Presentations in this series 1.Introduction 2.Self-matching 3.Proxies 4.Intermediates 5.Instruments 6.Equipoise Avoiding Bias Due to Unmeasured Covariates Alec Walker

T D X Self-matching Proxies Randomization Intermediates

T D X Self-matching Proxies Randomization Intermediates Instruments

4 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 Adherence Hospital Admission

6 Adherence Hospital Admission Severity

7 Adherence Hospital Admission Severity

8 Adherence Hospital Admission Severity Copayment 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.

9 Hospital Admission Copayment To what degree is Copayment a cause of Hospital Admission?

10 Adherence Hospital Admission Copayment Adherence is an intermediate variable.

11 Adherence Hospital Admission Severity Copayment Severity confounds the relation between Adherence and Hospital Admission, but because Severity is unrelated to Copayment, …

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

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

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

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

17 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.

18 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

19 Predict the Explanatory Variable Adherence in 2002 As a function of observed values Copayment in 2002 Predict the Outcome Hospitalization for CHF (yes/no) in 2003 As a function of the fitted value for Adherence in 2002

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21 per $10 Δ Copayment +0.8% ∆ Hospitalization -1.8% ∆ Adherence

22 per $10 Δ Copayment +0.8% ∆ Hospitalization -1.8% ∆ Adherence +4.4% ∆ Hospitalization -10% ∆ Adherence

23 Predict the Explanatory Variable Adherence in 2002 As a function of observed values Copayment in 2002 First stage Predict the Outcome Hospitalization for CHF (yes/no) in 2003 As a function of the fitted value for Adherence in 2002 Second 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.

24 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 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 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.

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% Metoprolol tartarate* -5.9% 1.0% Metoprolol succinate* -2.5% 1.0% Atenolol* -4.1% 1.1% *Versus carvedilol

Distance to care provider Preference-based – Region – Hospital – Team – Provider Day of week Calendar time Randomized encouragement Copayment 26 From: Brookhart MA, Rassen JA, Schneeweiss S. Instrumental variable methods in comparative safety and effectiveness research. Pharmacoepidemiol Drug Saf Jun;19(6):

27 How strongly does the Instrument predict the Target Exposure? – Perfect  No room for unmeasured confounders – Weak  Highly model-dependent Does the Instrument predict Outcome? – Directly? --> Do not use – Through unmeasured covariates? --> Do not use – Through measured covariates? (Other treatments?) Including the covariates makes results model-dependent Match on or balance on covariates Does the Instrument affect the effect of exposure?

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 28 From: Brookhart MA, Rassen JA, Schneeweiss S. Instrumental variable methods in comparative safety and effectiveness research. Pharmacoepidemiol Drug Saf Jun;19(6):

29 Conditionally on Unmeasured covariates are uncorrelated with RandomizationTreatment Self-matching Treatment (time-invariant covariates only) Proxies Outcome or Treatment Intermediates Outcome or Treatment InstrumentsTreatment

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