# On the identification of individual principal stratum direct, natural direct and pleiotropic effects without cross world independence assumptions

## TL;DR

This paper shows that natural direct, principal stratum direct, and pleiotropic effects can be identified without relying on untestable cross-world independence assumptions, broadening causal inference methods.

## Contribution

It introduces a novel identification approach for these effects without cross-world assumptions and defines pleiotropy with empirical detection conditions.

## Key findings

- Identification of effects without cross-world assumptions
- Definition of pleiotropy in causal inference
- Applicable to all distribution types

## Abstract

The analysis of natural direct and principal stratum direct effects has a controversial history in statistics and causal inference as these effects are commonly identified with either untestable cross world independence or graphical assumptions. This paper demonstrates that the presence of individual level natural direct and principal stratum direct effects can be identified without cross world independence assumptions. We also define a new type of causal effect, called pleiotropy, that is of interest in genomics, and provide empirical conditions to detect such an effect as well. Our results are applicable for all types of distributions concerning the mediator and outcome.