Instrumental Variables

1. Instrumental Variables October 2013 Alexander M. Walker MD, DrPH

2. X Randomization Self-matching Propensity D T

3. X Randomization Self-matching Propensity Instruments D T

4. Definition • An instrument is a measured variable that is • known to be uncorrelated with the unmeasured predictors • a correlate of treatment • not in itself a direct cause of the outcome • Any correlation between the instrument and outcome is • unconfounded by unmeasured predictors • mediated only by treatment, • permitting unconfounded estimates of treatment effect

5. Does Adherence to Preventative Therapy Reduce Hospitalization? Adherence Hospital Admission

6. Severity of Disease is a Confounder Adherence Severity Hospital Admission

7. Severity is Unmeasured Adherence Severity Hospital Admission

8. Copayment Influences Adherence In the United States, the amount that a patient must pay for a drug (“copayment”) depends on administrative arrangements between the employer and the private insurance company. Copayment Adherence Severity Hospital Admission

9. A Question in Health Economics Copayment To what degree is Copayment a cause of Hospital Admission? Hospital Admission

10. A Question in Health Economics Copayment Adherence is an intermediate variable. Adherence Hospital Admission

11. A Question in Health Economics Severity confounds the relation between Adherence and Hospital Admission, but because Severity is unrelated to Copayment, … Copayment Adherence Severity Hospital Admission

12. A Question in Health Economics Copayment Severity of disease does not confound the association between Copayment and Hospital Admission and is ignorable for the health economist. Adherence Severity Hospital Admission

13. In Words … • Adherence varies with • Severity • Copayment for drug • Severity • Unmeasured • Predicts hospitalization, and therefore is a • Confounder of adherence • Copayment for drug • Well-measured • Does not predict hospitalization • Not correlated with Severity • The association between Copayment and Hospitalization is not confounded by severity

14. Estimating the Effect of Adherence Copayment Adherence Severity Hospital Admission If ∆Copayment affects hospital admission rates, it can only be through the mediating effect of ∆Adherence. A test of the effect of Copaymentis a test of the effect of Adherence.

15. The size of the effect of adherence can be deduced from the associations between copay and (1) adherence and (2) admission rates. Estimating the Effect of Adherence Copayment, unconfounded by severity, is an instrument for adherence. Copayment Adherence Severity Hospital Admission If ∆Copayment affects hospital admission rates, it can only be through the mediating effect of ∆Adherence.

16. The slope of the regression line of outcome variable against the instrument Divided by The slope of the regression line of the predictor variable against the instrument All regressions are made conditionally on other known predictors of outcome and target variable, e.g. with covariate control. The Instrumental Variable Estimate

17. Specifics: Copay, Adherence to Beta Blockers, and Hospital Admission for CHF • Members of a large health plan • With a diagnosis of CHF • Treatment with a single beta blocker in 2002 • Adherence in 2002 measured by days treated / days eligible • Many medical covariates identified in 2002 diagnoses, drugs, costs • Copay in 2002 identified for the beta blocker of treatment • Tiers • Variations according to employer contract • CHF hospitalization if any identified in 2003 Cole JA et al 2006

18. Component regressions Predict the Outcome • Hospitalization for CHF (yes/no) in 2003 As a function of the fitted value for • Adherence in 2002 Second stage Predict the Explanatory Variable • Adherence in 2002 As a function of observed values • Copayment in 2002 First stage Any factor that is correlated with copayment and that predicts outcome will invalidate copayment as an instrument. We can however, condition on that factor by including it in a larger regression model.

19. Effect of $10 Change in Copayment for Beta-Blocker -1.8% Adherence +0.8% Risk of Hospitalization

20. Calibrate the Regression Slope +0.8% ∆Hospitalization per $10 ΔCopayment -1.8% ∆Adherence per $10 ΔCopayment +4.4% ∆ Hospitalization -10% ∆ Adherence

21. Relative Risk for a 10% Improvement in Beta Blocker Adherence RR 95% CI 0.62 0.48 - 0.81 This comes from the outcome model, and can be seen as reinterpreting the copay effect as a diluted effect of adherence.

22. Relax assumptions bymodeling Predict the Outcome • Hospitalization for CHF in 2003 As a function of the fitted value for • Adherence in 2002 with concurrent control for • Type of beta-blocker 2002 • Other diseases 2002 • Age, region, sex 2002 Predict the Explanatory Variable • Adherence in 2002 As a function of observed values • Copayment in 2002 with concurrent control for • Type of beta-blocker 2002 • Other diseases 2002 • Age, region, sex 2002 Unmeasured characteristics that are not associated with Copayment conditionally on type of beta-blocker, other disease, age, region and sex do not affect the coefficient associated with copayment for either regression.

23. First stage predictors 2002 Fitted 2002 Adherence Characteristic Effect SE $10 higher copayment -1.8% 0.2% Tablets per day -2.1% 0.6% Acute Myocardial Infarction +2.6% 0.9% Cardiac Dysrhythmias +2.1% 0.6% Chronic renal failure -2.4% 1.0% Metoprololtartarate* -5.9% 1.0% Metoprolol succinate* -2.5% 1.0% Atenolol* -4.1% 1.1% *Versus carvedilol

24. Instruments in drug studies • Distance to care provider • Preference-based • Region • Hospital • Team • Provider • Day of week • Calendar time • Randomized encouragement • Copayment From: Brookhart MA, Rassen JA, Schneeweiss S. Instrumental variable methods in comparative safety and effectiveness research. Pharmacoepidemiol Drug Saf. 2010 Jun;19(6):537-54.

25. Reporting instruments • Justify the motivation • Describe the theoretical basis • Report the strength of the instrument • Report risk factors in relation to the instrument • Report other treatments in relation to the instrument • Consider to whom the effect really generalizes From: Brookhart MA, Rassen JA, Schneeweiss S. Instrumental variable methods in comparative safety and effectiveness research. Pharmacoepidemiol Drug Saf. 2010 Jun;19(6):537-54.

26. Thank You!