Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2025 Feb;67(1):e70026.
doi: 10.1002/bimj.70026.

A Principled Approach to Adjust for Unmeasured Time-Stable Confounding of Supervised Treatment

Jeppe Ekstrand Halkjær Madsen  1   2 , Thomas Delvin  1 , Thomas Scheike  2 , Christian Pipper  3   4
Affiliations

A Principled Approach to Adjust for Unmeasured Time-Stable Confounding of Supervised Treatment

Jeppe Ekstrand Halkjær Madsen et al. Biom J. 2025 Feb.

Abstract

We propose a novel method to adjust for unmeasured time-stable confounding when the time between consecutive treatment administrations is fixed. We achieve this by focusing on a new-user cohort. Furthermore, we envisage that all time-stable confounding goes through the potential time on treatment as dictated by the disease condition at the initiation of treatment. Following this logic, we may eliminate all unmeasured time-stable confounding by adjusting for the potential time on treatment. A challenge with this approach is that right censoring of the potential time on treatment occurs when treatment is terminated at the time of the event of interest, for example, if the event of interest is death. We show how this challenge may be solved by means of the expectation-maximization algorithm without imposing any further assumptions on the distribution of the potential time on treatment. The usefulness of the methodology is illustrated in a simulation study. We also apply the methodology to investigate the effect of depression/anxiety drugs on subsequent poisoning by other medications in the Danish population by means of national registries. We find a protective effect of treatment with selective serotonin reuptake inhibitors on the risk of poisoning by various medications (1- year risk difference of approximately - 3 % $-3\%$ ) and a standard Cox model analysis shows a harming effect (1-year risk difference of approximately 2 % $2\%$ ), which is consistent with what we would expect due to confounding by indication. Unmeasured time-stable confounding can be entirely adjusted for when the time between consecutive treatment administrations is fixed.

Keywords: EM algorithm; causal inference; confounding by indication; directed acyclic graph; unmeasured confounding.

PubMed Disclaimer

References

    1. Baiocchi, M., J. Cheng, and D. S. Small. 2014. “Instrumental Variable Methods for Causal Inference: Instrumental Variable Methods for Causal Inference.” Statistics in Medicine 33, no. 13: 2297–2340.
    1. Bosco, J. L., R. A. Silliman, S. S. Thwin, et al. 2010. “A Most Stubborn Bias: No Adjustment Method Fully Resolves Confounding by Indication in Observational Studies.” Journal of Clinical Epidemiology 63, no. 1: 64–74.
    1. Braun, C., T. Bschor, J. Franklin, and C. Baethge. 2016. “Suicides and Suicide Attempts During Long‐Term Treatment With Antidepressants: A Meta‐Analysis of 29 Placebo‐Controlled Studies Including 6,934 Patients With Major Depressive Disorder.” Psychotherapy and Psychosomatics 85, no. 3: 171–179.
    1. Chen, H. Y., and R. J. A. Little. 1999. “Proportional Hazards Regression With Missing Covariates.” Journal of the American Statistical Association 94, no. 447: 896–908.
    1. Dempster, A. P., N. M. Laird, and D. B. Rubin. 1977. “Maximum Likelihood From Incomplete Data Via the EM Algorithm.” Journal of the Royal Statistical Society: Series B (Methodological) 39, no. 1: 1–22.

Substances

LinkOut - more resources