Identification and responses to positivity violations in longitudinal studies: an illustration based on invasively mechanically ventilated ICU patients

Abstract

Identification and estimation of causal effects relies on the positivity assumption, which states that there should be some positive probability of having each treatment level of interest, regardless of covariate levels. Violations of positivity can lead to both non-identified target causal parameters, estimator bias and inflated variance. We discuss reasons for and responses to positivity violations when the causal effect of interest involves treatments or exposures at multiple time points. For illustration, we use a data example involving the cumulative effect of controlling arterial oxygen tension over time on death among ICU patients receiving invasive mechanical ventilation. We distinguish between practical (by chance) violations that relate to sample size and structural violations in which certain treatment levels occur with zero probability for certain covariate levels. We focus on responses that either redefines the target population, e.g. via trimming or redefines the intervention making it more dynamic or more stochastic. Supported by a simulation study, we illustrate how these responses help restore needed positivity but also modify the target causal parameter. We further introduce an inability to intervene variable and show how such a variable will often be a time-dependent confounder and essential when addressing structural positivity violations in longitudinal settings.

Keywords:

• Positivity violations
• causal inference
• longitudinal studies
• IPTW
• ICU
• mechanical ventilation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Approval to use data from patient databases without individual consent was granted by the Danish Patient Safety Authority (3-3013-1864/1/) and the study was registered at the Danish Data Protection Agency (2008-58-0028; internal reference 2016-2). All in accordance with Danish regulations.

Additional information

Notes on contributors

Aksel K.G. Jensen

Aksel K.G. Jensen is Assistant Professor at the Section of Biostatistics, Department of Public Health, University of Copenhagen. Postboks 2099, Øster Farimagsgade 5, opg. B, 1014 Copenhagen, Building: 10-2-23.

Theis Lange

Theis Lange is Professor of Biostatistics and Head of Department of Public Health, University of Copenhagen. Postboks 2099, Øster Farimagsgade 5, opg. B, 1014 Copenhagen, Building: 24-1-08.

Olav L. Schjørring

Olav L. Schjørring is Clinical Associate Professor at Department of Clinical Medicine, Faculty of Medicine and the Department of Anaesthesiology and Intensive Care Medicine, Aalborg University Hospital, Denmark. Hobrovej 18-22, 9000 Aalborg.

Maya L. Petersen

Maya L. Petersen is Professor of Epidemiology and Biostatistics and co-director of the Joint Program in Computational Precision Health and co-director of the Center for Targeted Machine Learning and Causal Inference, Department of Public Health, University of California Berkeley. 2121 Berkeley Way #5315 Berkeley, CA 94720.