{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T04:59:13Z","timestamp":1791435553924,"version":"4.3.3"},"reference-count":26,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2022,8,19]],"date-time":"2022-08-19T00:00:00Z","timestamp":1660867200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["RF1AG074328"],"award-info":[{"award-number":["RF1AG074328"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R01-AI170254"],"award-info":[{"award-number":["R01-AI170254"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R01-AG066883"],"award-info":[{"award-number":["R01-AG066883"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R01-ES031651"],"award-info":[{"award-number":["R01-ES031651"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,5,15]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>Zero-inflated nonnegative outcomes are common in many applications. In this work, motivated by freemium mobile game data, we propose a class of multiplicative structural nested mean models for zero-inflated nonnegative outcomes which flexibly describes the joint effect of a sequence of treatments in the presence of time-varying confounders. The proposed estimator solves a doubly robust estimating equation, where the nuisance functions, namely the propensity score and conditional outcome means given confounders, are estimated parametrically or nonparametrically. To improve the accuracy, we leverage the characteristic of zero-inflated outcomes by estimating the conditional means in two parts, that is, separately modelling the probability of having positive outcomes given confounders, and the mean outcome conditional on its being positive and given the confounders. We show that the proposed estimator is consistent and asymptotically normal as either the sample size or the follow-up time goes to infinity. Moreover, the typical sandwich formula can be used to estimate the variance of treatment effect estimators consistently, without accounting for the variation due to estimating nuisance functions. Simulation studies and an application to a freemium mobile game dataset are presented to demonstrate the empirical performance of the proposed method and support our theoretical findings.<\/jats:p>","DOI":"10.1093\/biomet\/asac050","type":"journal-article","created":{"date-parts":[[2022,8,19]],"date-time":"2022-08-19T13:17:27Z","timestamp":1660915047000},"page":"519-536","source":"Crossref","is-referenced-by-count":5,"title":["A multiplicative structural nested mean model for zero-inflated outcomes"],"prefix":"10.1093","volume":"110","author":[{"given":"Miao","family":"Yu","sequence":"first","affiliation":[{"name":"North Carolina State University Department of Statistics, , 2311 Stinson Drive, Raleigh, North Carolina 27695, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenbin","family":"Lu","sequence":"additional","affiliation":[{"name":"North Carolina State University Department of Statistics, , 2311 Stinson Drive, Raleigh, North Carolina 27695, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shu","family":"Yang","sequence":"additional","affiliation":[{"name":"North Carolina State University Department of Statistics, , 2311 Stinson Drive, Raleigh, North Carolina 27695, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pulak","family":"Ghosh","sequence":"additional","affiliation":[{"name":"Indian Institute of Management Decision Sciences & Centre for Public Policy, , Bangalore 560076, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2022,8,19]]},"reference":[{"key":"2023051508564399900_B1","volume-title":"Free: The Future of a Radical Price","author":"Anderson,","year":"2009"},{"key":"2023051508564399900_B2","doi-asserted-by":"crossref","first-page":"458","DOI":"10.1017\/S0266466600013396","article-title":"Laws of large numbers for dependent non-identically distributed random variables","volume":"4","author":"Andrews,","year":"1988","journal-title":"Economet. 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