The Annals of Statistics

Counterfactual analyses with graphical models based on local independence

Kjetil Røysland

Full-text: Open access

Abstract

We show that one can perform causal inference in a natural way for continuous-time scenarios using tools from stochastic analysis. This provides new alternatives to the positivity condition for inverse probability weighting. The probability distribution that would govern the frequency of observations in the counterfactual scenario can be characterized in terms of a so-called martingale problem. The counterfactual and factual probability distributions may be related through a likelihood ratio given by a stochastic differential equation. We can perform inference for counterfactual scenarios based on the original observations, re-weighted according to this likelihood ratio. This is possible if the solution of the stochastic differential equation is uniformly integrable, a property that can be determined by comparing the corresponding factual and counterfactual short-term predictions.

Local independence graphs are directed, possibly cyclic, graphs that represent short-term prediction among sufficiently autonomous stochastic processes. We show through an example that these graphs can be used to identify and provide consistent estimators for counterfactual parameters in continuous time. This is analogous to how Judea Pearl uses graphical information to identify causal effects in finite state Bayesian networks.

Article information

Source
Ann. Statist., Volume 40, Number 4 (2012), 2162-2194.

Dates
First available in Project Euclid: 23 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.aos/1358951379

Digital Object Identifier
doi:10.1214/12-AOS1031

Mathematical Reviews number (MathSciNet)
MR3059080

Zentralblatt MATH identifier
1257.62112

Subjects
Primary: 92D30: Epidemiology 62N04 60G44: Martingales with continuous parameter 60G55: Point processes

Keywords
Causal inference stochastic analysis event history analysis marked point processes change of probability measures local independence

Citation

Røysland, Kjetil. Counterfactual analyses with graphical models based on local independence. Ann. Statist. 40 (2012), no. 4, 2162--2194. doi:10.1214/12-AOS1031. https://projecteuclid.org/euclid.aos/1358951379


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