{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T03:48:41Z","timestamp":1791517721097,"version":"4.3.4"},"reference-count":42,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T00:00:00Z","timestamp":1599177600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,8,12]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>Advances in digital technology and wearables have made it possible to deliver behavioural mobile health interventions to individuals in their everyday lives. Micro-randomized trials are increasingly used to provide data to inform the construction of these interventions. In a micro-randomized trial, each individual is repeatedly randomized among multiple intervention options, often hundreds or even thousands of times over the course of the trial. The work reported in this article is motivated by multiple micro-randomized trials that have been conducted or are currently in the field, in which the primary outcome is a longitudinal binary outcome. The primary aim of such micro-randomized trials is to examine whether a particular time-varying intervention has an effect on the longitudinal binary outcome, often marginally over all, but a small subset of the individual\u2019s data. We propose the concept of causal excursion effect, which can be used in such a primary-aim analysis for micro-randomized trials with binary outcomes. Under rather restrictive assumptions one can derive, based on existing literature, a semiparametric, locally efficient estimator of the causal effect. Starting from this estimator, we develop an estimator that can be used as the basis of a primary-aim analysis under more plausible assumptions. Simulation studies are conducted to compare the estimators. We illustrate the proposed methods using data from the micro-randomized trial BariFit, the goal of which is to support weight maintenance for individuals who have undergone bariatric surgery.<\/jats:p>","DOI":"10.1093\/biomet\/asaa070","type":"journal-article","created":{"date-parts":[[2020,8,26]],"date-time":"2020-08-26T15:13:19Z","timestamp":1598454799000},"page":"507-527","source":"Crossref","is-referenced-by-count":48,"title":["Estimating time-varying causal excursion effects in mobile health with binary outcomes"],"prefix":"10.1093","volume":"108","author":[{"given":"Tianchen","family":"Qian","sequence":"first","affiliation":[{"name":"Department of Statistics, University of California, Irvine, Donald Bren Hall, Irvine, California 92697, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hyesun","family":"Yoo","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Michigan, 323 West Hall, 1085 South University, Ann Arbor, Michigan 48109, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Predrag","family":"Klasnja","sequence":"additional","affiliation":[{"name":"School of Information, University of Michigan, 4364 North Quad, 105 South State Street, Ann Arbor, Michigan 48109, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniel","family":"Almirall","sequence":"additional","affiliation":[{"name":"Department of Statistics,\u00a0University of Michigan, 323 West Hall, 1085 South University, Ann Arbor, Michigan 48109, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Susan A","family":"Murphy","sequence":"additional","affiliation":[{"name":"Department of Statistics, Harvard University, 1 Oxford Street, Cambridge, Massachusetts 02138, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2020,9,4]]},"reference":[{"key":"2021081218511340400_asaa070-B1","doi-asserted-by":"crossref","first-page":"e10123","DOI":"10.2196\/10123","article-title":"To prompt or not to prompt? 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