Using Instrumental Variable Analyses to Inform ... - The Lewin Group

Anirban Basu, PhD
The University of Chicago &
The National Bureau of Economic Research
Lewin Group, Center for Comparative Effectiveness Research
CER Symposium: Responding to the National CER Agenda:
Evolving Data Sources and Analytics
June 15, 2010

• Review basic principles of IV analysis
• Present a graphical representation of counterfactual
outcomes and treatment effects
• Study how IV identifies casual treatment effects –
conceptual discussions rather than statistics
• Complications in the presence of heterogeneity of
treatment effects
• Local Instrumental Variables (LIV) approach
• An empirical example on evaluating breast cancer
treatments

• Identify instrumental variables that:
• Are correlated with treatment receipt but are uncorrelated
with outcomes.
• Can effectively randomize subjects across treatment arms
achieve equal distribution of both observed and
unobserved confounders across treatment groups.
• Address both overt and hidden biases in estimating the
average treatment effect.
• Split the variation in treatment variable into an exogenous
part and an endogenous part ‐ only the exogenous part is
used to estimate treatment effect

Outcome
0 1 2 3 4
Potential Outcomes
With Control Treatment
Levels of Unobserved confounder

Outcome
0 1 2 3 4
Potential Outcomes
With New Treatment
Potential Outcomes
With Control Treatment
Levels of Unobserved confounder

Outcome
0 1 2 3 4
AVERAGE TREATMENT
EFFECT
Potential Outcomes
With New Treatment
Potential Outcomes
With Control Treatment
Levels of Unobserved confounder

Outcome
0 1 2 3 4
Levels of Unobserved confounder

Outcome
0 1 2 3 4
Patients Select to Receive
New Treatment
Levels of Unobserved confounder
Patients Select to Receive
Control Treatment

Outcome
0 1 2 3 4
Levels of Unobserved confounder
An IV effect
= ATE

Outcome
0 1 2 3 4
Another IV effect
= ATE
Levels of Unobserved confounder

Outcome
0 1 2 3 4
Levels of Unobserved confounder

Outcome
0 1 2 3 4
Levels of Unobserved confounder

Outcome
0 1 2 3 4
Effect of IV2
Effect of IV3
Effect of IV1
Levels of Unobserved confounder
Angrist, Imbens, Rubin, 1996; Brooks, Chrischilles, Scott, Chen‐Hardee, 2003

• LATE ‐ the average treatment effect for
individuals who would change their treatment
choice when instrument level moves
• But who are these “marginal” patients?
• At what margins will my policy induce changes in
treatment choices?
• IV effects (combinations of LATEs) are
misleading as they can be arbitrarily weighted.
Heckman, 1997; McClellan, Newhouse, 1998; Harris, Remler, 1998; Heckman, Vytlacil, 1999

• Mirrors control function and selection models in
economics
• Requires an explicit choice model
• LIV is a method to estimate the Marginal Treatment
Effects:
• treatment effect among patients who are at the margin of
choice – the combination of IVs & observed confounders
balances the effects of unobserved confounders on choice
• a small perturbation in IV will change the treatment choice
for these patients
Heckman and Vytlacil, 1999, 2000, 2001; Heckman, Urzua, Vytlacil, 2006

Outcome
0 1 2 3 4
TE for combination
of margins
TE for a margin
Levels of Unobserved confounder
TE for a margin
Heckman and Vytlacil, 1999, 2000, 2001

Outcome
0 1 2 3 4
Levels of Unobserved confounder

• Identify the profile of MTE over the entire support of
the [1‐Pr(Trt Choice)] ~ scaled version of
unobserved confounders at the margins
• Compute ATE, TT, TUT and other policy effects by
simple weighting of the MTEs.
• Can identify situations where current data wont
allow to estimate an ATE.
• Can identify situations where complications due to
heterogeneity can be ignored.
Heckman and Vytlacil, 1999, 2000, 2001

MTE(UD) ( in $)
-100000 0 100000 200000 300000
MTE(UD) Profile and 95% CI with IV = NORTH, FEEDIF
0 .2 .4 .6 .8 1
UD
Propensity to choose BCSRT due to unobserved confounders
Linear IV approach:
IV(North): $45K
IV(Feedif): $13K
Local IV approach:
ATE(emp): $41K
ATE(extrp): $88K
TT: $52K
Basu, Heckman, Navarro, Urzua, 2007

• In IV analyses, the focus has been more on trying to
find good instrument and less on interpretation of
results.
• In health, unique opportunity to exploit providerlevel
and system level variations that are not linked
to outcomes.
• Careful attention is necessary to interpret IV results
in the face heterogeneity of treatment effects
• Local instrumental variable approaches can help in
identifying the proper treatment effects relevant for
policy making.

V
( Z , X ) U E ( U )=0
D 1( V
0),
V V V
V ( Z, X) U E( U D 1( V 0),
V V V )=0
Population level:
P( z) Pr( D 1| Z z )
Pr( U ( z ))
V
V
1 F ( ( z ))
U
V
F ( ( z )) = 1 - P( z )
U
V
V
V
Individual level:
D 1( V 0)
1( U ( z ))
V
V
1( F ( U ) F ( ( z )))
U V U V
V
1( F ( U ) 1 P( z ))
U
V
V
1( U 1 P( z))
D
V
where F ( U ) U ~ Uniform[0,1]
U V D
V

D 1( V 0)
=
=
Let
D 1( V 0) 1( U 1 P( z))
D
S( z) 1 P( z)
UD < S(z)
=> D=0
UD > S(z)
=> D=1
Treatment Effects
S(z)
0 1
UD

D 1( V 0)
=
=
Let
D 1( V 0) 1( U 1 P( z))
D
S( z) 1 P( z)
UD < S(z)
=> D=0
UD > S(z)
=> D=1
UD S(z’)
Treatment Effects
=> D=0 => D=1
S(z’)
S(z)
0 1
UD

D 1( V 0)
=
=
Let
D 1( V 0) 1( U 1 P( z))
D
S( z) 1 P( z)
--> S(z')