---
title: Nonparametric Bounds for the Risk Function
description: >-
  Explore this publication on real-world evidence: Nonparametric Bounds for the
  Risk Function.
date: '2019-01-01'
author: M. Alan Brookhart, PhD
category: Publications
tags:
  - University of North Carolina at Chapel Hill
  - Approval & Commercialization
  - American Journal of Epidemiology
  - 'Yes'
  - Health System Partner
  - Oral Presentation
  - Methods/Pharmacoepi
  - R&D
canonical_url: >-
  https://www.headwaterscience.com/resources/publications/acad-university-of-north-carolina-at-chapel-hill/nonparametric-bounds-for-the-risk-function/
source: Headwater Science
license: © 2026 Headwater Science. All rights reserved.
slug: nonparametric-bounds-for-the-risk-function
id: 4Z6pJRMYfWfYFw8NGBkiAD
contentType: article
---

## Challenge

Nonparametric bounds for risk functions—which characterize the range of causal effects consistent with observed data under partial identification—had not been derived in a form accessible for applied epidemiologic use.

## Solution

Target RWE researchers and UNC collaborators derived and published nonparametric bounds for the risk function, providing an accessible framework for epidemiologists to quantify the range of causal risk differences consistent with observed data.

## Impact

Providing nonparametric bounds methodology for risk functions expands Target RWE's sensitivity analysis toolkit, enabling pharma partners to demonstrate robustness of real-world effectiveness findings to unobserved confounding.

## Use Cases / Links

Nonparametric risk function bounds for sensitivity analysis of causal effects in RWE regulatory submissions, Applied epidemiology methods development advancing Target RWE's causal sensitivity analysis capabilities