Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Simple yet Sharp Sensitivity Analysis for Any Contrast Under Unmeasured Confounding

Jose M. Peña

TL;DR

It is proved that the bounds produced are still arbitrarily sharp, i.e. practically attainable, and the usability of the bounds is illustrated with real data.

Abstract

We extend our previous work on sensitivity analysis for the risk ratio and difference contrasts under unmeasured confounding to any contrast. We prove that the bounds produced are still arbitrarily sharp, i.e. practically attainable. We illustrate the usability of the bounds with real data.

Simple yet Sharp Sensitivity Analysis for Any Contrast Under Unmeasured Confounding

TL;DR

It is proved that the bounds produced are still arbitrarily sharp, i.e. practically attainable, and the usability of the bounds is illustrated with real data.

Abstract

We extend our previous work on sensitivity analysis for the risk ratio and difference contrasts under unmeasured confounding to any contrast. We prove that the bounds produced are still arbitrarily sharp, i.e. practically attainable. We illustrate the usability of the bounds with real data.
Paper Structure (4 sections, 2 theorems, 16 equations, 2 figures, 4 tables)

This paper contains 4 sections, 2 theorems, 16 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Sharp Bounds
  3. Example
  4. Discussion

Key Result

Theorem 1

The lower bound for $p(D_1=1)$ and the upper bound for $p(D_0=1)$ in Equation eq:D1bound are simultaneously arbitrarily sharp.

Figures (2)

  • Figure 1: Causal graph where $U$ is unmeasured.
  • Figure 2: Lower and upper bound distributions for the risk difference.

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof