Presentations in this series1. Introduction2. Self-matching3. Proxies4. Intermediates5. Instruments6. Equipoise

Avoiding Bias Due toUnmeasured Covariates

Alec Walker

T D

XSelf-matchingProxies Proxies

Randomization

IntermediatesIntermediates

T D

XSelf-matchingProxies Proxies

Randomization

IntermediatesIntermediates

Instruments

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• 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

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Adherence

HospitalAdmission

Does adherence to beta-blocker therapy reduce hospitalization for CHF?

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Adherence

HospitalAdmission

Severity of disease is a confounder

Severity

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Adherence

HospitalAdmission

Severity is unmeasured

Severity

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Adherence

HospitalAdmission

Copay also influences adherence

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.

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HospitalAdmission

A question in health economicsCopayment

To what degree is Copayment a cause of Hospital Admission?

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A question in health economics

Adherence

HospitalAdmission

Copayment

Adherence is an intermediate variable.

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Adherence

HospitalAdmission

Severity

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

A question in health economics

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Adherence

HospitalAdmission

Severity

Copayment

A question in health economicsSeverity of disease does not confound the association between Copayment and Hospital Admission and is ignorable for the health economist.

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• 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

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Copayment

Adherence

HospitalAdmission

Severity

Estimating the effect of adherence

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 .

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Copayment

Adherence

HospitalAdmission

Severity

Estimating the effect of adherence

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.

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Copayment

Adherence

HospitalAdmission

Severity

Estimating the effect of adherence

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.

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The instrumental variable estimate• 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.

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Copayment, 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

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Component regressions

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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

2003As a function of the fitted value for• Adherence in 2002

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Fitted effects of an increase in copay

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Fitted effects of an increase in copay

per $10 Δ Copayment

+0.8% ∆ Hospitalization -1.8% ∆ Adherence

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Fitted effects of an increase in copay

per $10 Δ Copayment

+0.8% ∆ Hospitalization -1.8% ∆ Adherence

+4.4% ∆ Hospitalization-10% ∆ Adherence

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Component regressions

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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

2003As 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.

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Relax the assumptions through modeling

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Predict the Explanatory Variable• Adherence in 2002 As a function of observed values• Copayment in 2002with concurrent control for • Type of beta-blocker 2002• Other diseases 2002• Age, region, sex 2002

Predict the Outcome • Hospitalization for CHF in 2003As a function of the fitted value for• Adherence in 2002with 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.

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Predictors of “exposure” (First Stage) are of interest

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2002 Fitted 2002 AdherenceCharacteristic 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

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Examples of 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 incomparative safety and effectiveness research. Pharmacoepidemiol Drug Saf. 2010Jun;19(6):537-54.

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Questions to ask about instruments• 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?

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Reporting instruments in drug studies• 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.

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Disarming unmeasured covariates

Conditionally onUnmeasured covariates are uncorrelated with

Randomization Treatment

Self-matching Treatment (time-invariant covariates only)

Proxies Outcome or Treatment

Intermediates Outcome or Treatment

Instruments Treatment

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Thank you!