{"title":"τ\u0000 $tau$\u0000 -Inflated Beta Regression Model for Estimating \u0000 \u0000 τ\u0000 $tau$\u0000 -Restricted Means and Event-Free Probabilities for Censored Time-to-Event Data","authors":"Yizhuo Wang, Susan Murray","doi":"10.1002/bimj.70009","DOIUrl":"10.1002/bimj.70009","url":null,"abstract":"<p>In this research, we propose analysis of <span></span><math>\u0000 <semantics>\u0000 <mi>τ</mi>\u0000 <annotation>$tau$</annotation>\u0000 </semantics></math>-restricted censored time-to-event data via a <span></span><math>\u0000 <semantics>\u0000 <mi>τ</mi>\u0000 <annotation>$tau$</annotation>\u0000 </semantics></math>-inflated beta regression (<span></span><math>\u0000 <semantics>\u0000 <mi>τ</mi>\u0000 <annotation>$tau$</annotation>\u0000 </semantics></math>-IBR) model. The outcome of interest is <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>min</mi>\u0000 <mo>(</mo>\u0000 <mi>τ</mi>\u0000 <mo>,</mo>\u0000 <mi>T</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>${rm min}(tau,T)$</annotation>\u0000 </semantics></math>, where <span></span><math>\u0000 <semantics>\u0000 <mi>T</mi>\u0000 <annotation>$T$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mi>τ</mi>\u0000 <annotation>$tau$</annotation>\u0000 </semantics></math> are the time-to-event and follow-up duration, respectively. Our analysis goals include estimation and inference related to <span></span><math>\u0000 <semantics>\u0000 <mi>τ</mi>\u0000 <annotation>$tau$</annotation>\u0000 </semantics></math>-restricted mean survival time (<span></span><math>\u0000 <semantics>\u0000 <mi>τ</mi>\u0000 <annotation>$tau$</annotation>\u0000 </semantics></math>-RMST) values and event-free probabilities at <span></span><math>\u0000 <semantics>\u0000 <mi>τ</mi>\u0000 <annotation>$tau$</annotation>\u0000 </semantics></math> that address the censored nature of the data. In this setting, it is common to observe many individuals with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>min</mi>\u0000 <mo>(</mo>\u0000 <mi>τ</mi>\u0000 <mo>,</mo>\u0000 <mi>T</mi>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <mi>τ</mi>\u0000 </mrow>\u0000 <annotation>${rm min}(tau,T)=tau$</annotation>\u0000 </semantics></math>, a point mass that is typically overlooked in <span></span><math>\u0000 <semantics>\u0000 <mi>τ</mi>\u0000 <annotation>$tau$</annotation>\u0000 </semantics></math>-restricted event-time analyses. Our proposed <span></span><math>\u0000 <semantics>\u0000 <mi>τ</mi>\u0000 <annotation>$tau$</annotation>\u0000 </semantics></","PeriodicalId":55360,"journal":{"name":"Biometrical Journal","volume":"66 8","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/bimj.70009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142741342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}