1. 1 Arlene Ash QMC - Third Tuesday September 21, 2010 (as amended, Sept 23) Analyzing Observational Data: Focus on Propensity Scores

2. 2 The Problem Those with the intervention and those without have markedly different values for important measured risk factors & Outcome is related to the risk factors that are imbalanced between the groups & It is not clear how the risk factors and outcome are related Why may standard analyses be misleading?

3. 3 True and Modeled Relationship Between Risk and Outcome

4. 4 Is Imbalance in Risk a Problem? If we correctly model the relationship between risk factors and outcome, we correctly estimate effect of the intervention With many risk factors, hard to know if the relationship between risk factors and outcome is correctly modeled Propensity score - a way to reduce the effect of imbalance in measured risk when models may be inadequate

5. 5 Propensity Score Method (Key Idea) The propensity score (PS) for an observation is the probability that the observation is “exposed” or “got the intervention” Use the PS model in pre-processing the data –To draw a sub-sample where the exposed and non- exposed groups are fairly balanced on risk factors. Then –Use standard techniques to analyze the sub-sample

6. 6 Simple Propensity Score Approach Estimate a model to predict the “probability of intervention/exposure” –This is “the propensity score” Divide the population into PS quintiles Create a subsample by taking equal numbers of exposed and unexposed observations from each quintile Use a subsequent regression model to estimate the effect of the intervention in the subsample

7. 7 Propensity Score Sampling Example PS Quintile# Cases# Controls# Sampled Lowest128124 2nd306760 Middle443876 4th531530 Highest78 816 Total 217 209 206

8. 8 Propensity Score Sampling Example: Treatments for Drug Abusers Patients seeking substance abuse detoxification in Boston receive either Residential detoxification Lasts ~ one week + encouragement for post- detox treatment, or Acupuncture Acute (daily) detox + 3-6 months of maintenance with acupuncture and motivational counseling

9. 9 Data From Boston’s publicly-funded substance abuse treatment system All cases discharged from residential detox or acupuncture between 1/93 and 9/94 Client classified (only once) as residential or acupuncture based on the modality of first discharge

10. 10 Outcome Is client re-admitted to detox within 6 months? (Y/N) Study question: Are acupuncture clients more likely to be re-admitted than residential detox clients? –Exposure = assigned to accupuncture

11. 11 Client Characteristics Available At Time Of Admission Gender Race/ethnicity Age Education Employment status Income Health insurance status Living situation Prior mental health treatment Primary drug Substance abuse treatment history

12. 12 Residential Detox & Acupuncture Cases: % with Various Characteristics Characteristic Residential (n = 6,907) Acupuncture (n = 1,104) Gender: female 2933 Race/ethnicity: black 46 Hispanic 12 10 White4143 Education: HS grad5659 College graduate413

13. Employment: unemployed 86.8 43.2 Insurance: uninsured 65.4 52.3 Medicaid 28.221.2 Private insurance 3.015.4 Lives: with child 9.519.3 In shelter 30.32.9 Characteristic Residential (n = 6,907) Acupuncture (n = 1,104) Characteristics of Residential Detox & Acupuncture Clients (2)

14. 14 Prior mental health treatment 12.327.8 Primary drug: alcohol 42.332.4 Cocaine 16.2 16.6 Crack 15.920.2 Heroin 24.619.0 Characteristic Residential (n = 6,907) Acupuncture (n = 1,104) Characteristics of Residential Detox & Acupuncture Clients (3)

15. 15 Substance abuse admits in the last year Residential detox: 0 1 2+ Short-term residential: 0 Long-term residential: 0 Outpatient: None Acupuncture: None 56.7 20.2 23.1 76.2 80.5 80.6 95.9 81.0 12.1 7.0 94.8 93.5 54.3 90.1 Characteristic Residential (n = 6,907) Acupuncture (n = 1,104) Characteristics of Residential Detox & Acupuncture Clients (4)

16. 16 Results Of Standard Analysis Percentage of clients re-admitted to detox within 6 months Among 1,104 acupuncture cases, 18% re-admitted Among 6,907 residential detox cases, 36% re-admitted Raw odds ratio = 0.40 From a multivariable stepwise logistic regression model: Odds ratio for acupuncture:0.71 (CI = 0.53-0.95)

17. 17 What’s the Worry? How Do We Address It? Given how different the two groups are, can we trust a model to correctly estimate the effect of acupuncture? PS methods generalize (long-standing) matching-within- strata methods that work well with 1 or 2 predictors PS can address imbalances in many important predictors simultaneously Both traditional and PS matching allow for –A pooled estimate (across all strata) or –When N is large enough, stratum-specific estimates

18. 18 Propensity Score Application Use stepwise logistic regression to build a model to predict whether a client “is exposed”(i.e., receives acupuncture) Select sub-samples of exposed and non-exposed with similar distributions of the “propensity score” (predicted probability of being exposed) Model (as before) on the sub-sample

19. 19 Sampling Results Able to match 740 who received acupuncture (out of 1,104) with 740 people who did not (out of 6,907) The risk factors in this subsample of 1480 are much more balanced between the two groups

20. 20 Characteristic Residential Acupuncture College graduate Employed Private Insurance Lives with child or adult Lives in shelter Prior mental health Rx 7% 41% 9% 72% 5% 21% (4%) (13%) (3%) (55%) (30%) (12%) 7% 42% 6% 77% 4% 21% (13%) (57%) (15%) (76%) (3%) (28%) Characteristics of Clients in Subsample (vs. Full Sample)

21. 21 Comparing Standard and Propensity Score Findings From the multivariable model fit to all cases: Odds Ratio for acupuncture: 0.71 95% Confidence Interval: 0.53-0.95 From multivariable model fit to more comparable sub- sample: OR for acupuncture: 0.61 95% CI:0.39-0.94

22. 22 Summary In this case, results were similar - Why? Original model was very good (C-statistic = 0.96) What we learned from the PS analysis: –Could find a subset of (about 10% of) patients who got residential detox who look very similar to those who got acupuncture –Skeptics were more receptive to findings from the PS analysis

23. 23 Which X’s Belong in the PS Model? The goal is to estimate the effect of exposure E on outcome Y Confounders (Brookhart’s X 1 variables)? –Directly affect both E and Y Simple predictors (X 2 s)? –Affect Y but not E Simple selectors (X 3 s)? –Affect E but not Y

24. 24 Example The goal is to estimate the effect of E = CABG surgery on Y = 30-day mortality following admission for a heart attack –Confounder (e.g., disease severity) –Simple predictors (e.g., home support) –Simple selectors, aka “instrumental variables” (e.g., random assignment)

25. Variable typeDirectly affects Belongs in which model Outcome (Y) Exposure (E)PS Subsequent Regression X1Confounder11Yes X2Predictor10?Yes X3Selector01No? 25 ? = inclusion should neither harm nor help

26. Discussion The “pre-processing” that occurs when sub- sampling to create “PS-balanced” comparison groups protects against bias from confounding variables Putting selector variables in the PS model will hurt accuracy (by reducing the numbers of good matches) without making the groups more comparable Subsequent regression improves accuracy 26