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Causal Inference for fMRI Time Series Data With Systematic Errors of Measurement in a Balanced On/Off Study of Social Evaluative Threat

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  • Michael E. Sobel
  • Martin A. Lindquist

Abstract

Functional magnetic resonance imaging (fMRI) has facilitated major advances in understanding human brain function. Neuroscientists are interested in using fMRI to study the effects of external stimuli on brain activity and causal relationships among brain regions, but have not stated what is meant by causation or defined the effects they purport to estimate. Building on Rubin's causal model, we construct a framework for causal inference using blood oxygenation level dependent (BOLD) fMRI time series data. In the usual statistical literature on causal inference, potential outcomes, assumed to be measured without systematic error, are used to define unit and average causal effects. However, in general the potential BOLD responses are measured with stimulus dependent systematic error. Thus we define unit and average causal effects that are free of systematic error. In contrast to the usual case of a randomized experiment where adjustment for intermediate outcomes leads to biased estimates of treatment effects, here the failure to adjust for task dependent systematic error leads to biased estimates. We therefore adjust for systematic error using measured "noise covariates," using a linear mixed model to estimate the effects and the systematic error. Our results are important for neuroscientists, who typically do not adjust for systematic error. They should also prove useful to researchers in other areas where responses are measured with error and in fields where large amounts of data are collected on relatively few subjects. To illustrate our approach, we reanalyze data from a social evaluative threat task, comparing the findings with results that ignore systematic error.

Suggested Citation

  • Michael E. Sobel & Martin A. Lindquist, 2014. "Causal Inference for fMRI Time Series Data With Systematic Errors of Measurement in a Balanced On/Off Study of Social Evaluative Threat," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 967-976, September.
  • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:507:p:967-976
    DOI: 10.1080/01621459.2014.922886
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    Cited by:

    1. Yenny Webb-Vargas & Shaojie Chen & Aaron Fisher & Amanda Mejia & Yuting Xu & Ciprian Crainiceanu & Brian Caffo & Martin A. Lindquist, 2017. "Big Data and Neuroimaging," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(2), pages 543-558, December.
    2. Tianqi Sun & Weiyu Li & Lu Lin, 2024. "Matrix-variate generalized linear model with measurement error," Statistical Papers, Springer, vol. 65(6), pages 3935-3958, August.
    3. Dominik Poß & Dominik Liebl & Alois Kneip & Hedwig Eisenbarth & Tor D. Wager & Lisa Feldman Barrett, 2020. "Superconsistent estimation of points of impact in non‐parametric regression with functional predictors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(4), pages 1115-1140, September.
    4. Georgia Papadogeorgou & Kosuke Imai & Jason Lyall & Fan Li, 2022. "Causal inference with spatio‐temporal data: Estimating the effects of airstrikes on insurgent violence in Iraq," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 1969-1999, November.
    5. Zhao, Yi & Luo, Xi, 2023. "Multilevel mediation analysis with structured unmeasured mediator-outcome confounding," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).

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