Figure - PMC

Skip to main content

An official website of the United States government

Here's how you know

Here's how you know

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

View full-text article in PMC

. 2021 Dec 30;23(4):1115–1132. doi: 10.1093/biostatistics/kxab049

Search in PMC
Search in PubMed
View in NLM Catalog
Add to search

© he Author 2021. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model)

PMC Copyright notice

Fig. 1. — Illustration of Assumption 3 and its distinction compared to the monotonicity assumption using seven hypothetical units. Units and are allowed under both assumptions, Assumption 3 and monotonicity. For unit , APOE expedites both AD and death, but in a way that AD remains before death. For unit 2, APOE impedes AD but expedites death. Nevertheless, unit 2 would live long enough under APOE for AD to occur. Similar protective effect occurs for unit , however, this unit violates monotonicity at time (as an example). Unit also violates monotonicity (at and ) but not Assumption 3. Unit does not suffer from AD under any APOE value, hence it is allowed by Assumption 3 but it does violate monotonicity (at and ) as AD carries a protective effect against death. Unit violates Assumption 3 but not monotonicity. Arguably, for this unit the APOE effect on death is so strong the unit would have died under APOE before getting the chance to have AD. Finally, unit violates both assumptions.

Inline graphic — Illustration of Assumption 3 and its distinction compared to the monotonicity assumption using seven hypothetical units. Units and are allowed under both assumptions, Assumption 3 and monotonicity. For unit , APOE expedites both AD and death, but in a way that AD remains before death. For unit 2, APOE impedes AD but expedites death. Nevertheless, unit 2 would live long enough under APOE for AD to occur. Similar protective effect occurs for unit , however, this unit violates monotonicity at time (as an example). Unit also violates monotonicity (at and ) but not Assumption 3. Unit does not suffer from AD under any APOE value, hence it is allowed by Assumption 3 but it does violate monotonicity (at and ) as AD carries a protective effect against death. Unit violates Assumption 3 but not monotonicity. Arguably, for this unit the APOE effect on death is so strong the unit would have died under APOE before getting the chance to have AD. Finally, unit violates both assumptions.