SLIDE 1
Introduction
Goal: Estimate the distribution of outcome Y given exposure A and covariates X from non-experimental data.
Learning Models from Data with Measurement Error: Tackling - - PowerPoint PPT Presentation
Learning Models from Data with Measurement Error: Tackling - - PowerPoint PPT Presentation
Learning Models from Data with Measurement Error: Tackling Underreporting Roy Adams, Yuelong Ji, Xiaobin Wang, and Suchi Saria Introduction Goal: Estimate the distribution of outcome Y given exposure A and covariates X from non-experimental data.
SLIDE 2
SLIDE 3
Introduction
Measurement error is common source of bias when using non- experimental data. Goal: Estimate the distribution of outcome Y given exposure A and covariates X from non-experimental data.
SLIDE 4
Introduction
Measurement error is common source of bias when using non- experimental data.
- We focus on underreporting error.
Goal: Estimate the distribution of outcome Y given exposure A and covariates X from non-experimental data.
SLIDE 5
Introduction
Measurement error is common source of bias when using non- experimental data.
- We focus on underreporting error.
- E.g. survey data of sensitive variables such as drug use.
Goal: Estimate the distribution of outcome Y given exposure A and covariates X from non-experimental data.
SLIDE 6
A X Y Ã
Model
Updated goal: Estimate the distribution of outcome Y given exposure A and covariates X when exposure observations à are subject to underreporting errors.
Model
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A X Y Ã
Model
Updated goal: Estimate the distribution of outcome Y given exposure A and covariates X when exposure observations à are subject to underreporting errors. Assumptions:
Model
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A X Y Ã
Model
Updated goal: Estimate the distribution of outcome Y given exposure A and covariates X when exposure observations à are subject to underreporting errors. Assumptions:
- 1. Strict underreporting (A = 0 ⟹ Ã = 0)
Model
SLIDE 9
A X Y Ã
Model
Updated goal: Estimate the distribution of outcome Y given exposure A and covariates X when exposure observations à are subject to underreporting errors. Assumptions:
- 1. Strict underreporting (A = 0 ⟹ Ã = 0)
- 2. Ã is independent of X given A
Model
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A X Y Ã
Model
)
Outcome model … p𝜄(Y | A, X) Exposure model … p𝜚(A | X) Error model ……… p𝜐(Ã | A)
Model
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A X Y Ã
Model
max
θ,ϕ,τ ∑ i
log∑
a
pθ(yi|a, xi)pτ( ˜ ai|a)pϕ(a|xi)
)
Maximize the log marginal likelihood: Outcome model … p𝜄(Y | A, X) Exposure model … p𝜚(A | X) Error model ……… p𝜐(Ã | A)
Model
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Identifiability Identifiability
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Identifiability
We prove three separate identifiability conditions:
Identifiability
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Identifiability
We prove three separate identifiability conditions:
- 1. The error distribution is known
Identifiability
SLIDE 15
Identifiability
We prove three separate identifiability conditions:
- 1. The error distribution is known
- 2. We have a second error-prone exposure observation
Identifiability
SLIDE 16
Identifiability
We prove three separate identifiability conditions:
- 1. The error distribution is known
- 2. We have a second error-prone exposure observation
- 3. Under assumptions about the form of the exposure
distribution (see paper/poster for details)
Identifiability
SLIDE 17
Identifiability
We prove three separate identifiability conditions:
- 1. The error distribution is known
- 2. We have a second error-prone exposure observation
- 3. Under assumptions about the form of the exposure
distribution (see paper/poster for details)
Identifiability
In particular: If X is not independent of A and p(A | X) is a logit, probit, or cloglog regression model, then p(Y, Ã | X) is identifiable.
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Drug use and childhood obesity
0.0 0.1 0.2 0.3 0.4 0.5 0.6
τ
0.00 0.05 0.10 0.15 0.20 0.25
5isk difference
6mRking (a)
sensitivity analysis subject-reSRrt subject-reSRrt + cRtinine
Maternal drug use and childhood obesity
Underreporting rate Average causal effect
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