ICSA Book Series in Statistics Series Editor: Ding-Geng (Din) Chen Jianguo Sun Ding-Geng Chen   Editors Emerging Topics in Modeling Interval-Censored Survival Data ICSA Book Series in Statistics SeriesEditor Ding-Geng (Din) Chen, College of Health Solutions, Arizona State University, ChapelHill,NC,USA The ICSA Book Series in Statistics showcases research from the International Chinese Statistical Association that has an internationalreach. It publishes books instatisticaltheory,applications,andstatisticaleducation.Allbooksareassociated withtheICSAorareauthoredbyinvitedcontributors.Booksmaybemonographs, editedvolumes,textbooksandproceedings. Jianguo Sun • Ding-Geng Chen Editors Emerging Topics in Modeling Interval-Censored Survival Data Editors JianguoSun Ding-GengChen DepartmentofStatistics CollegeofHealthSolutions UniversityofMissouri ArizonaStateUniversity Columbia,MO,USA Goodyear,AZ,USA ISSN2199-0980 ISSN2199-0999 (electronic) ICSABookSeriesinStatistics ISBN978-3-031-12365-8 ISBN978-3-031-12366-5 (eBook) https://doi.org/10.1007/978-3-031-12366-5 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNatureSwitzerland AG2022 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewhole orpart ofthematerial isconcerned, specifically therights oftranslation, reprinting, reuse ofillustrations, recitation, broadcasting, reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface This book is intended primarily to discuss the emerging topics in statistical methods for interval-censored survival data. This book is prepared for booster research,education,andtrainingtoadvancestatisticalmodelingininterval-censored data, which are commonly collected from public health and biomedical research. However,thistypeofdatacanbeeasilymistakenfortypicalright-censoreddatathat wouldresultinerroneousstatisticalinferenceduetothecomplexityofthistypeof data.Thisbookisthenconstructedtoinviteagroupofnationallyandinternationally leadingresearcherstosystematicallydiscussandexplorethehistoricaldevelopment of the associated methods, their computationalimplementations, and some newly emerging topics related to interval-censored data. We aim to cover a variety of topics, including univariate interval-censored, multivariate interval-censored, clustered interval-censored, and competing risk interval-censored data, data with interval-censoredcovariates,interval-censoreddatainelectricmedicalrecords,and misclassified interval-censored data. We invited a group of leading experts at the forefront of modeling interval-censored survival data to prepare book chapters, and received many excellent papers on this topic. Fifteen high-quality chapters are includedin thiswonderfulbook.Eachchapter hasbeen peer reviewedby two editors and revised several times before final acceptance. Therefore, this volume reflects new advances in statistical methods for interval-censored survival data analysisacrossbiostatisticsandinterdisciplinaryareas.Thisbookhasthepotential tohaveasignificantimpactonsurvivaldataanalysisasbothanauthoritativesource and reference, as it will identify new directions of interval-censoredsurvival data modelingusing modern statistical methods. This book will appeal to statisticians, biostatisticians, health-related researchers, graduate students, etc. This book will aidresearchers,students,andpractitionersontheleadingedgeofresearchmethods enablingthemtotackleproblemsinresearch,education,training,andconsultation. This book is organized into three parts. Part I includes three chapters, which presentan overviewof historicaldevelopmentas well as recenttopicsin interval- censoredmodeling.PartII consists ofsix chaptersonemergingtopicsin method- ologicaldevelopment,andPartIIIiscomposedofsixchaptersthatpresentemerging topics in real-life applications of interval-censored data and analysis. All the v vi Preface chapters are organized as self-contained units with references at the end of each chapter.Toaidthereaderinrecreatingthesetechniques,allthestatisticalprocedures inpractice,computerprograms,anddatasetsareincludedorreferencedinthisbook. The readersmay request guidancefrom the chapter authorsto facilitate statistical approaches. Part I:Introduction andReview (Chapters 1–3) In first chapter, “Overview of historic developmentin modeling interval-censored survivaldata,” Dr. Finkelstein presents an overview of the historical development ofthe methodsforthe analysisofinterval-censoredsurvivaldata. Itbeginswith a descriptionofhowtheinterval-censoreddataarisefromstudieswherethesubjects are followedperiodically,and the time to the eventof interestcannotbe observed exactly. From a historical perspective, such data became more common with the emergenceof new clinical and epidemiologicalstudy designs. However,the well- developed methods that are used for right-censored survival data analysis could notbe applied.Thischapterfollowsthe methodologicaldevelopmentof this area, startingin1970fromabroadhistoricalperspective. In second chapter, “Overview of recent advances on the analysis of interval- censoredfailuretimedata,”Dr.Duprovidesareviewofrecentadvancesonseveral topics related to regression analysis of interval-censored data, mainly from the last five to seven years. These topics include the analysis of univariate interval- censored data with time-varying covariates in the presence of a cured subgroup and in the presence of informative interval censoring, respectively. This chapter discusses some recent advances in the analysis of interval-censored data arising fromcase-cohortstudiesandthevariableselectionbasedoninterval-censoreddata. Furthermore, some recent work on regression analysis of multivariate interval- censoreddataisdescribedaswellasregressionanalysisofdoublycensoreddata. Inthirdchapter,“Predictiveaccuracyofpredictionmodelsforinterval-censored data,” Dr. Kim proposes a prognostic tool based on survival model to assist in predicting the occurrence of a clinical event, defining better prescription, and assessing cost-effectiveness. In this chapter, she comprehensively reviews sev- eral recently proposed time-varying prognostic tools for interval-censored data. A classification index including time-dependent receiver operating characteristic (ROC),time-dependentconcordanceindex,andcalibrationssuchasBrierscoreand integratedBRIRscorehavebeenadoptedinthecontextofinterval-censoreddata.A riskscoredefinedaseitherasinglebiomarkerorariskprobabilitycombinedwith potentialpredictorscanhavetime-varyingvalues.Shehasalsoincludedlongitudinal riskscorestoillustratemethodsusingasetofdementiadatasets. Preface vii Part II:Emerging Topicsin Methodology (Chapters 4–9) Infourthchapter,“Apracticalguidetoexactconfidenceintervalsforadistribution of currentstatus data using the binomialapproach,”Drs. Kim, Fay, and Proschan consider the construction of pointwise confidence intervals for the distribution of the failure time of interestbased on currentstatus data. In particular,they discuss two methods recently developed by the authors using the binomial approach and comparethemtoothermethodsdevelopedwiththeuseoftheasymptoticapproach. One advantage of the methods based on the binomialapproach is that they apply tobothcontinuousanddiscreteassessmentdistributions.Inaddition,therelatedR packagecsciandRcodesusedarediscussedandprovided. In fifth chapter, “Accelerated hazards model and its extension for interval- censored data,” Dr. Xiang discusses the analysis of interval-censored data under theacceleratedhazardsmodelandtheirgeneralizations.Inparticular,ageneralized accelerated hazard mixture cure model is presented for situations where there existsa subgroupofcuredsubjects.For example,sheinvestigatestheuse ofsieve maximumlikelihoodestimation approachbasedon spline functions.She provides extensivesimulationresultsandtworealdataapplicationsinthischapter. Insixthchapter,“Maximumlikelihoodestimationofsemiparametricregression modelswithinterval-censoreddata,”Drs.LinandZengconsiderregressionanalysis of interval-censored data with time-dependent covariates under the semiparamet- ric Cox proportional-hazards model. For example, the nonparametric maximum likelihoodestimationapproachwas developedthattreats the unknowncumulative hazard function to be a step function and a simple and stable EM algorithm basedonPoissonlatentvariableswasprovided.Furthermore,themethodologywas generalized to competing risks interval-censored data as well as multivariate or clusteredinterval-censoreddata. In seventh chapter, “Use of the INLA approach for the analysis of interval- censored data,” Drs. van Niekerk and Rue present the integrated nested Laplace approximation(INLA)methodologyforinterval-censoreddata.Mostsurvivalmod- els, includingthose with intervalcensoring,can be shown to be a latent-Gaussian modelandassuch INLAcan beused fornearreal-timeBayesianinference.They providea briefsummaryofthe INLAmethodologyandillustratethe approachon realdataexampleswithintervalcensoring,includingajointmodel.Theanalysisis doneusingtheRpackageINLAandallcodeisavailableforreproducibility. In eighth chapter, “Copula models and diagnostics for multivariate interval- censored data,” Drs. Ding and Sun discuss the use of the copula model-based approach for regression analysis of multivariate interval-censored data and the goodness-of-fittestfortheassumedcopulamodelwithafocusonbivariateinterval- censored data. On the regression analysis, a class of flexible semiparametric transformation models was employed to describe covariate effects and a sieve maximumlikelihoodestimationapproachwasdevelopedforinference.Totestthe assumed copula model, they introduce a general goodness-of-fit test procedure based on the information ratio this method applies to any copula family with a viii Preface parametric form. Finally, the authors discuss the R package CopulaCenR for the implementationof the presentedmethodsand illustrate it throughtwo sets of real multivariateinterval-censoreddata. In ninth chapter, “Efficient estimation of the additive risks model for interval- censored data,” Drs. Wang, Bandyopadhyay, and Sinha discuss the fitting of the semiparametric additive risks model to interval-censored data. Under the case- II interval censoring scenario, in contrast to the commonly used EM algorithm, the authors presented a minorize-maximize (MM) algorithm for nonparametric maximum likelihood estimators of both nonparametric and finite-dimensional componentsofthemodel.Themethodappliestobothtime-independentandtime- varyingcovariatesandhastheadvantageofallowingseparatemaximizationoverthe nonparametricand finite components, thus yielding a stable and fast computation process. The operatingcharacteristics of the proposedMM approachare assessed viasimulationstudiesandacorrespondingRpackage,MMIntAdd,isprovidedand illustratedthroughasetofrealdata. Part III:EmergingTopicsinApplications (Chapters 10–15) In tenth chapter, “Modeling and analysis of chronic disease processes under intermittentobservation,”Drs.CookandLawlessdescribeindependenceconditions needed for valid likelihood-based inference about multistate disease processes under intermittent observation schemes. They further describe how joint models fordiseaseandobservationprocessescanbeusedtoaddressdisease-relatedclinic visits and how joint models can be used to deal with internal time-dependent markerswhenmarkervaluesareobservedonlyatclinicvisits.Theyalsoinvestigate the limiting values of regression coefficients of marker effects when the common approachofcarryingforwardthemostrecentlyrecordedvalueisused. In eleventh chapter, “Case-cohort studies with time-dependent covariates and interval-censored outcome,” Drs. Gao, Hudgens, and Zou provide an inverse probabilityweightinglikelihoodapproachforfittingaparametricmodeltointerval- censored data with both fixed and time-dependent covariates arising from case- cohort studies. The method is a generalization of that given in Sparling et al. (2006)forusualinterval-censoreddatawithtime-dependentcovariates.Simulation resultsdemonstratedthattheproposedestimatorisapproximatelyunbiasedandthe standarderrorsare wellestimated fromthe sandwichestimators. The methodwas appliedtoanobservationalstudythatexaminedtheassociationbetweenhormonal contraceptiveuseandtheriskofHIVacquisition. In twelfth chapter, “The BivarIntCensored: An R package for nonparametric inferenceofbivariateinterval-censoreddata,”Drs.Zhou,Wu,andZhangconsider nonparametricestimation of a bivariate cumulative distribution function based on bivariateinterval-censoreddata. After reviewingtwo existing sieve nonparametric maximumlikelihoodestimationapproaches,theypresentanddiscusstheuseofan R package,BivarIntCensored, which implementsthe two estimation procedures. Preface ix Inthemethods,B-orI-splinefunctionswereused.Inaddition,anassociationtest isprovidedanddiscussed. In thirteenth chapter, “Joint modeling for longitudinal and interval-censored survivaldata:applicationtoIMPImulti-centerHIV/AIDSclinicaltrial,”Drs.Chen andSinginidiscussthejointmodelsforlongitudinalandinterval-censoredsurvival datausingacardiologymulti-centerclinicaltrialwiththeillustrationofRstatistical software. Infourteenthchapter,“Regressionwithinterval-censoredcovariates:application to liquid chromatography,”motivated by the data from the metabolomic analysis area,Drs.Melis,Marhuenda-Muñoz,andLangohrdiscusstheanalysisofgeneral- izedlinearmodelswhenthereexistsacovariatethatsuffersintervalcensoring.They use an extensionofthe methodfromthe linear regressionmodelgivenin Gómez, Espinal, and Lagakos(2003)to accommodatenon-normalresponsesbelongingto an exponentialfamily. In addition,they discuss two goodness-of-fitmeasuresthat accommodateinterval-censoredcovariatesandapplythemethodstodeterminethe associationbetweenglucose,acompletelyobservedresponsevariable,andthesum of carotenoids, an interval-censored explanatory variable. The implementation of thediscussedmethodsinRisalsodiscussed. In fifteenth chapter, “Misclassification simulation extrapolation procedure for interval-censoredlog-logisticacceleratedfailuretimemodel,”Drs.Sevilimedu,Yu, Chen,andLiodiscussthemisclassificationofbinarycovariatessinceitoftenoccurs in survival data. Any survival data analysis ignoring such misclassification will result in estimation bias. To handle such misclassification, the misclassification simulationextrapolation(MC-SIMEX)procedureisaflexiblemethodproposedin survival data analysis, which has been investigated extensively for right-censored survivaldata. However,the performanceof the MC-SIMEX method has not been explored much for interval-censored survival data. This chapter is then aimed at investigatingtheperformanceoftheMC-SIMEXprocedurewithinterval-censored survivaldata throughMonte-Carlo simulations and real data analysis. They focus this investigation on the log-logistic accelerated failure time (AFT) model since the log-logistic distribution plays an important role in evaluating non-monotonic hazardsforsurvivaldata. We sincerely thank all of the people who have given us strong support for the publication of this book on time. Our acknowledgmentsgo to all the chapter authors(in the “List of Contributors”)for submitting their excellentworksto this book.We also thankMs. AnneRubio atthe Collegeof HealthSolutions,Arizona State University,andMs. JennyK. Chen at Morgan-StanleyWealth Management, for their professional editing of this book, which has substantially improved the qualityofthe chaptersandthe entirebook.Furthermore,we areso gratefulto Dr. Eva Hiripi and Ms. Faith Su (Statistics Editors, Springer Nature) from Springer and Kirthika Selvaraju (Project Coordinator of Books, Springer Nature) for their full support during the long publication process. In addition, this book was made possiblethroughfundingprovidedbyDST-NRF-SAMRC-SARChIResearchChair inBiostatistics,Grantnumber:114613.