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

TL;DR

This paper introduces an extended sensitivity analysis method for observational studies that accounts for both maximal and typical hidden biases, demonstrated through sibling studies on education and earnings.

Contribution

It develops a novel approach allowing simultaneous bounding of maximal and typical biases, improving robustness assessment in observational research.

Findings

Method effectively bounds both maximal and typical biases.

Application to sibling studies illustrates practical utility.

Quadratic programming simplifies implementation.

Abstract

The conventional model for assessing insensitivity to hidden bias in paired observational studies constructs a worst-case distribution for treatment assignments subject to bounds on the maximal bias to which any given pair is subjected. In studies where rare cases of extreme hidden bias are suspected, the maximal bias may be substantially larger than the typical bias across pairs, such that a correctly specified bound on the maximal bias would yield an unduly pessimistic perception of the study's robustness to hidden bias. We present an extended sensitivity analysis which allows researchers to simultaneously bound the maximal and typical bias perturbing the pairs under investigation while maintaining the desired Type I error rate. We motivate and illustrate our method with two sibling studies on the impact of schooling on earnings, one containing information of cognitive ability of siblings and the other not. Cognitive ability, clearly influential of both earnings and degree of schooling, is likely similar between members of most sibling pairs yet could, conceivably, vary drastically for some siblings. The method is straightforward to implement, simply requiring the solution to a quadratic program.