Instrumental variables for comparative effectiveness research: a review of

applications

M. Alan Brookhart, Ph.D.

Division of Pharmacoepidemiology,Brigham & Women’s Hospital, Harvard Medical School

Overview of Lecture

• Brief introduction to instrumental variable analysis

• Examples of instrumental variables, some characteristics

• Role of IV in observational studies of medical interventions

The Challenge of Observational Studies of Intended Effects

• Confounding by indication is strong• Patients who need treatment are more

likely to receive treatment• Indications unmeasured or poorly

measured– > Unmeasured confounding bias

Instrumental Variables

• Can permit estimation of causal effects even when important confounders are unmeasured

• Instrument should be correlated with treatment• Instrument should be related to outcome only

through association with treatment (often termed the exclusion restriction)– Empirically unverifiable, but can be explored in

observed data.

Confounding and Instrumental Variables

Received Received TreatmeTreatmentnt

OutcomeOutcome

ConfoundersConfoundersTreatment Arm AssignmentTreatment Arm Assignment

Example: Randomized Controlled Trial with Non-Compliance

RandomizationRandomization

BlindingBlinding

CC

XX YY

ZZ

InstrumentInstrument

Intention-to-treat and (Wald) IV Estimator

α

ITT Estimator = E[Y|Z=1] - E[Y|Z=0]

E[Y|Z=1] - E[Y|Z=0] IV Estimator = -------------------------

E[X|Z=1] - E[X|Z=0]

Effect of the Instrument on the Outcome = ------------------------------------------------------------

Effect of the Instrument on the Exposure

Interpretation of an IV

• When treatment effects are heterogeneous, IV estimator may be biased for average treatment effect (ATE)

• IV estimates a weighted average of causal treatment effects

• Subgroups of patients whose treatment status is more likely to be influenced by the IV are weighted up

• Empirical data, subject-matter knowledge may be used to anticipate direction of bias in IV relative to ATE

IVs For Comparative Effectiveness

Preference-based Instrumental Variables

• Substantial variation in medical practice across regions, hospitals, physicians

• Differences in medical practice may represent a natural experiment

• Suggests IVs defined at level of provider

Observational Study of Non-steroidal Anti-Inflammatory Drugs

and GI bleeding risk in an elderly population(Brookhart et al, Epidemiology 2006)

• Compare short-term risk of GI outcomes between – Non-selective NSAIDs– COX-2 selective NSAIDs

• Coxibs are slightly less likely to cause GI problems

• Coxibs are likely to be selectively prescribed to patients at increased GI risk

• Classic problem of confounding by indication

Characteristics of Cohort

Variable Coxib NS NSAID

Female Gender 86% 81%

Age > 75 75% 65%

Charlson Score>1 76% 71%

History of Hospitalization 31% 26%

History of Warfarin Use 13% 7%

History of Peptic Ulcer Disease 4% 2%

History of GI Bleeding 2% 1%

Concomitant GI drug use 5% 4%

History GI drug use 27% 20%

History of Rheumatoid Arthritis 5% 3%

History of Osteoarthritis 49% 33%

COXIB

COX-2 Preferring Physician

NS NSAID Preferring Physician

NS NSAID

“Marginal Patient”

COXIB

COXIBNS NSAID

NS NSAID

Low Moderate High

Patient’s GI Risk

Estimating Preference– Volume of NSAID prescribing varies

considerably among physicians

– Our approach: use the type of the last NSAID prescription written by each physician as a measure of current preference

– If for last patient, physician wrote a coxib prescription, for the current patient he is classified as a “coxib preferring physician” other he is classified as an “non-selective NSAID preferring physician.”

Index Patient’s IV isPrevious Patient’s Treatment

Treatment

Previous PatientTreated with NSAIDs

Index Patient

Treatment = ?

Time

Instrument should be related to treatment

LastNSAID

Prescription(IV)

Current Prescription (Actual Treatment)

CoxibX=1

Non-Selective NSAIDX=0

CoxibZ=1

(73%) (27%)

Non-Selective NSAIDZ=0

(50%) (50%)

Instrument should be unrelated to observed patient risk factors

Variable Coxib PrefZ=1

NS NSAID PrefZ=0

Female Gender 84% 84%

Age > 75 73% 72%

Charlson Score > 1 75% 73%

History of Hospitalization 29% 27%

History of Warfarin Use 12% 10%

History of Peptic Ulcer Disease 3% 3%

History of GI Bleeding 1% 1%

Concomitant GI drug use 5% 5%

History GI drug use (e.g., PPIs) 25% 24%

History of Rheumatoid Arthritis 4% 4%

History of Osteoarthritis 45% 41%

IV estimate of the effect of coxib exposure on GI outcome

IV Estimate E[Y|Z=1]-E[Y|Z=0] -0.21% ------------------------- = -------- = -0.92% E[X|Z=1]-E[X|Z=0] 22.8%

Crude

E[Y|X=1]-E[Y|X=0] = +0.03%

After multivariable adjustment= -0.04%

Other examples of preference-based instrument

• Clinic, hospital as IV – Johnston SC, J Clin Epi– Schneeweiss, Seeger, Walker NEJM 2008: Aprotinin during

CABG

• Geographic region as instrument– Wen, J & Kramer J Clin Epi 1997 – Brooks et al, HSR, Breast cancer treatment– Stuckel T, et. al JAMA – Cardiac catheterization

• Generally available, but vulnerable to case-mix bias, concomitant treatments associated with the IV

Distance to Specialty Provider as IV

McClellan, M., B. McNeil and J. Newhouse, JAMA, 1994. "Does More Intensive Treatment of Acute Myocardial Infarction Reduce

Mortality?”

• Medicare claims data identify admissions for AMI, 1987-91

• Treatment: Cardiac catheterization (marker for aggressive care)

• Outcome: Survival to 1 day, 30 days, 90 days, etc.

• Instrument: Indicator of whether the hospital nearest to a patient’s residence does catheterizations.

Are assumptions valid ?1. Is IV associated with treatment?

26.2% get cath if nearest hospital does caths19.5% get cath if nearest hospital does not do caths

2. Is IV associated with outcome other than through it effect on treatment?

They demonstrated IV is largely unassociated with observed patient characteristics.

McClellan, et al. results

α

1. Conventional methods - Crude estimate -30% (17% 1-year mortality if catheterized vs. 47%) - OLS estimate is -24%, adjusting for observable risk factors

2. IV estimator suggest catheterization associated with 10 percentage point reduction in mortality

E[Y|Z=1]-E[Y|Z=0] -0.7% ------------------------- = -------- = -10.4% E[X|Z=1]-E[X|Z=0] 6.7%

Other Examples of Distance IVs

• Brooks et al -- Effect of dialysis center profit status on survival

• McConnell KJ et al -- Treatment of head injuries at level I vs level II trauma centers

• Must be used studying a treatment that is dispensed at particular locations– Not applicable to many prescription medications

• Treatment must depend on distance

Beta blocker after HF hospitalization and 1-year mortality

IV status:Before

IV status:After

Calendar Time as an IV

% B

B u

s e a

f ter H

F h o

s pi ta

l.Johnston et al. Stat Med 2008

Bias: Secular trends in other things related to the outcome

Best used when there is a dramatic shift in practice in a short time period: e.g, changes in guidelines, or safety warnings.

IVs can also be created

• ‘Randomized encouragement’ designs (Ten Have et al)

• Designed delays (McClure M., Dormuth C; work in British Columbia)

One-off Instruments• Day of the week of hospital admission as an instrument

for waiting time for surgery (Ho et al.)• Surgeons operate only on weekdays and therefore

patients admitted on the weekend may have to wait longer for surgical treatment.

• Bias: patients admitted on the weekend were different from those admitted on the weekday.

• Bias: IV could be independently related to the outcome if other aspects of hospital care that could affect the outcome were different over the weekend.

Characteristics of Good Application of IVs

• IV should be have theoretical motivation• IV should be strongly associated with

treatment• IV should be largely unrelated to patient

characteristics• Some consideration should be given to

generalizing the estimate• Used in the setting of a large sample

Role of Instrumental Variable

• IV assumptions are different from those underlying conventional approaches

• Makes IV excellent for secondary analysis– Wang et al, NEJM 2005

• Problem arises if methods given different results• IV method deserve primary status if IV is

strong&valid, sample size is large, and unmeasured confounding expected to be great

Coming soon to the AHRQ website…

Practical guide to IV Methods for Comparative

Effectiveness Research, by Brookhart, Rassen, and Schneeweiss