Transcript Introduction to causal inference from observational data

Beyond the ITT principle
Are randomized trials and observational
studies so different after all?
Miguel A. Hernán
Department of Epidemiology
Harvard School of Public Health
www.hsph.harvard.edu/causal
Setting: Randomized trial
with noncompliance
 Randomized assignment R
 Dichotomous for simplicity
 R=1 active treatment, 0 placebo
 Treatment received A(t)
 Time-varying
 A(t)=1 active treatment at t, 0 otherwise
 Outcome Y
 For simplicity continuous, measured at the end
of follow-up t=K+1
 Discussion applies to non continuous, timevarying outcomes Y(t) as well
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Goal
 To estimate the effect of treatment on the
mean outcome E[Y]
 Too vague
 Effect of treatment initiation vs no
initiation?
 Intent-to-treat (ITT)
 Effect of continuous treatment vs no
treatment?
 What if everyone had followed their assigned
treatment R?
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ITT effect
E
Y|R 1E
Y|R 0
 Measures effect of treatment initiation
under the particular noncompliance
structure of the trial
 Problems:
 Not biological effect of treatment but
effect of randomized assignment
 May not be transportable to settings with
different noncompliance patterns
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Effect of continuous treatment
 Alternative to ITT effect
 Can be estimated under certain
assumptions using
 Inverse probability weighting (IPW)
 G-estimation
 This talk reviews these methods
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Why not standard methods?
 Because they may result in invalid
estimates of causal effect when there
are time-varying risk factors L(t) that
are
 Time-dependent confounders for the
effect of A on Y
 Affected by prior treatment
 See the work by Robins et al
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IPW
Method 1: censoring + weighting
 Censor subjects when they stop their
assigned treatment R
 C(t)=1 if A(t)≠R
 Restrict analysis to uncensored patients
 C(t)=0 for 0≤t<K+1
 Compute
E
Y|R 1E
Y|R 0
 Full compliance but selection bias
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IPW
Method 1: censoring + weighting
 To adjust for selection bias, weight subjects
by the inverse of their probability of
remaining uncensored
K
1
W 
k1
1
Pr
C
k0|R, C
k 10, L
0
, . . . , L
k
 Estimate denominator by using, for
example, a pooled logistic model
 Separately for R=1 and R=0
 Can use sandwich estimator of the variance
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Aside:
 Weight W is not used in practice because it
leads to a greatly inefficient estimator
 Rather, we use the stabilized weight
K
1
SW  
k1
Pr
C
k0|R, C
k 10, V
Pr
C
k0|R, C
k 10, L
0
, . . . , L
k
 where V is a subset of L(0)
 Estimate numerator by using, for example,
a pooled logistic model
 Separately for R=1 and R=0
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IPW
Method 1: censoring + weighting
 Key assumption:
 Time-varying risk factors L(t)
 are available
 include all joint determinants of
treatment choice and outcome
 i.e., are sufficient to adjust for selection
bias
 Same assumption as in observational
studies with time-varying exposures
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IPW
Method 2: regression + weighting
 Do not censor patients when they do not
comply
 Rather propose a regression model to
describe the effect of treatment, e.g.,
where
E
Y|Ā 0 1 cum
Ā
0
, A
1
. . . A
K is treatment history
 Ā A
K
Ā  t0 A
t
 cum
 Problem: time-dependent confounding even
if model includes baseline confounders
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IPW
Method 2: regression + weighting
 To adjust for time-varying
confounding, weight subjects by
K
SW  
k0
f
A
k
|A
0
, . . . , A
k 1
, V
f
A
k
|A
0
, . . . , A
k 1
, L
0
, . . . , L
k
 Now fit the weighted regression
model
E
Y|Ā 0 1 cum
ĀT2 V
 using sandwich estimator of the variance
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IPW
Method 2: regression + weighting
 The parameters of the weighted regression
model can now be interpreted as the
parameters of the marginal structural
model
E
Yā  0 1 cum
āT2 V
 where Y ā is the counterfactual outcome under
0
, a
1
. . . a
K
regime ā a
 The effect of continuous treatment vs. no
treatment is 1 K
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IPW
Method 2: regression + weighting
 Two key assumptions:
 The structural model is correct
 Time-varying risk factors L(t) at all times t
 are available
 include all joint determinants of treatment
choice and outcome
 i.e., are sufficient to adjust for confounding bias
 Same assumptions as in observational
studies with time-varying exposures
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G-estimation
 Propose a structural model, e.g.,
E
Yā  0 1 cum
ā
 and estimate the parameter 1 by gestimation
 The effect of continuous treatment
vs. no treatment is 1 K
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G-estimation
 Can’t describe g-estimation in a 20-min
talk!
 Robins (1989, 1991, …)
 Simple introduction: Hernán et al (PDS 2005)
 G-estimation can be used in 2 ways
1. Disregarding the fact that the initial treatment
was randomized
 Observational analysis like IPW
2. Using the fact that the initial treatment was
randomized
 General form of instrumental variable methods
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G-estimation
Method 1: observational analysis
 To estimate the parameter 1 by gestimation
 One needs to estimate
f
A
k
|A
0
, . . . , A
k 1
, L
0
, . . . , L
k
for some times 0≤k≤K
 For example, by fitting a logistic
model like the one used for the
denominator of SW
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G-estimation
Method 1: observational analysis
 Two key assumptions:
 The structural model is correct
 Time-varying risk factors L(t) at some times
t
 are available
 include all joint determinants of treatment
choice and outcome
 Same assumptions as in observational
studies with time-varying exposures
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G-estimation
Instrumental variable assumption

 To estimate the parameter
by g-estimation, no
data on time-dependent confounders1 L(t) are required
 In the simplest case of binary non time-varying
treatment A, g-estimation reduces to the standard IV
estimator
E
Y|R 1E
Y|R 0
E
A|R 1E
A|R 0
 In more complex cases with non binary, time-varying
treatments A, g-estimation still requires same
assumptions as IV methods
 For simple introduction see Hernán and Robins
(Epidemiology 2006)
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Summary of methods
Effect
Method
Initiation vs.
No initiation
Intent-totreat
Continuous use vs. No use
G-estimation
Inverse
probability
weighting
Sequential
randomization
(exchangeability +
modeling assumptions)
No
No
Yes
Yes
Yes
Structural doseresponse model
(modeling assumption)
No
Yes
Yes
No
Yes
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Conclusions
 When interested in the effect of continuous
treatment, randomized trials are essentially
observational studies with baseline
randomization
 There are 2 options:
 Methods that do not use the fact that initial
treatment was randomized (IPW, g-estimation)
 A method that uses randomization (gestimation)
 Why is this method not routinely used?
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