Modelling Survival Data in Medical Research

Preface to the second edition Preface to the first edition Survival analysis 1(14) Special features of survival data 1(4) Some examples 5(6) Survivor function and hazard function 11(2) Further reading 13(2) Some non-parametric procedures 15(40) Estimating the survivor function 15(8) Standard error of the estimated survivor function 23(6) Estimating the hazard function 29(4) Estimating the median and percentiles of survival times 33(2) Confidence intervals for the median and percentiles 35(2) Comparison of two groups of survival data 37(11) Comparison of three or more groups of survival data 48(1) Stratified tests 49(2) Log-rank test for trend 51(2) Further reading 53(2) Modelling survival data 55(56) Modelling the hazard function 55(3) The linear component of the proportional hazards model 58(5) Fitting the proportional hazards model 63(6) Confidence intervals and hypothesis tests for the β's 69(4) Comparing alternative models 73(7) Strategy for model selection 80(9) Interpretation of parameter estimates 89(8) Estimating the hazard and survivor functions 97(9) Proportional hazards modelling and the log-rank test 106(3) Further reading 109(2) Model checking in the Cox regression model 111(40) Residuals for the Cox regression model 111(10) Assessment of model fit 121(10) Identification of influential observations 131(10) Testing the assumption of proportional hazards 141(7) Recommendations 148(1) Further reading 149(2) Parametric proportional hazards models 151(44) Models for the hazard function 151(4) Assessing the suitability of a parametric model 155(3) Fitting a parametric model to a single sample 158(10) A model for the comparison of two groups 168(7) The Weibull proportional hazards model 175(8) Comparing alternative Weibull models 183(7) The Gompertz proportional hazards model 190(2) Model choice 192(1) Further reading 193(2) Accelerated failure time and other parametric models 195(36) Probability distributions for survival data 195(4) Exploratory analyses 199(1) The accelerated failure time model for comparing two groups 200(6) The general accelerated failure time model 206(3) Parametric accelerated failure time models 209(7) Fitting and comparing accelerated failure time models 216(7) The proportional odds model 223(4) Some other distributions for survival data 227(1) Further reading 228(3) Model checking in parametric models 231(20) Residuals for parametric models 231(3) Residuals for particular parametric models 234(6) Comparing observed and fitted survivor functions 240(2) Identification of influential observations 242(5) Testing proportional hazards in the Weibull model 247(1) Further reading 248(3) Time-dependent variables 251(22) Types of time-dependent variables 251(1) A model with time-dependent variables 252(6) Model comparison and validation 258(2) Some applications of time-dependent variables 260(2) Three examples 262(9) Further reading 271(2) Interval-censored survival data 273(26) Modelling interval-censored survival data 273(3) Modelling the recurrence probability in the follow-up period 276(3) Modelling the recurrence probability at different times 279(7) Arbitrarily interval-censored survival data 286(10) Parametric models for interval-censored data 296(1) Discussion 297(1) Further reading 297(2) Sample size requirements for a survival study 299(14) Distinguishing between two treatment groups 299(1) Calculating the required number of deaths 300(6) Calculating the required number of patients 306(5) Further reading 311(2) Some additional topics 313(18) Non-proportional hazards 313(5) Informative censoring 318(2) Frailty models 320(3) Multistate models 323(4) Effect of covariate adjustment 327(1) Measures of explained variation 328(1) Modelling a cure probability 329(1) Some other designs in survival analysis 329(2) Computer software for survival analysis 331(22) Use of SAS in survival analysis 331(4) Illustration of the use of SAS 335(11) Use of SAS in some other analyses 346(6) Further reading 352(1) Appendix A Maximum likelihood estimation 353(4) A.1 Inference about a single unknown parameter 353(2) A.2 Inference about a vector of unknown parameters 355(2) Appendix B Likelihood function for randomly censored data 357(2) Appendix C Standard error of percentiles 359(4) C.1 Standard error of a percentile of the Weibull distribution 359(1) C.2 Standard error of a percentile in the Weibull model 360(2) C.3 Standard error of a percentile in the AFT model 362(1) Appendix D Additional data sets 363(8) D.1 Chronic active hepatitis 363(1) D.2 Recurrence of bladder cancer 364(1) D.3 Survival of black ducks 364(3) D.4 Bone marrow transplantation 367(1) D.5 Chronic granulomatous disease 367(4) References 371(12) Index of examples 383(2) Index 385