Adjustment for time-invariant and time-varying confounders in ‘unexplained residuals’ models for longitudinal data within a causal framework and associated challenges

Arnold, K.F., Ellison, G.T.H., Gadd, S., Textor, J., Tennant, P.W.G., Heppenstall, A. and Gilthorpe, M.S. (2019) Adjustment for time-invariant and time-varying confounders in ‘unexplained residuals’ models for longitudinal data within a causal framework and associated challenges. Statistical Methods in Medical Research, 28(5), pp. 1347-1364. (doi: 10.1177/0962280218756158) (PMID:29451093) (PMCID:PMC6484949)

Abstract

‘Unexplained residuals’ models have been used within lifecourse epidemiology to model an exposure measured longitudinally at several time points in relation to a distal outcome. It has been claimed that these models have several advantages, including: the ability to estimate multiple total causal effects in a single model, and additional insight into the effect on the outcome of greater-than-expected increases in the exposure compared to traditional regression methods. We evaluate these properties and prove mathematically how adjustment for confounding variables must be made within this modelling framework. Importantly, we explicitly place unexplained residual models in a causal framework using directed acyclic graphs. This allows for theoretical justification of appropriate confounder adjustment and provides a framework for extending our results to more complex scenarios than those examined in this paper. We also discuss several interpretational issues relating to unexplained residual models within a causal framework. We argue that unexplained residual models offer no additional insights compared to traditional regression methods, and, in fact, are more challenging to implement; moreover, they artificially reduce estimated standard errors. Consequently, we conclude that unexplained residual models, if used, must be implemented with great care.

• Item Type: Articles
• Additional Information: Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: KFA and SCG were supported by the Economic and Social Research Council [grant numbers ES/J500215/1 and ES/P000746/1, respectively]. GTHE, PWGT, AH, and MSG were supported by the Higher Education Funding Council for England.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Heppenstall, Professor Alison
• Authors: Arnold, K.F., Ellison, G.T.H., Gadd, S., Textor, J., Tennant, P.W.G., Heppenstall, A., and Gilthorpe, M.S.
• College/School: College of Social Sciences > School of Social and Political Sciences > Urban Studies
• Journal Name: Statistical Methods in Medical Research
• Publisher: SAGE Publications
• ISSN: 0962-2802
• ISSN (Online): 1477-0334
• Published Online: 16 February 2018
• Copyright Holders: Copyright © The Author(s) 2018
• First Published: First published in Statistical Methods in Medical Research 28(5):1347-1364
• Publisher Policy: Reproduced under a creative commons licence