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Statistical methods for survival data analysis PDF

535 Pages·2003·4.05 MB·English
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Statistical Methods for Survival Data Analysis Statistical Methods for Survival Data Analysis Third Edition ELISA T. LEE JOHN WENYU WANG Department of Biostatistics and Epidemiology and Center for American Indian Health Research College of Public Health University of Oklahoma Health Sciences Center Oklahoma City, Oklahoma A JOHN WILEY & SONS, INC., PUBLICATION Copyright(cid:1)2003byJohnWiley&Sons,Inc.Allrightsreserved. PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey. PublishedsimultaneouslyinCanada. Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedinany formorbyanymeans,electronic,mechanical,photocopying,recording,scanning,orotherwise, exceptaspermittedunderSection107or108ofthe1976UnitedStatesCopyrightAct, withouteitherthepriorwrittenpermissionofthePublisher,orauthorizationthroughpaymentof theappropriateper-copyfeetotheCopyrightClearanceCenter,Inc.,222RosewoodDrive, Danvers,MA01923,978-750-8400,fax978-750-4470,oronthewebatwww.copyright.com. RequeststothePublisherforpermissionshouldbeaddressedtothePermissionsDepartment, JohnWiley&Sons,Inc.,111RiverStreet,Hoboken,NJ07030,(201)748-6011,fax(201)748-6008, e-mail:permreq(cid:2)wiley.com. LimitofLiability/DisclaimerofWarranty:Whilethepublisherandauthorhaveusedtheirbest effortsinpreparingthisbook,theymakenorepresentationsorwarrantieswithrespecttothe accuracyorcompletenessofthecontentsofthisbookandspecificallydisclaimanyimplied warrantiesofmerchantabilityorfitnessforaparticularpurpose.Nowarrantymaybecreatedor extendedbysalesrepresentativesorwrittensalesmaterials.Theadviceandstrategiescontained hereinmaynotbesuitableforyoursituationYoushouldconsultwithaprofessionalwhere appropriate.Neitherthepublishernorauthorshallbeliableforanylossofprofitoranyother commercialdamages,includingbutnotlimitedtospecial,incidental,consequential,orother damages. ForgeneralinformationonourotherproductsandservicespleasecontactourCustomerCare DepartmentwithintheU.S.at877-762-2974,outsidetheU.S.at317-572-3993orfax317-572-4002. Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsin print,however,maynotbeavailableinelectronicformat. LibraryofCongressCataloging-in-PublicationData: Lee,ElisaT. Statisticalmethodsforsurvivaldataanalysis.--3rded./ElisaT.LeeandJohnWenyuWang. p.cm.--(Wileyseriesinprobabilityandstatistics) Includesbibliographicalreferencesandindex. ISBN0-471-36997-7(cloth:alk.paper) 1.Medicine--Research--Statisticalmethods.2.Failuretimedataanalysis.3. Prognosis--Statisticalmethods.I.Wang,JohnWenyu.II.Title.III.Series. R853.S7L432003 610(cid:1).72--dc21 2002027025 PrintedintheUnitedStatesofAmerica. 10987654321 To the memory of our parents Mr. Chi-Lan Tan and Mrs. Hwei-Chi Lee Tan (E.T.L.) Mr. Beijun Zhang and Mrs. Xiangyi Wang (J.W.W.) Contents Preface xi 1 Introduction 1.1 Preliminaries, 1 1.2 Censored Data, 1 1.3 Scope of the Book, 5 Bibliographical Remarks, 7 2 Functions of Survival Time 8 2.1 Definitions, 8 2.2 Relationships of the Survival Functions, 15 Bibliographical Remarks, 17 Exercises, 17 3 Examples of Survival Data Analysis 19 3.1 Example 3.1: Comparison of Two Treatments and Three Diets, 19 3.2 Example 3.2: Comparison of Two Survival Patterns Using Life Tables, 26 3.3 Example 3.3: Fitting Survival Distributions to Remission Data, 29 3.4 Example 3.4: Relative Mortality and Identification of Prognostic Factors, 32 3.5 Example 3.5: Identification of Risk Factors, 40 Bibliographical Remarks, 47 Exercises, 47 vii viii  4 Nonparametric Methods of Estimating Survival Functions 64 4.1 Product-Limit Estimates of Survivorship Function, 65 4.2 Life-Table Analysis, 77 4.3 Relative, Five-Year, and Corrected Survival Rates, 94 4.4 Standardized Rates and Ratios, 97 Bibliographical Remarks, 102 Exercises, 102 5 Nonparametric Methods for Comparing Survival Distributions 106 5.1 Comparison of Two Survival Distributions, 106 5.2 Mantel—Haenszel Test, 121 5.3 Comparison of K (K(cid:2)2) Samples, 125 Bibliographical Remarks, 131 Exercises, 131 6 Some Well-Known Parametric Survival Distributions and Their Applications 134 6.1 Exponential Distribution, 134 6.2 Weibull Distribution, 138 6.3 Lognormal Distribution, 143 6.4 Gamma and Generalized Gamma Distributions, 148 6.5 Log-Logistic Distribution, 154 6.6 Other Survival Distributions, 155 Bibliographical Remarks, 160 Exercises, 160 7 Estimation Procedures for Parametric Survival Distributions without Covariates 162 7.1 General Maximum Likelihood Estimation Procedure, 162 7.2 Exponential Distribution, 166 7.3 Weibull Distribution, 178 7.4 Lognormal Distribution, 180 7.5 Standard and Generalized Gamma Distributions, 188 7.6 Log-Logistic Distribution, 195 7.7 Other Parametric Survival Distributions, 196 Bibliographical Remarks, 196 Exercises, 197  ix 8 Graphical Methods for Survival Distribution Fitting 198 8.1 Introduction, 198 8.2 Probability Plotting, 200 8.3 Hazard Plotting, 209 8.4 Cox—Snell Residual Method, 215 Bibliographical Remarks, 219 Exercises, 219 9 Tests of Goodness of Fit and Distribution Selection 221 9.1 Goodness-of-Fit Test Statistics Based on Asymptotic Likelihood Inferences, 222 9.2 Tests for Appropriatenessof a Family of Distributions, 225 9.3 Selection of a Distribution Using BIC or AIC Procedures, 230 9.4 Tests for a Specific Distribution with Known Parameters, 233 9.5 Hollander and Proschan’s Test for Appropriateness of a Given Distribution with Known Parameters, 236 Bibliographical Remarks, 238 Exercises, 240 10 Parametric Methods for Comparing Two Survival Distributions 243 10.1 Likelihood Ratio Test for Comparing Two Survival Distributions, 243 10.2 Comparison of Two Exponential Distributions, 246 10.3 Comparison of Two Weibull Distributions, 251 10.4 Comparison of Two Gamma Distributions, 252 Bibliographical Remarks, 254 Exercises, 254 11 Parametric Methods for Regression Model Fitting and Identification of Prognostic Factors 256 11.1 Preliminary Examination of Data, 257 11.2 General Structure of Parametric RegressionModels and Their Asymptotic Likelihood Inference, 259 11.3 Exponential Regression Model, 263 11.4 Weibull Regression Model, 269 11.5 Lognormal Regression Model, 274 11.6 Extended Generalized Gamma Regression Model, 277

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