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Arlene Ash

QMC - Third TuesdaySeptember 21, 2010

Analyzing Observational Data: Focus on Propensity Scores

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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?

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0.2

0.4

0.6

0.8

1.0

0 0.5 1.0 1.5 2.0

Risk

Out

com

eTrue and Modeled Relationship

Between Risk and Outcome

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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

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Propensity Score Method (Key Idea)

• Draw a sub-sample that is more balanced on

risk factors • Use standard techniques to analyze the sub-

sample

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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

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Propensity Score Sampling Example

PS Quintile # Cases # Controls # Sampled

Lowest 12 81 24

2nd 30 67 60

Middle 44 38 76

4th 53 15 30

Highest 78 8 16

Total 217 209 206

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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

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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

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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

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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

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Residential Detox & Acupuncture Cases:% with Various Characteristics

CharacteristicResidential (n = 6,907)

Acupuncture(n = 1,104)

Gender: female 29 33

Race/ethnicity: black 46 46

Hispanic 12 10

White 41 43

Education: HS grad 56 59

College graduate 4 13

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Employment: unemployed 86.8 43.2

Insurance: uninsured 65.4 52.3

Medicaid 28.2 21.2

Private insurance 3.0 15.4

Lives: with child 9.5 19.3

In shelter 30.3 2.9

CharacteristicResidential (n = 6,907)

Acupuncture(n = 1,104)

Characteristics of Residential Detox & Acupuncture Clients (2)

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Prior mental health treatment 12.3 27.8

Primary drug: alcohol 42.3 32.4

Cocaine 16.2 16.6

Crack 15.9 20.2

Heroin 24.6 19.0

CharacteristicResidential (n = 6,907)

Acupuncture(n = 1,104)

Characteristics of Residential Detox & Acupuncture Clients (3)

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Substance abuse admits in the last yearResidential detox: 0

12+

Short-term residential: 0Long-term residential: 0Outpatient: NoneAcupuncture: None

56.7

20.223.176.280.580.695.9

81.012.17.0

94.893.554.390.1

CharacteristicResidential (n = 6,907)

Acupuncture(n = 1,104)

Characteristics of Residential Detox & Acupuncture Clients (4)

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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 = 0.40From a multivariable stepwise logistic regression model:• Odds ratio for acupuncture: 0.71 (CI = 0.53-0.95)

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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

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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

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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

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Characteristic Residential Acupuncture

College graduateEmployedPrivate InsuranceLives with child or adultLives in shelterPrior 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 (Full Sample)

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Comparing Standard and Propensity Score Findings

From the multivariable model fit to all cases:Odds Ratio for acupuncture: 0.7195% Confidence Interval: 0.53-

0.95From multivariable model fit to more comparable sub-

sample:OR for acupuncture: 0.6195% CI: 0.39-

0.94

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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

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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

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Variable type Directly affectsBelongs in

which modelOutcome

(Y) Exposure

(E) PS Regression

X1 Confounder 1 1 ? ?

X2 Predictor 1 0 ? ?

X3 Selector 0 1 ? ?