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.

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Outline

1. Randomized clinical trials

2. Non-randomized studies and a potential problem

3. Propensity scores methods for bias reduction

4. Practical issues with the application of propensity score methodology

5. Limitations of propensity score methods

6. Conclusions

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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.

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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.

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Nonrandomized Studies and a Potential Problem

• None of advantages provided by randomized trials is available in non-randomized studies.

• A potential problem:

Two treatment groups were not comparable before the start of treatment.

i.e., not comparable due to imbalanced covariates between two treatment groups.

• So, direct treatment comparisons are invalid.

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Adjustments for Covariates

• Three common methods of adjusting for confounding covariates:

– Matching

– Subclassification (stratification)

– Regression (Covariate) adjustment

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• 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: 32 subclasses

– Regression adjustment may not be possible: Potential problem: over-fitting

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Propensity Score Methodology

• Replace the collection of confounding covariates with one scalar function of these covariates: the propensity score.

Age Gender

Duration…….

1 composite covariate:

Propensity Score

Balancing score

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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.

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• 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,…

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• Propensity scores construction

– Clinical outcome variable, e.g., major complication event, is NOT involved 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

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• 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.

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“Randomized After the Fact”

PS=0.7

Trt A Trt B

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– 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.

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• Compare treatments adjusting for propensity score

– Matching – Subclassification (stratification)– Regression (Covariate) adjustment

•Matching based on propensity scores (PS)

PS Trt A vs. Trt B

• Compare treatments based on matched pairs• Problem: may exclude unmatched patients

PS1

PS2

PSm

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•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

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• 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

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Propensity Score Methods

• Summary

Fit propensity score (PS) model using all measured covariates

Estimate PS for all patientsusing PS model

Compare treatments adjusting for propensity scores

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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

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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• Primary effectiveness endpoint: 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

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Enrollment Time

0

5

10

15

20

25

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

Ctl Trt

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• 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

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• 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.

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Estimated Propensity Scores (with time)

Ctl Trt

0.0

0.2

0.4

0.6

0.8

1.0Es

timat

ed P

rope

nsity

Sco

re

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Estimated Propensity Scores (w/o time)

Ctl Trt

0.0

0.2

0.4

0.6

0.8

1.0E

stim

ated

Pro

pens

ity S

core

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Patients in Propensity Score Quintile 1 2 3 4 5 Total Ctl 38 18 8 1 0 65(w/time) 58% 28% 12% 2% 0%

Trt 1 21 31 38 39 130 1% 16% 24% 29% 30%

Ctl 29 24 8 4 0 65 (w/o time) 45% 37% 12% 6% 0%

Trt 10 14 32 35 39 130 8% 11% 24% 27% 30%

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Treatment Success 1 2 3 4 5 Total

Crl S 16 8 1 0 25 N 38 18 8 1 0 65

Trt S 0 14 25 24 23 86 N 1 21 31 38 39 130

• 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

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• 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.

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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.

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Covariate balance checking before and after propensity score stratification adjustment

Mean p-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

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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.

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Table 2. Distribution of patients at five strata

Subclass Control New Total 1 142 28 170

2 127 43 170

3 122 48 170

4 119 51 170

5 50 120 170

Total 560 290 850

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Estimated Propensity Scores

N(new)=560, N(control)=290

Control New

0.0

0.2

0.4

0.6

0.8

1.0

Est

imat

ed P

rop

ensi

ty S

core

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Covariate balance checking before and after propensity score stratification adjustment

Mean p-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

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•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

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Percentage of patients with prior Mi

0

10

20

30

40

50

60

70

80

1st 2nd 3rdsubcla

4th 5th BeforeAdj

NewCtl

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• 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

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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

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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.

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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.

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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!

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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

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References

• Blackstone, EH, Comparing apples and oranges, J. Thoracic and 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

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Thanks!