[...]... 4A 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Remission DurationA 33.7; 3.8 6.3 2.3 6.4 23.8; 1. 8 5.5 16 .6; 33.7; 17 .1; 4.3 26.9; 21. 4; 18 .1; 5.8 3.0 11 .0; 22 .1 23.0; 6.8 10 .8; 2.8 9.2 15 .9 4.5 9.2 8.2; 8.2; 7.8; Survival TimeA 33.7; 3.9 10 .5 5.4 19 .5 23.8; 7.9 16 .9; 16 .6; 33.7; 17 .1; 8.0 26.9; 21. 4; 18 .1; 16 .0; 6.9 11 .0; 24.8; 23.0; 8.3 10 .8; 12 .2; 12 .5; 24.4 7.7 14 .8; 8.2;... survival 19 20 EXAMPLES OF SURVIVAL DATA ANALYSIS Table 3 .1 Data for 30 Resected Melanoma Patients Patient 1 2 3 4 5 6 7 8 9 10 11 12 13 14 f15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Age Gender? Initial Stage Treatment Received@ 59 50 76 66 33 23 40 34 34 38 54 49 35 22 30 26 27 45 76 48 91 82 50 40 34 38 50 53 48 40 2 2 1 2 1 2 2 1 1 2 2 1 1 1 1 2 1 2 2 1 1 2 2 1 1 1 1 2 2 2 3B 3B 3B 3B 3B 3B 3B 3B... 0 1 1—5 5 10 10 15 15 —20 20—25 25—30 30—35 35—40 40—45 45—50 50—55 55—60 60—65 65—70 70—75 75—80 80—85 85 and over Number Living at Beginning of Age Interval Number Dying in Age Interval 10 0,000 97,407 96,998 96,765 96,5 51 96 ,11 1 95, 517 94,905 94 ,14 4 93,064 91, 378 88,756 84, 711 79,067 71, 147 60,857 48 ,17 0 33,576 18 ,542 2,593 409 233 214 440 594 612 7 61 1,080 1. 686 2,622 4,045 5,644 7,920 10 ,290 12 ,687... hazard function Exercise Table 2 .1 Year of Follow-up 0 1 1—2 2—3 3—4 4—5 5—6 6—7 7—8 8—9 9 Number Alive at Beginning of Interval Number Dying in Interval 11 00 860 680 496 358 240 18 0 12 8 84 52 240 18 0 18 4 13 8 11 8 60 52 44 32 28     18 2.2 Exercise Table 2.2 is a life table for the total population (of 10 0,000 live births) in the United States, 19 59 19 61 Compute and plot the estimated... Model, 269 11 .5 Lognormal Regression Model, 274 11 .6 Extended Generalized Gamma Regression Model, 277 256  x 11 .7 Log-Logistic Regression Model, 280 11 .8 Other Parametric Regression Models, 283 11 .9 Model Selection Methods, 286 Bibliographical Remarks, 295 Exercises, 295 12 Identification of Prognostic Factors Related to Survival Time: Cox Proportional Hazards Model 12 .1 12.2 12 .3 12 .4 Partial... Distributions, 2 51 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 11 .1 Preliminary Examination of Data, 257 11 .2 General Structure of Parametric Regression Models and Their Asymptotic Likelihood Inference, 259 11 .3 Exponential Regression Model, 263 11 .4 Weibull Regression... Appendix B Statistical Tables 433 References 488 Index 511 Preface Statistical methods for survival data analysis have continued to flourish in the last two decades Applications of the methods have been widened from their historical use in cancer and reliability research to business, criminology, epidemiology, and social and behavioral sciences The third edition of Statistical Methods for Survival Data Analysis. .. us E T L J W W Oklahoma City, OK April 18 , 20 01 CHAPTER 1 Introduction 1. 1 PRELIMINARIES This book is for biomedical researchers, epidemiologists, consulting statisticians, students taking a first course on survival data analysis, and others interested in survival time study It deals with statistical methods for analyzing survival data derived from laboratory studies of animals, clinical... 48 ,17 0 33,576 18 ,542 2,593 409 233 214 440 594 612 7 61 1,080 1. 686 2,622 4,045 5,644 7,920 10 ,290 12 ,687 14 ,594 15 ,034 18 ,542 Source: U.S National Center for Health Statistics, Life Tables 19 59 19 61, Vol 1, No 1, ‘‘United States Life Tables 19 59— 61, ’’ December 19 64, pp 8—9 2.3 Derive (2.2 .1) using (2 .1. 6) and basic definitions of conditional probability 2.4 Given the hazard function h(t) : c derive the... patients (2 .1. 3) where the circumflex denotes an estimate of the function When censored observations are present, the numerator of (2 .1. 3) cannot always be determined For example, consider the following set of survival data: 4, 6, 6;, 10 ;, 15 , 20 Figure 2 .1 Two examples of survival curves     10 Using (2 .1. 3), we can compute S(5) : 5/6 : 0.833 However, we cannot obtain  S (11 ) since .