https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2755131/

Cornfield's Inequality

The Book of why gives the example of Cornfield's refutation of R. A. Fisher's claim that a "Smoking Gene" could be the true cause of lung cancer deaths.

Given that studies showed that smokers were nine times more likely to develop lung cancer than non smokers, it would follow that if 11 percent of non-smokers have the “smoking gene,” then 99 percent of the
smokers would have to have the smoking gene to hold the relationship. Further, if 12% of non-smokers had the gene, it would be mathematically impossible for the smoking gene to account for the association. 

Example: Cornfield's Inequality

 Also known as the "smoking gene," hypothesis, R.A. Fisher claimed:

1.  Specific genes, whichever they may be, negatively influence an individual's risk for lung cancer.  
2.  Some of such genes also negatively influence whether people become smokers.

Constitutional Hypothesis

Cornfield's inequality was the first formal method for sensitivity analysis in observational studies. It provides a way to prevent causal relationships from being immediately refuted with the assertion that a new factor is the true cause. 

University of Michigan - Ann Arbor

Sensitivity analysis refers to investigating whether the specified outcome could have resulted from alternative hypotheses and how strong those other hypotheses would need to be in order to explain the observed data.

The resulting relationships can be used to contrast the likelihoods with the original hypothesis. 

Sensitivity Analysis

Pearl, Judea, et al. “Sensitivity Analysis of Linear Structural Causal Models.”

http://proceedings.mlr.press/v97/cinelli19a/cinelli19a.pdf

Sensitivity Analysis of Linear Structural Causal Models

Informally, a model is identifiable if it is theoretically possible to learn the true values of this model's parameters after obtaining an infinite number of observations from it. 

Identification Problems are part of inferences, where we want to learn the true value of parameters from infinite observational data. When we cannot do it even through infinite data points, we fail to do identification.

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