Patsi Sinnott, PT, PhD

August 8, 2012

Instrumental Variables 

Models
Outline

1. Causation Review

2. The IV approach

3. Examples

4. Testing the Instruments

5. Limitations

2
Causation

 Randomized trial provides the structure 

for understanding causation

– Does daily dark chocolate affect health?

– Does PT treatment following hip fracture 

reduce the risk of death?

3
RCT Review

4

Recruit

Participants Randomization

Treatment

Group (A)

Comparison

Group (B)

Outcome (Y)

Outcome (Y)
Randomization

 In OLS (yi = α + βxi + εi )

–The x’s explain the variation in y

– ε = the random error

–Randomization assumes a high 

probability that the two groups are 

similar

5
However

 Randomized trials may be

– Unethical

– Infeasible

– Impractical

– Not scientifically justified 

6
Observational Studies

 Natural Experiment

 Administrative Data

 Many observable characteristics (e.g. age, 

gender, smoking status) can be included 

in the model, BUT.......

7
Observational Studies

 Non-randomized groups differ in both 

observed AND unobserved 

characteristics

8
Unobserved characteristics....

 Covariates or confounders that may skew 

the data

 Can lead to violations of the assumptions 

of OLS

 Can lead to bias in the results

 Faulty inference of causality

9
The IV approach

 When randomization does not produce 

even distribution of characteristics

10
Mortality after AMI = fn

(cardiac cath.) + other var.

 Does more intensive treatment of AMI in 

the elderly reduce mortality (McClellan; 

McNeil; Newhouse. JAMA. 9/21/94)

– Elderly patients

– Medicare claims data

– Survival 4 years after AMI

11
Even distribution of observed?

No Cath Cath w/in 90 d.

Female 53.5% 39.7%

Age in years 77.4 71.6

Black 6.0% 4.3%

Cancer 2.2% 0.8%

Pulm. disease (uncompl.) 11.1% 9.3%

Dementia 1.2% 0.1%

Diabetes 18.3% 17.1%

Renal dis. (uncompl.) 2.3% 0.7%

CV disease 5.4% 2.8%

12
Even distribution of observed?

No Cath Cath w/in 90 days

Admit to cath/revasc

hospital

40.9% 62.9%

One day mortality 10.3% .9%

7-day Mortality 22.0% 3.3%

30-day mortality 26.6% 7.4%

1-year mortality 47.1% 16.6%

2-year mortality 55.3% 21.3%

4-year mortality 66.7% 29.9%

No. of observations 158,261 46,760

13
Mortality differences (adjusted)*

Mortality Unadjusted 

Differences

Adj. for 

demographic 

characteristics

Adj. for 

demographic and 

co-morbidity 

differences

One day -9.4 (0.2) -6.7 (0.2) -6.8(0.2)

7-day -18.7 (0.2) -13.7 (0.2) -13.5(0.2)

30-day -19.2 (0.3) -18.7 (0.3) -17.9 (0.3)

1-year -30.5 (0.3) -26.0 (0.3) -24.1 (0.3)

2-year -34.0 (0.3) -28.7 (0.3) -26.6 (0.3)

4-year -36.8 (0.3) -30.4 (0.3) -28.1 (0.3)

14 *ANOVA
The IV approach

 When randomization does not produce 

even distribution of characteristics

 When unmeasured/unobserved 

characteristics potentially skew results

15
Unmeasured/unobserved 

characteristics....

 Are there differential/varying reasons 

why some patients receive care

–Do sicker patients get treatment ?

–Does distance from a hospital 

determine treatment?

–Do certain physicians prefer specialty 

treatments?

16
Unobserved characteristics.....

 Are there differential determinants of 

return for f/u care

–Economic/financial issues

–Distance and transportation

–Other insurance?

17
Choosing the IV

 Face validity

 Exogenous

 Strong predictor

 Just identified

18
Face validity

 Irrefutable relationship to treatment

19
Exogenous

 No direct or indirect effect on outcome

20

Instrumental variable 

Treatment

Outcome

Other variables
Strong Predictor

 Cause substantial variation in the variable 

of interest

21
Just identified

 Number of IVs ≤ number of exogenous 

variables

22
Example

 Mortality = fn(cath)

 What’s missing?

23
Mortality after AMI = fn

(cardiac cath.) + other var.

 No direct or indirect effect on outcome

24

Differential distance to nearest cath. hospital

Cardiac cath (+/-)

Mortality

Other variables
Face validity

 Differential distance between nearest 

hospital and nearest catheterization 

facility/hospital

– Pts w/AMI will go to nearest hospital

– Distance from nearest hospital to nearest 

cath hospital will be independently 

predictive of catheterization for similar 

patients.

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Strong predictor

DD ≤ 2.5 miles DD > 2.5 miles

Female 51.3% 49.5%

Age 76.1 76.1

Admit to cath hospital 45.4% 5.0%

90 day cath 26.2% 19.5%

1-day mortality 7.5% 8.88%

7-day mortality 16.80% 18.59%

30-day mortality 24.86% 26.35%

1-year mortality 39.79% 40.54%

2-year mortality 47.20% 47.89%

4-year mortality 58.06% 58.52%

No. of observations 102,516 102,505

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Results w/DD IV

 That variation in IV causes variation in 

the treatment variable (cath) is satisfied

– 26.2-19.5 = 6.75% point greater chance of 

getting cath within 90 days following AMI 

when differential distance is <=2.5 miles 

27
 Multiple regression results

28

 Patient characteristics 

 Three IVs

– High volume hospital (1,0), 

– Rural residence (1,0)

– DD IV
Multiple regression w/IV results

Rec’d cath Admit hi-volume Rural residence

1-day mortality -5.0(1.1)* -.88 (0.24) 0.57 (0.19)

7-day mortality -8.0(1.8) -1.23 (0.33) 0.49(0.26)

30-day mortality -6.8(2.6) -1.45(0.38) 0.50 (0.30)

1-year mortality -4.8(3.2) -1.07(0.88) -0.15 (0.33)

2-year mortality -5.4(3.3) -.88 (0.43) -0.02 (0.33)

4-year mortality -5.1(3.2) -.75 (0.42) 0.14 (0.32)

29

* In percentage points, standard errors in parens.
Summary of results

 Unadjusted – 37 % points effect on four 

year mortality

 Adjusted w/out IV – 28 % points effect

 Adjusted w/DD IV – 6.9 % points effect 

 Adjusted with DD, high volume hospital 

and rural IVs – approx 5 percentage pts.

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Interpretation

 Beneficial effects on mortality 

– (5.0 percentage points)

 At day one...

– before the procedure could have any 

beneficial effect. 

 Interpretation...is likely due to something 

other than cath

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Examples

 Wage = fn (years of education) + ?

 School performance = fn (class size) + ?

32
IV Example

 Wage = fn (years of education) + ?

 What instrument ?

– Years of education, but not ability nor wage

33
Wage = fn(years of education) + 

ability

 No direct or indirect effect on outcome

34

Distance to nearest college

Years of education

Wage

Other variables
Example

 School performance = fn (class size)

 What’s missing?

35
School performance = fn(class 

size)

 No direct or indirect effect on outcome

36

Dummy variable – split class

Class size

School performance

Other variables
Inference

 RCT provides the average effect for the 

population eligible for the study

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Inference

 Wide angle view of the effects of treatment

– More general population than RCT

– External validity

 Marginal effect on a selection of the 

population:

– Problematic for clinicians

– Policy implications – incremental effects

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Testing the instruments

 Face validity

 Exogenous

 Strong predictor

 Just identified

39
Testing – Face Validity

 Tells a good story

 Does the instrument have the expected 

sign and is significant

 Compare to alternative instruments (if 

available)

40
Testing

 Defend assumption that instrument is 

NOT an explanatory variable

 Explain why instrument is not correlated 

with omitted explanatory variable

41
Testing - Exogenous

 Test if errors are correlated with regressors

– Hausman test

 Test if instrument is uncorrelated with the 

error

– Sargan test

42
Testing – Strong Predictor

 Test if the correlation between the instrument 

and the troublesome variable is strong enough

– F statistic, regressing troublesome variable 

on all instruments – to test the null that the 

slopes of all instruments equal zero (F>10.)

 Staiger Stock test

43
Testing – Just identified

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Conclusion

 Instrumental variables mimic 

randomization

 But good instruments are hard to find.

 An estimate of the marginal 

effect/influence on outcome

 CASE (copy and steal everything)

 But make sure the IV works for the study

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VA IVs

 Distance to nearest VA/treatment (Slade , 

McCarthy; Pracht, Bass; Kim, Eisenberg)

 Distance to nearest VHA hospital minus 

distance to nearest non-VHA hospital (Helmer, 

Sambamoorthi)

 Racial mix by enrollees/utilizers (Simeonova)

 Visit intensity for all enrollees of a class 

(Kim, Eisenberg) (local practice)

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References

1.McClellan M, McNeil BJ, Newhouse JP. Does more intensive treatment of acute 

myocardial infarction in the elderly reduce mortality? Analysis using instrumental 

variables. JAMA 1994;272:859-66.

2.Newhouse JP, McClellan M. Econometrics in outcomes research: the use of 

instrumental variables. Annu Rev Public Health 1998;19:17-34.

3.Rassen JA, Brookhart MA, Glynn RJ, Mittleman MA, Schneeweiss S. Instrumental 

variables I: instrumental variables exploit natural variation in nonexperimental data to 

estimate causal relationships. J Clin Epidemiol 2009;62:1226-32.

4.Rassen JA, Brookhart MA, Glynn RJ, Mittleman MA, Schneeweiss S. Instrumental 

variables II: instrumental variable application-in 25 variations, the physician 

prescribing preference generally was strong and reduced covariate imbalance. J Clin

Epidemiol 2009;62:1233-4

5.Humphreys K, Phibbs CS, Moos RH. Addressing self-selection effects in evaluations 

of mutual help groups and professional mental health services: an introduction to twostage sample selection models. Evaluation and Program Planning 1996;19:301-8.

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References

6.Kennedy P. A Guide to Econometrics. Sixth ed. Malden, MA: Blackwell Publishing; 

2008. 

7. Kim HM, Eisenberg D, Ganoczy D, et al. Examining the Relationship between 

Clinical Monitoring and Suicide Risk among Patients with Depression: Matched Case–

Control Study and Instrumental Variable Approaches. Health Services Research. 

2010;45(5p1):1205-1226.

8. Pracht EE, Bass E. Exploring the Link between Ambulatory Care and Avoidable 

Hospitalizations at the Veteran Health Administration. Journal for Healthcare Quality. 

2011;33(2):47-56.

9. Simeonova E. Race, Quality of Care and Patient Outcomes: What Can We Learn 

from the Department of Veterans Affairs? Atlantic Economic Journal. 2009;37(3):279-

298.

10. Slade EP, McCarthy JF, Valenstein M, Visnic S, Dixon LB. Cost Savings from 

Assertive Community Treatment Services in an Era of Declining Psychiatric Inpatient 

Use. Health Services Research. 2012.

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Other IV methods

 Randomization

 2SLS

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 Watch for HERC Technical Report, 

Wagner, Cowgill, 2012.

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