# Models for Additive and Sufficient Cause Interaction

**Time: **
Thu 2019-10-10 10.00

**Location: ** F11, Lindstedtsvägen 22, KTH Stockholm, (English)

**Subject area: **
Mathematical Statistics

**Doctoral student: **
Daniel Berglund
, Matematisk statistik

**Opponent: **
Professor Ola Hössjer, Department of Mathematics, Stockholm University

**Supervisor: **
Professor Timo Koski, Matematisk statistik; Assistant professor Helga Westerlind, Department of Medicine, Karolinska Institutet

## Abstract

The aim of this thesis is to develop and explore models in, and related to, the sufficient cause framework, and additive interaction. Additive interaction is closely connected with public health interventions and can be used to make inferences about the sufficient causes in order to find the mechanisms behind an outcome, for instance a disease.

In paper A we extend the additive interaction, and interventions, to include continuous exposures. We show that there does not exist a model that does not lead to inconsistent conclusions about the interaction.

The sufficient cause framework can also be expressed using Boolean functions, which is expanded upon in paper B. In this paper we define a new model based on the multifactor potential outcome model (MFPO) and independence of causal influence models (ICI).

In paper C we discuss the modeling and estimation of additive interaction in relation to if the exposures are harmful or protective conditioned on some other exposure. If there is uncertainty about the effects direction there can be errors in the testing of the interaction effect.