Analyzing Observational Data: Focus on Propensity Scores

1. Analyzing Observational Data: Focus on Propensity Scores Arlene Ash QMC - Third Tuesday September 21, 2010

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. True and Modeled Relationship Between Risk and Outcome 1.0 0.8 0.6 Outcome 0.4 0.2 0 0 0.5 1.0 1.5 2.0 Risk

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. Propensity Score Method (Key Idea) • Draw a sub-sample that is more balanced on risk factors • Use standard techniques to analyze the sub-sample

6. Typical Propensity Score Approach • Estimate a model to predict the “probability of receiving the intervention” • This is “the propensity score” • Divide the full population into quintiles of the propensity score • Sample equal numbers of cases and controls from each quintile • Re-fit the model to estimate the effect of the intervention in the sampled cases

7. Propensity Score Sampling Example

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. 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. 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

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

12. Gender: female 29 33 Race/ethnicity: black 46 46 Hispanic 12 10 White 41 43 Education: HS grad 56 59 College graduate 4 13 Residential Detox & Acupuncture Cases:% with Various Characteristics Residential Acupuncture Characteristic (n = 6,907) (n = 1,104)

13. Characteristics of Residential Detox & Acupuncture Clients (2) Residential Acupuncture Characteristic (n = 6,907) (n = 1,104) Employment: unemployed 86.8 43.2 Insurance: uninsured 52.3 65.4 Medicaid 28.2 21.2 3.0 15.4 Private insurance 9.5 19.3 Lives: with child 30.3 2.9 In shelter

14. Characteristics of Residential Detox & Acupuncture Clients (3) Residential Acupuncture (n = 6,907) (n = 1,104) Characteristic Prior mental health treatment 12.3 27.8 42.3 32.4 Primary drug: alcohol 16.2 Cocaine 16.6 Crack 15.9 20.2 Heroin 24.6 19.0

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

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. Concern • Given large differences in risk adjustors between the groups and possibility of model mis-specification, should we be concerned about the estimated effect of acupuncture? • Stratum-specific modeling has been used to address such concerns historically • Strata defined by a limited number of particularly important risk adjustors • Propensity scores, a generalization • Used when there are many important predictors

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

19. Sampling Results • Able to match 740 cases (out of the full sample of 1,104 cases) with 740 comparable controls (out of the full sample of 6,907 controls) • Much more balance in terms of risk in this sub-sample

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

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. Summary • In this case, results were similar - Why? • Original model was very good (C-statistic = 0.96) • What was learned from the propensity score analysis: • Could find a subset of controls (about 10%) who look very similar to cases • Found similar results in this subset, increasing the credibility of the findings

23. Which Belong in the PS Model? • Confounders (Brookhart’s X1 variables)? • Simple predictors (X2 s)? • Simple selectors (X3 s)? • Let’s work together to fill in the following table