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A Formal Treatment of Sequential Ignorability.

A Philip Dawid1, Panayiota Constantinou2

  • 1Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge , CB3 0WB UK.

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|December 9, 2014
PubMed
Summary

This study introduces methods for sequential decision-making with unobserved variables. We show that under specific conditions, like sequential irrelevance with discrete variables, we can achieve simple stability for accurate analysis.

Keywords:
Observational studyCausal inferenceInfluence diagramSequential decision theoryStability[Formula: see text]-computation

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Area of Science:

  • Causal inference
  • Sequential decision analysis
  • Statistical modeling

Background:

  • Sequential decision problems often involve observable, unobservable, and action variables.
  • Extended stability allows consequence identification when unobserved variables are observed.
  • Inferring simple stability (sequential ignorability) from observed data alone is challenging.

Purpose of the Study:

  • To explore conditions for inferring simple stability (sequential ignorability) using only observed variables.
  • To investigate the role of sequential randomization and sequential irrelevance in achieving ignorability.
  • To determine if positivity conditions are necessary for deducing sequential ignorability with discrete variables.

Main Methods:

  • Formal mathematical approach to sequential decision problems.
  • Analysis of extended stability and its relation to simple stability (sequential ignorability).
  • Examination of conditions such as sequential randomization and sequential irrelevance.

Main Results:

  • Extended stability enables consequence identification if unobserved variables are observed.
  • Simple stability (sequential ignorability) can be inferred under specific conditions like sequential irrelevance.
  • Positivity conditions are not required for deducing sequential ignorability when all variables are discrete.

Conclusions:

  • The study provides a formal framework for analyzing sequential decisions with unobserved confounders.
  • Sequential irrelevance, particularly with discrete variables, offers a pathway to robust causal inference without positivity assumptions.
  • Findings advance the understanding of causal inference in complex sequential settings.