{"doi":"10.1093/biomet/asab033","title":"Rejoinder: ‘Estimating time-varying causal excursion effects in mobile health with binary outcomes’","abstract":"We would like to thank the editor for making this a discussion paper. We are honoured that these three groups of researchers agreed to be discussants. Reading their discussions has been an enjoyable and thought-provoking journey for us. We organize our rejoinder by topic, as some topics have been discussed by multiple discussants. In general, the causal excursion effect in (2) of the main manuscript depends on the randomization probability of past treatment assignments (⁠$$\\bar{A}_{t-1}$$⁠), which we refer to as the treatment protocol. This feature distinguishes the excursion effect from most other causal effects in time-varying treatment settings, such as causal effects in marginal structural models or structural nested mean models. Guo et al. (2021) and Zhang & Laber (2021) provided numerical examples to illustrate this feature of the excursion effect. Guo et al. (2021, Equation...","journal":"Biometrika","year":2021,"id":201540,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":7,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9618,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2021-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":396601,"name":"Hyesun Yoo","orcid":null,"position":1,"is_corresponding":false},{"id":232381,"name":"Predrag Klasnja","orcid":"0000-0002-4570-703X","position":2,"is_corresponding":false},{"id":454311,"name":"Daniel Almirall","orcid":"0000-0002-9697-6600","position":3,"is_corresponding":false},{"id":74886,"name":"Susan A. Murphy","orcid":"0000-0002-2032-4286","position":4,"is_corresponding":false},{"id":428083,"name":"Tianchen Qian","orcid":"0000-0003-4282-7826","position":0,"is_corresponding":true}],"reference_count":9,"raw_metadata":null,"created_at":"2026-07-18T23:50:56.394488Z","pmid":"34400906","pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}