ANOCE: ANALYSIS OF CAUSAL EFFECTS WITH MULTIPLE MEDIATORS VIA CONSTRAINED STRUCTURAL LEARNING

Abstract

In the era of causal revolution, identifying the causal effect of an exposure on the outcome of interest is an important problem in many areas, such as epidemics, medicine, genetics, and economics. Under a general causal graph, the exposure may have a direct effect on the outcome and also an indirect effect regulated by a set of mediators. An analysis of causal effects that interprets the causal mechanism contributed through mediators is hence challenging but on demand. To the best of our knowledge, there are no feasible algorithms that give an exact decomposition of the indirect effect on the level of individual mediators, due to common interaction among mediators in the complex graph. In this paper, we establish a new statistical framework to comprehensively characterize causal effects with multiple mediators, namely, ANalysis Of Causal Effects (ANOCE), with a newly introduced definition of the mediator effect, under the linear structure equation model. We further propose a constrained causal structure learning method by incorporating a novel identification constraint that specifies the temporal causal relationship of variables. The proposed algorithm is applied to investigate the causal effects of 2020 Hubei lockdowns on reducing the spread of the coronavirus in Chinese major cities out of Hubei.

1. INTRODUCTION

In the era of causal revolution, identifying the causal effect of an exposure on the outcome of interest is an important problem in many areas, such as epidemics (Hernán, 2004 ), medicine (Hernán et al., 2000) , education (Card, 1999) , and economics (Panizza & Presbitero, 2014) . Under a general causal graph, the exposure may have a direct effect on the outcome and also an indirect effect regulated by a set of mediators (or intermediate variables). For instance, during the outbreak of Coronavirus disease 2019 (COVID-19), the Chinese government has taken extreme measures to stop the virus spreading such as locking Wuhan down on Jan 23rd, 2020, followed by 12 other cities in Hubei, known as the "2020 Hubei lockdowns". This approach (viewed as the exposure), directly blocked infected people leaving from Hubei; and also stimulated various quarantine measures taken by cities outside of Hubei (as the mediators), which further decreased the migration countrywide in China, and thus indirectly control the spread of COVID-19. Quantifying the causal effects of 2020 Hubei lockdowns on reducing the COVID-19 spread regulated by different cities outside Hubei is challenging but of great interest for the current COVID-19 crisis. An analysis of causal effects that interprets the causal mechanism contributed via individual mediators is thus very important. Many recent efforts have been made on studying causal effects that are regulated by mediators. Chakrabortty et al. (2018) specified the individual mediation effect in a sparse high-dimensional causal graphical model. However, the sum of marginal individual mediation effect is not equal to the effect of all mediators considered jointly (i.e. the indirect effect) due to the common interaction among mediators (VanderWeele & Vansteelandt, 2014) . Here, 'interaction' means that there exists at

