An Analytic Road Map for Incomplete Longitudinal Clinical Trial Data

Craig Mallinckrodt

Graybill ConferenceJune 12, 2008Fort Collins, CO

PhRMA Expert Team on Missing DataPeter Lane GSKCraig Mallinckrodt LillyJames Mancuso PfizerYahong Peng MerckDan Schnell P&G

Geert Molenberghs

Ray Carroll

Many Lilly colleagues

Acknowledgements

Why do we care What do we know

Theory

Application

What we should do

Outline

Every hour we expect

195 deaths due to cancer 1950 new diagnoses of anxiety disorders 15 new diagnoses of schizophrenia 30 osteoporosis related hip fractures1500 surgeries requiring pain treatment 70 deaths due to cardiovascular disease

Alan Breier – Nov 2006

Medical Needs

Need for More Effective Medicines

Therapeutic Area Efficacy rate(%)

Alzheimer’s 30Analgesic’s (Cox-2) 80Asthma 60Cardiac Arrhythmias 60Depression (SSRI) 62Diabetes 57HCV 47Incontinence 40Migraine (acute) 52Migraine (prophylaxis) 50Oncology 25Osteoporosis 48Rheumatoid arthritis 50Schizophrenia 60

Trends in Molecular Medicine 7(5):201-204, 2001

There is an efficacy gap in terms of customer

expectations andthe drugs we

prescribe

R&D Productivity Decreasing

Source: PhRMA, FDA, Lehman Brothers; [Dr. Robert Ruffolo]

$0

$5

$10

$15

$20

$25

$30

$35

$40

$45

$50

0

20

40

60

80

100

120

140

160

180

200

Annual NMEApprovals

Industry R&D Expense

($ Billions)

R&D InvestmentNME & Biologics Approvals

Why do we care What do we know

Theory

Application

What we should do

Outline

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

Starting Point

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

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

Missing Data Mechanisms

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

Consequences

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

Implications

• All analyses rely on missing data assumptions

• Any options in the trial design to minimize dropout should be strongly considered

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

1. Arch. Gen. Psych. 50: 739-750.

2. Arch. Gen. Psych. 61: 310-317.

3. Biol. Psychiatry. 53: 754-760.

4. Biol. Psychiatry. 59: 1001-1005.

5. Biometrics. 52: 1324-1333.

6. Biometrics. 57: 43-50.

7. Biostatistics. 5:445-464.

8. BMC Psychiatry. 4: 26-31.

9. Clinical Trials. 1: 477–489.

10. Computational Statistics and Data Analysis. 37: 93-113.

11. Drug Information J. 35: 1215-1225.

12. J. Biopharm. Stat. 8: 545-563.

13. J. BioPharm. Stat. 11: 9-21.

Research Showing MAR Is Useful And / Or Better Than LOCF

14. J. Biopharm. Stat. 12: 207-212.

15. J. Biopharm. Stat. 13:179-190.

16. J. Biopharm. Stat. 16: 365-384.

17. Neuropsychopharmacol. 6: 39-48.

18. Obesity Reviews. 4:175-184.

19. Pharmaceutical Statistics. 3:161-170.

20. Pharmaceutical Statistics. 3:171-186.

21. Pharmaceutical Statistics. 4:267-285.

22. Pharmaceutical Statistics (2007 early view) DOI: 10.1002/pst.267

23. Statist. Med. 11: 2043-2061.

24. Statist. Med. 14: 1913-1925.

25. Statist. Med. 22: 2429-2441.

Research Showing MAR Is Useful And / Or Better Than LOCF

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

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.

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.267JSM Proceedings. 2006. pp. 668-676. 2006.

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.

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

• 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

Non-longitudinal Interpretation Of LOCF

Proportion of completers

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Study

Drug PLA

Completion Rates in Depression Trials

Drug Placebo

Placebo Dropout Rates Influenced by Design In a Recent MDD NDA

% % Trial DC-AE Dropout

1 4.3 34.32 6.7 41.3 3 3.3 31 4 9.0 42 5 3.2 19 6 1.0 9 7 2.5 29.5 8 4.3 35.3

Lillytrials.com

Trials 5 and 6 had titration dosing and extension phases

Why do we care What do we know

Theory

Application What we should do

Outline

Modeling Philosophies

• Restrictive modeling

• Simple models with few independent variables

• Often include only the design factors of the experiment

Psychological Methods, 6, 330-351.

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.

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

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.

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

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

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

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

Primary Analysis: LB-MEM

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

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

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

Selection Model Results

MAR MNAR

Contrast (p-value)

2.20 (0.0179)

2.18 (0.0177)

Missingness Parameters

Estimate SE

0-2.46 0.27

1 0.11 0.05

2-0.08 0.06

Local Influence: Influential Patients

Patient

Ci

0 50 100 150 200 250

02

46

81

01

2

#6

#30

#50 #154

#179

iC

Individual Profiles with Influential Patients Highlighted

placebo

Weeks

ch

an

ge

in

HA

MD

17

2 4 6 8

-30

-20

-10

01

0

Duloxetine

Weeks

ch

an

ge

in

HA

MD

17

2 4 6 8

-30

-20

-10

01

0

# 30

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

Selection Model: Influential Patients RemovedRemoved Subjects ( 30, 191) (6, 30, 50, 154, 179,

191)

MAR

MNAR MAR MNAR

Diff. at endpoint(p-value)

2.07 (0.0241)

2.07 (0.0237)

2.40 (0.0082)

2.40 (0.0083)

Missingness Parameters

0-2.22 (0.14) -2.44 (0.27) -2.23 (0.15) -2.47 (0.28)

10.05 (0.02) 0.11 (0.05) -0.05 (0.02) 0.11 (0.06)

2-0.07 (0.06) -0.08 (0.06)

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

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

• 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

Opinions

• 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

Conclusions

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