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. 2019 Nov 19;9:17097. doi: 10.1038/s41598-019-52853-8

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© The Author(s) 2019

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Directed acyclic graph illustrating pathways between dates of birth (DOB), parental age (PA), unmeasured confounders (U) and mortality outcomes (Y). Subscripts p and o represent variables at the parental and offspring level, respectively. PA_p represents a parent’s tendency to earlier or later parenthood, not the age of the parent’s parents. Note that DOB_o is completely determined by DOB_p and PA_o; effects c and g both have known linear coefficients of 1. A primary analysis of the effect of PA_o on Y_o comprises a direct effect (i), an effect mediated by DOB_o (gk) and associations due to family-level confounding (fedh, fbadh). When the primary analysis is adjusted for DOB_o the mediated effect is blocked but a perfect negative association between PA_o and DOB_p is induced, changing the nature of the family-level confounding [gc]adh. If the primary analysis is adjusted for DOB_p the direct (i) and indirect (gk) causal effects of PA_o on Y_o apply but the pathways for family-level confounding (fedh) are reduced. In a sibling-comparison analysis all family-level confounding is blocked and individual-level confounding is unlikely given that the exposure is determined before birth. Adjustment for DOB_o is impossible because it is perfectly positively associated within families with PA_o. The estimates from the sibling comparison analysis thus comprise the direct (i) and indirect (gk) causal effects of PA_o on Y_o.