# Arvid Sjölander and Ola Hössjer: Covariance inequalities, and bounds for causal effects under unmeasured confounding

**Time: **
Wed 2021-09-08 15.15 - 16.15

**Location: **
Zoom, registration required

**Lecturer: **
Arvid Sjölander (Karolinska Institute) and Ola Hössjer (Stockholm University)

### Abstract

In this seminar we will present a joint effort between Stockholm University and Karolinska Institute. The seminar consists of two parts. In the first part we will derive bounds for the covariance of two bounded random variables, given the expectations and/or covariances, and the upper and lower limits of the variables. This result can be viewed as a generalization of the Cauchy–Schwarz inequality and the Bhatia–Davis inequality (which gives an upper bound on the variance of a bounded random variable, given its expectation and upper and lower limits). In the second part of the presentation we will use the theoretical results from the first part to derive bounds on the causal effect of an exposure on an outcome, in the presence of unmeasured confounding. The problem of bounding causal effects has received much attention in the causal inference literature. Previous papers have constructed bounds by making assumptions on the degree of confounding on the risk ratio scale. Our results complement this previous work by allowing for such assumptions to be formulated on the risk difference scale.

**Zoom notes:** In order to get registered, please send an email to
matteo.sfragara@math.su.se
.