the application of propensity score analysis to non-randomized medical device clinical studies: a...
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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!