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. 2023 Oct 26;47(12):1309–1317. doi: 10.1038/s41366-023-01396-0

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© The Author(s) 2023

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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Fig. 1 — METHOD 1 (Upper Panel): B₀ is weight at time 0 and B₁ is weight at 2 years. C₀ are the confounders at time 0 and C₁ are the confounders at 2 years and O is the outcome. Time is split into two phases. Phase I is between weight measurements at time 0 and the 1st follow-up. Phase II is after the weight measurement at the 1st follow-up weight change is only observed at 2 years (end of Phase I), i.e. when we can measure A = B₁-B₀. A and B₁ can be used in the DAG interchangeably, as they are deterministically related. Our aim is to find the effect of A (weight change) on the outcome O. From this DAG, we stratify for B₀ and we control for C₀. However, we do not control for C₁ (or exclude individuals based on levels of chronic disease at the 1st follow-up). Our aim is to find the effect of A (weight change) on the outcome O. If we do not control for C₁, we leave the backdoor path A<--C₁-->O open. METHOD 2 (Middle Panel): B₀ is weight at time 0 and B₁ is weight at 2 years. C₀ are the confounders at time 0 and C₁ are the confounders at 2 years and O is the outcome. Time is split into two phases. Phase I is between weight measurements at time 0 and the 1st follow-up. Phase II is after the weight measurement at the 1st follow-up. weight change is only observed at 2 years (end of Phase I), i.e. when we can measure A = B₁–B₀. Our aim is to find the effect of A (weight change) on the outcome O. From this DAG, we stratify for B₀ and we control for C₁. However, we do not control for C₀ (or exclude individuals based on levels of chronic disease at the time 0). If we do not control for C₀, we leave the backdoor path A<--C₀-->O open. METHOD 3 (Lower Panel): B₀ is weight at time 0 and B₁ is weight at the 1st follow-up (at 2 years). C₀ are the confounders at time 0 and C₁ are the confounders at 2 years and O is the outcome. Time is split into two phases. Phase I is between weight measurements at time 0 and the 1st follow-up. Phase II is after the weight measurement at the 1st follow-up. Weight change is only observed at the 1st follow-up (end of Phase I), i.e. when we can measure A = B₁–B₀. A and B₁ can be used in the DAG interchangeably, as they are deterministically related. Our aim is to find the effect of A (weight change) on the outcome O. From this DAG, we stratify for B₀ and we control for C₀ and C₁. In other words, there is no backdoor path open.