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Graphical models for inference under outcome-dependent sampling. (English) Zbl 1329.62042
Summary: We consider situations where data have been collected such that the sampling depends on the outcome of interest and possibly further covariates, as for instance in case-control studies. Graphical models represent assumptions about the conditional independencies among the variables. By including a node for the sampling indicator, assumptions about sampling processes can be made explicit. We demonstrate how to read off such graphs whether consistent estimation of the association between exposure and outcome is possible. Moreover, we give sufficient graphical conditions for testing and estimating the causal effect of exposure on outcome. The practical use is illustrated with a number of examples.

MSC:
62-09 Graphical methods in statistics (MSC2010)
62G05 Nonparametric estimation
62G10 Nonparametric hypothesis testing
62D05 Sampling theory, sample surveys
62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H20 Measures of association (correlation, canonical correlation, etc.)
62P10 Applications of statistics to biology and medical sciences; meta analysis
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