also obtain local influence to assess impact of influential patients on treatment contrasts and non-random dropout

37. Selection Model Results

38. Local Influence: Influential Patients

39. Individual Profiles with Influential Patients Highlighted

40. Investigating The Influential Patients • The most influential patient was #30, a drug-treated patient that had the unusual profile of a big improvement but dropped out at week 1 • This patient was in his/her first MDD episode when s/he was enrolled • This patient dropped out based on his/her own decision claiming that the MDD was caused by high carbon monoxide level in his/her house • This patient was of dubious value for assessing the efficacy of the drug

41. Selection Model: Influential Patients Removed

42. Implications • Comforting that no subjects had a huge influence on results. Impact bigger if it were a smaller trial • Similar to other depression trials we have investigated, results not influenced by MNAR data • We can be confident in the primary result

43. Discussion • MAR with restrictive modeling was a reasonable choice for the primary analysis • MAR with inclusive modeling and MNAR was useful in assessing sensitivity • Sensitivity analyses promote the appropriate level of confidence in the primary result and lead us to an alternative analysis in which we can have the greatest possible confidence

44. Opinions • Inclusive modeling has been under utilized • More research to understand dropout would be useful • Did not discuss pros and cons of various ways to implement inclusive modeling. Use the one you know? Be careful to not dilute treatment • The road map for analyses used in the example data is specific to that scenario

45. Conclusions • No universally best method for analyzing longitudinal data • Analysis must be tailored to the specific situation at hand • Considering the missingness mechanism and the modeling philosophy provides the framework in which to choose an appropriate primary analysis and appropriate sensitivity analyses

46. Conclusion • LOCF and BOCF are not acceptable choices for the primary analysis • MAR is a reasonable choice for the primary analysis in the highly controlled situation of confirmatory clinical trials • MNAR can never be ruled out • Sensitivity analyses and efforts to understand and lower rates of dropout are essential