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We construct a single\u2010step norm penalty procedure that maintains the hierarchical structure of interactions in the sense that a treatment\u2010covariate interaction term is included in the model only when either the covariate or both the covariate and treatment have nonzero main effects. We developed a constrained Lasso approach with two parameterization schemes that enforce the hierarchical interaction restriction differently. We solved the resulting constrained optimization problem using a spectral projected gradient method. We compared our methods to the unstructured Lasso using simulation studies including a scenario that violates the hierarchical condition (misspecified model). The simulations showed that our methods yielded more parsimonious models and outperformed the unstructured Lasso for correctly identifying nonzero treatment\u2010covariate interactions. The superior performance of our methods are also corroborated by an application to a large randomized clinical trial data investigating a drug for treating congestive heart failure (N\u00a0=\u00a02569). Our methods provide a well\u2010suited approach for doing secondary analysis in clinical trials to analyze heterogeneous treatment effects and to identify predictive biomarkers.<\/jats:p>","DOI":"10.1002\/sim.9132","type":"journal-article","created":{"date-parts":[[2021,7,9]],"date-time":"2021-07-09T05:06:10Z","timestamp":1625807170000},"page":"5417-5433","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Lasso estimation of hierarchical interactions for analyzing heterogeneity of treatment effect"],"prefix":"10.1002","volume":"40","author":[{"given":"Yu","family":"Du","sequence":"first","affiliation":[{"name":"Department of Biometrics Eli Lilly and Company Indianapolis Indiana USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huan","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Biostatistics Johns Hopkins Bloomberg School of Public Health Baltimore Maryland USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ravi","family":"Varadhan","sequence":"additional","affiliation":[{"name":"Department of Biostatistics Johns Hopkins Bloomberg School of Public Health Baltimore Maryland USA"},{"name":"Division of Biostatistics and Bioinformatics, Department of Oncology Johns Hopkins School of Medicine Baltimore Maryland USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2021,7,8]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0140-6736(95)90120-5"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/0197-2456(94)90024-8"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.1001\/jama.298.10.1209"},{"key":"e_1_2_7_5_1","doi-asserted-by":"publisher","DOI":"10.1093\/jnci\/djm022"},{"key":"e_1_2_7_6_1","doi-asserted-by":"publisher","DOI":"10.1177\/1740774508091815"},{"key":"e_1_2_7_7_1","doi-asserted-by":"publisher","DOI":"10.1038\/clpt.2009.68"},{"key":"e_1_2_7_8_1","doi-asserted-by":"publisher","DOI":"10.1158\/1078-0432.CCR-09-1357"},{"key":"e_1_2_7_9_1","doi-asserted-by":"publisher","DOI":"10.1177\/1740774510373120"},{"key":"e_1_2_7_10_1","doi-asserted-by":"publisher","DOI":"10.1158\/2159-8274.CD-10-0010"},{"key":"e_1_2_7_11_1","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxq060"},{"key":"e_1_2_7_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cct.2014.09.001"},{"key":"e_1_2_7_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/s12561-014-9117-1"},{"key":"e_1_2_7_14_1","doi-asserted-by":"publisher","DOI":"10.1002\/pst.1761"},{"key":"e_1_2_7_15_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.7042"},{"key":"e_1_2_7_16_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10742-016-0159-3"},{"key":"e_1_2_7_17_1","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2014.975555"},{"key":"e_1_2_7_18_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1614732113"},{"key":"e_1_2_7_19_1","unstructured":"ShalitU JohanssonFD SontagD. 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