title: Mediation analysis for count and zero-inflated count data.
abstract: Different conventional and causal approaches have been proposed for mediation analysis to better understand the mechanism of a treatment. Count and zero-inflated count data occur in biomedicine, economics, and social sciences. This paper considers mediation analysis for count and zero-inflated count data under the potential outcome framework with nonlinear models. When there are post-treatment confounders which are independent of, or affected by, the treatment, we first define the direct, indirect, and total effects of our interest and then discuss various conditions under which the effects of interest can be identified. Proofs are provided for the sensitivity analysis proposed in the paper. Simulation studies show that the methods work well. We apply the methods to the Detroit Dental Health Project's Motivational Interviewing DVD trial for the direct and indirect effects of motivational interviewing on count and zero-inflated count dental caries outcomes.
authors.affiliation: 1 Division of Oral Epidemiology & Dental Public Health, University of California at San Francisco, CA, USA.
authors.forename: Jing
authors.initials: J
authors.lastname: Cheng
authors.affiliation: 1 Division of Oral Epidemiology & Dental Public Health, University of California at San Francisco, CA, USA.
authors.forename: Nancy F
authors.initials: NF
authors.lastname: Cheng
authors.affiliation: 2 Department of Statistics, Wharton School, University of Pennsylvania, PA, USA.
authors.forename: Zijian
authors.initials: Z
authors.lastname: Guo
authors.affiliation: 3 Department of Medicine, School of Medicine, University of California at San Francisco, CA, USA.
authors.forename: Steven
authors.initials: S
authors.lastname: Gregorich
authors.affiliation: 4 Department of Restorative Dentistry, Maurice H. Kornberg School of Dentistry, Temple University, PA, USA.
authors.forename: Amid I
authors.initials: AI
authors.lastname: Ismail
authors.affiliation: 1 Division of Oral Epidemiology & Dental Public Health, University of California at San Francisco, CA, USA.
authors.forename: Stuart A
authors.initials: SA
authors.lastname: Gansky
mesh_terms: D000465:Algorithms; D002648:Child; D002675:Child, Preschool; D003731:Dental Caries / Q000453:epidemiology; D005260:Female; D006801:Humans; D008297:Male; D008824:Michigan / Q000453:epidemiology; D015233:Models, Statistical; D062405:Motivational Interviewing; D017711:Nonlinear Dynamics; D017063:Outcome Assessment, Health Care / Q000706:statistics & numerical data
keywords: Direct effect; indirect effect; post-treatment confounder; sensitivity analysis; sequential ignorability