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A Causal Mediation Model for Longitudinal Mediators and Survival Outcomes with an Application to Animal Behavior

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Abstract

In animal behavior studies, a common goal is to investigate the causal pathways between an exposure and outcome, and a mediator that lies in between. Causal mediation analysis provides a principled approach for such studies. Although many applications involve longitudinal data, the existing causal mediation models are not directly applicable to settings where the mediators are measured on irregular time grids. In this paper, we propose a causal mediation model that accommodates longitudinal mediators on arbitrary time grids and survival outcomes simultaneously. We take a functional data analysis perspective and view longitudinal mediators as realizations of underlying smooth stochastic processes. We define causal estimands of direct and indirect effects accordingly and provide corresponding identification assumptions. We employ a functional principal component analysis approach to estimate the mediator process and propose a Cox hazard model for the survival outcome that flexibly adjusts the mediator process. We then derive a g-computation formula to express the causal estimands using the model coefficients. The proposed method is applied to a longitudinal data set from the Amboseli Baboon Research Project to investigate the causal relationships between early adversity, adult physiological stress responses, and survival among wild female baboons. We find that adversity experienced in early life has a significant direct effect on females’ life expectancy and survival probability, but find little evidence that these effects were mediated by markers of the stress response in adulthood. We further developed a sensitivity analysis method to assess the impact of potential violation to the key assumption of sequential ignorability. Supplementary materials accompanying this paper appear on-line.

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Acknowledgements

We thank the guest editor Cory Zigler and a reviewer for constructive comments. The majority of the data represented here was supported by the National Institutes of Health and the National Science Foundation, currently through NIH R01 AG053330 and R01 AG053308, as well as R01 HD088558, P01 AG031719, and NSF IOS 1456832. We also thank Duke University, Princeton University, and the University of Notre Dame for financial and logistical support. For assistance and cooperation in Kenya, we are grateful to the Kenya Wildlife Service (KWS), University of Nairobi, Institute of Primate Research (IPR), National Museums of Kenya, National Environment Management Authority, and National Commission for Science, Technology, and Innovation (NACOSTI). We also thank the members of the Amboseli-Longido pastoralist communities, and the Enduimet Wildlife Management Area for their cooperation and assistance in the field. Particular thanks go to the Amboseli Baboon Project long-term field team (R.S. Mututua, S. Sayialel, J.K. Warutere, Siodi, I.L.), and to T. Wango and V. Oudu for their untiring assistance in Nairobi. The baboon project database, Babase, is expertly managed by N. Learn and J. Gordon. Database design and programming are provided by K. Pinc. This research was approved by the IACUC at Duke University, University of Notre Dame, and Princeton University and adhered to all the laws and guidelines of Kenya. For a complete set of acknowledgments of funding sources, logistical assistance, and data collection and management, please visit http://amboselibaboons.nd.edu/acknowledgements/.

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Authors and Affiliations

  1. Facebook, Inc., Seattle, WA, USA

    Shuxi Zeng

  2. Department of Biology, Duke University, Durham, NC, USA

    Elizabeth C. Lange & Susan C. Alberts

  3. Department of Biological Sciences, University of Notre Dame, Notre Dame, IN, USA

    Elizabeth A. Archie

  4. Department of Antropology, University of Texas at San Antonio, San Antonio, TX, USA

    Fernando A. Campos

  5. Department of Evolutionary Anthropology, Duke University, Durham, NC, USA

    Susan C. Alberts

  6. Department of Statistical Science, Duke University, 214 Old Chemistry Building, Durham, NC, 27708, USA

    Fan Li

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  1. Shuxi Zeng
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  2. Elizabeth C. Lange
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Correspondence to Fan Li.

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Zeng, S., Lange, E.C., Archie, E.A. et al. A Causal Mediation Model for Longitudinal Mediators and Survival Outcomes with an Application to Animal Behavior. JABES 28, 197–218 (2023). https://doi.org/10.1007/s13253-022-00490-6

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  • DOI: https://doi.org/10.1007/s13253-022-00490-6

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