Lilly Yue, Ph.D.* CDRH, FDA, Rockville MD 20850

1. The Application of Propensity Score Analysis to Non-randomized Medical Device Clinical Studies: A Regulatory Perspective Lilly Yue, Ph.D.* CDRH, FDA, Rockville MD 20850 *No official support or endorsement by the Food and Drug Administration of this presentation is intended or should be inferred.

2. Outline • Randomized clinical trials • Non-randomized studies and apotential problem • Propensity scores methods for bias reduction • Practical issues with the application of propensity score methodology • Limitations of propensity score methods • Conclusions

3. Randomized Trials • All patients have a specified chance of receiving each treatment. • Treatments are concurrent. • Data collection is concurrent, uniform, and high quality. • Expect that all patient covariates, measured or unmeasured, e.g., age, gender, duration of disease, …, are balanced between the two treatment groups.

4. Randomized Trials • Assumptions underlying statistical comparison tests are met. • So, the two trt groups are comparable and observed treatment difference is an unbiased estimate of true treatment difference. • But, the above advantages are not guaranteed for small, poorly designed or poorly conducted randomized trials.

5. Nonrandomized Studies and a Potential Problem • None of advantages provided by randomized trials is available in non-randomized studies. • A potential problem: Two treatment groupswere not comparablebefore the start of treatment. i.e., not comparable due to imbalanced covariates between two treatment groups. • So, direct treatment comparisons are invalid.

6. Adjustments for Covariates • Three common methods of adjusting for confounding covariates: • Matching • Subclassification (stratification) • Regression (Covariate) adjustment

7. Question: When there are many confounding covariates needed to adjust for,e.g., age, gender, … • Matching based on many covariates is not practical. • Subclassification is difficulty: As the number of covariates increases, the number of subclasses grows exponentially: Each covariate: 2 categories 5 covariates: 32subclasses • Regression adjustment may not be possible: Potential problem: over-fitting

8. Propensity Score Methodology • Replace the collectionof confounding covariates with one scalar function of these covariates: the propensity score. Age Gender Duration ……. 1 composite covariate: Propensity Score Balancing score

9. Propensity Score Methodology (cont.) • Propensity score (PS):conditional prob. of receiving Trt A rather than Trt B, given a collection of observed covariates. • Purpose:simultaneously balance many covariates in the two trt groups and thus reduce the bias.

10. Propensity scores construction • Statistical modeling of relationship between treatment membership and covariates • Statistical methods: multiple logistic regression or others • Outcome: event -- actual trt membership: A or B • Predictor variables: all measured covariates, some interaction terms or squared terms, e.g., age, gender, duration of disease,…, age*duration,…

11. Propensity scores construction • Clinical outcome variable, e.g., major complication event, is NOTinvolved in the modeling • No concern of over-fitting • Obtain a propensity score model: a math equation PS = f (age, gender, …) • Calculate estimated propensity scores for all patients

12. Properties of propensity scores • A group of patients with the same propensity score are equally likely to have been assigned to trt A. • Within a group of patients with the same propensity score, e.g., 0.7, some patients actually got trt A and some got trt B, just as they had been randomly allocated to whichever trt they actually received.

13. “Randomized After the Fact” PS=0.7 Trt A Trt B

14. When the propensity scores are balanced across two treatment groups, the distribution of all the covariates are balanced in expectation across the two groups. • Use the propensity scores as a diagnostic tool to measure treatment group comparability. • If the two treatment groups overlap well enough in terms of the propensity scores, we compare the two treatment groups adjusting for the PS.

15. Compare treatments adjusting for propensity score • Matching • Subclassification (stratification) • Regression (Covariate) adjustment

16. PS1 PS2 Matchingbased on propensity scores (PS) PSTrt A vs. Trt B Compare treatments based on matched pairs Problem: may exclude unmatched patients PSm

17. Stratification • All patients are sorted by propensity scores. • Divide into equal-sized subclasses. • Compare two trts within each subclass, as in a randomized trial; then estimate overall trt effect as weighted average. • It is intended to use all patients. • But, if trial size is small, some subclass may contain patients from only one treatment group. PS ……. 1 2 5

18. Regression (covariate) adjustment Treatment effect estimation model fitting: the relationship of clinical outcome and treatment Outcome: Clinical outcome, e.g., adverse events Predictor variables: trt received, propensity score, a subset of important covariates Statistical method: e.g., regression or logistical regression

19. Propensity Score Methods • Summary Fit propensity score (PS) model using all measured covariates Estimate PS for all patients using PS model Compare treatments adjusting for propensity scores

20. Practical Issues • Issues in propensity score estimation • How to handle missing baseline covariate values • What terms of covariates should be included • Evaluation of treatment group comparability • Assessment of the resulting balance of the distributions of covariates • Issues in treatment comparison: • Which method: matching, stratification, regression • Issues in study design with PS analysis • Pre-specified vs. post hoc PS analysis • Pre-specify the covariates needed to collect in the study and then included in PS estimation • Sample size estimation adjusting for the propensity scores

21. Example – Device A • Non-concurrent, two-arm, multi-center study • Control: Medical treatment without device, N=65, hospital record collection • Treatment: Device A, N = 130 • Primaryeffectivenessendpoint: Treatment success • Hypothesis testing: superiority in success rate • 20 imbalanced clinically important baseline covariates, e.g., prior cardiac surgery • 22% patients with missing baseline covariate values

22. Enrollment Time

23. Two treatment groups are not comparable • Imbalance in multiple baseline covariates • Imbalance in the time of enrollment • So, any direct treatment comparisons on the effectiveness endpoint are inappropriate. • And, p-values from direct treatment comparisons are un-interpretable. • What about treatment comparisons adjusting for the imbalanced covariates? • Traditional covariate analysis • Propensity score analysis

24. Performed propensity score (PS) analysis • Handed missing values • MI: generate multiple data sets for PS analysis • Generate one data set: generalized PS analysis • Others • Included all statistically significant and/or clinically important baseline covariates in PS modeling. • Checked comparability of two trt groups through estimated propensity score distributions. • Found that the two trt groups did not overlap well.

25. Estimated Propensity Scores (with time)

26. Estimated Propensity Scores (w/o time)

27. Patients in Propensity Score Quintile 1 2 3 4 5 Total Ctl38 18 8 10 65 (w/time)58% 28% 12% 2% 0% Trt1 21 31 3839 130 1% 16% 24% 29%30% Ctl 29 24 8 4 0 65 (w/o time)45% 37% 12% 6% 0% Trt10 14 32 35 39 130 8% 11% 24% 27% 30%

28. Treatment Success 1 2 3 4 5 Total Crl S 16 8 1 0 25 N38 18 8 10 65 Trt S0 14 25 24 23 86 N 1 21 31 3839 130 • Tried Cochran-Mantel-Haenszel test controlling for PS quintile, Logistic regression using PS as a continuous covariate • However, the sig. p-values are un-interpretable

29. Conclusion: • The two treatment groups did not overlap enough to allow a sensible treatment comparison. • So, any treatment comparisons adjusting for imbalanced covariates are problematic.

30. Example: Device B • New vs. control in a non-randomized study • Primary endpoint: MACE incidence rate at 6-month after treatment • Non-inferiority margin: 7%, in this study • Sample size: new: 290, control: 560 • 14 covariates were considered.

31. Covariate balance checking before and after propensity score stratification adjustment Meanp-value New Control Before After -------------------------------------------------------------------------------------- Mi 0.25 0.40 <.0001 0.4645 Diab 0.28 0.21 0.0421 0.8608 CCS 2.41 2.75 0.0003 0.3096 Lesleng 11.02 12.16 <.0001 0.5008 Preref 3.00 3.08 0.0202 0.2556 Presten 62.75 66.81 <.0001 0.4053

32. Model Building • The PS is conditional Prob. that a patient would have been assigned to new device, based on his or her baseline covariates. • A hierarchical logistic regression model with a stepwise selection process was used to build the propensity score model. • The final propensity score model includes all covariates as well as a quadratic term.

33. Table 2. Distribution of patients at five strata Subclass Control New Total 1 14228 170 2 12743 170 3 12248 170 4 11951 170 • 50120 170 Total 560 290 850

34. Estimated Propensity ScoresN(new)=560, N(control)=290

35. Covariate balance checking before and after propensity score stratification adjustment Meanp-value New Control Before After -------------------------------------------------------------------------------------- Mi 0.25 0.40 <.0001 0.4645 Diab 0.28 0.21 0.0421 0.8608 CCS 2.41 2.75 0.0003 0.3096 Lesleng 11.02 12.16 <.0001 0.5008 Preref 3.00 3.08 0.02020.2556 Presten 62.75 66.81 <.0001 0.4053

36. After adj. balance check: Prior Mi rate: • Overall: Group % patients with prior Mi New 25 Control 40 Diff 15 • After: Quintile Group 1 2 3 4 5 New 70.4 32.6 25.0 17.6 15.0 Control 75.2 32.8 30.0 24.8 10.4

37. Percentage of patients with prior Mi

38. Adjusted Difference: Mew – Control: • Point estimate: -1.5% • 2-sided 95% C.I. : (-6.6%, 3.6%) • Non-inferiority margin: 7% • Claim: Non-inferiority w.r.t. Mace 6-month

39. Study Design • Plan in advance • Pre-specify clinically relevant baseline covariates: as many as possible • Sample size estimation: • Ignore the propensity score adjustment? • Could be inappropriate

40. Limitations • Propensity score methods can only adjust for observed confounding covariates and not for unobserved ones. • Propensity score is seriously degraded when important variables influencing selection have not been collected. • Propensity score may not eliminate all selection bias.

41. Limitations • Propensity score methods work better in larger samples. • Propensity score is not only way of adjusting for covariates. And, it may or may not be helpful in a particular comparison study. • Randomized trials are considered the highest level of evidence for trt comparison. Propensity score methods lack the discipline and rigor of randomized trials, and not as definitive as randomized trials.

42. Conclusions • Propensity score methods generalize technique with one confounding covariate to allow simultaneous adjustment for many covariates and thus reduce bias. • Propensity score methodology is an addition to, not a substitute of traditional covariate adjustment methods. • Plan ahead and carefully consider the practical issues discussed above. • Randomized studies are still preferred and strongly encouraged whenever possible!

43. References • Rubin, DB, Estimating casual effects from large data sets using propensity scores. Ann Intern Med 1997; 127:757-763 • Rosenbaum, PR, Rubin DB, Reducing bias in observational studies using subclassification on the propensity score. JASA 1984; 79:516-524 • D’agostino, RB, Jr., Propensity score methods for bias reduction in the comparison of a treatment to a non-randomized control group, Statistics in medicine, 1998,17:2265-2281

44. References • Blackstone, EH, Comparing apples and oranges, J. Thoracicand Cardiovascular Surgery, January 2002; 1:8-15 • Grunkemeier, GL and et al, Propensity score analysis of stroke after off-pump coronary artery bypass grafting, Ann Thorac Surg 2002; 74:301-305 • Wolfgang, C. and et al, Comparing mortality of elder patients on hemodialysis versus peritoneal dialysis: A propensity score approach, J. Am Soc Nephrol 2002; 13:2353-2362

45. Thanks!