Reevaluating COVID-19 Mandates using Tensor Completion
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We propose a new method that uses tensor completion to estimate causal effects with multivariate longitudinal data – data in which multiple outcomes are observed for each unit and time period. Our motivation is to estimate the number of COVID-19 fatalities prevented by government mandates such as travel restrictions, mask-wearing directives, and vaccination requirements. In addition to COVID-19 fatalities, we also observe the number of fatalities from other diseases and injuries. The proposed method arranges the data as a tensor with three dimensions – unit, time, and outcome – and uses tensor completion to impute the missing counterfactual outcomes. We use the method to investigate an empirical paradox in which observational studies estimate the benefit of mask-wearing directives to be five times higher than a randomized controlled trial (cf. Talic et al., BMJ, 2021; Abaluck et al., Science, 2021); when applied to observational data, our estimate is more consistent with the randomized controlled trial, suggesting mandates prevent fewer fatalities than reported by the typical observational study. We then provide several justifications. Most notably, we show that under standard regularity conditions, combining multiple outcomes improves the accuracy of counterfactual imputations. Our method can be applied whenever multivariate longitudinal data are available, but we believe it is particularly timely as governments increasingly rely on this data to choose between mandates. Governments should use all available data to choose the mandates that best balance public health and individual liberties as new waves of COVID-19 variants are expected to follow delta and omicron.
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