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The conventional model for assessing insensitivity to hidden bias in pairedobservational studies constructs a worst-case distribution for treatmentassignments subject to bounds on the maximal bias to which any given pair issubjected. In studies where rare cases of extreme hidden bias are suspected,the maximal bias may be substantially larger than the typical bias acrosspairs, such that a correctly specified bound on the maximal bias would yield anunduly pessimistic perception of the study's robustness to hidden bias. Wepresent an extended sensitivity analysis which allows researchers tosimultaneously bound the maximal and typical bias perturbing the pairs underinvestigation while maintaining the desired Type I error rate. We motivate andillustrate our method with two sibling studies on the impact of schooling onearnings, one containing information of cognitive ability of siblings and theother not. Cognitive ability, clearly influential of both earnings and degreeof schooling, is likely similar between members of most sibling pairs yetcould, conceivably, vary drastically for some siblings. The method isstraightforward to implement, simply requiring the solution to a quadraticprogram.

Extended Sensitivity Analysis for Heterogeneous Unmeasured Confounding with An Application to Sibling Studies of Returns to Education