Handbook of Statistics 23: Advances in Survival Analysis

N. Balakrishnan, C.R. Rao9780080495118, 9780444500793, 0444500790

Handbook of Statistics 23The book covers all important topics in the area of Survival Analysis. Each topic has been covered by one or more chapters written by internationally renowned experts. Each chapter provides a comprehensive and up-to-date review of the topic. Several new illustrative examples have been used to demonstrate the methodologies developed. The book also includes an exhaustive list of important references in the area of Survival Analysis.

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Table of contents :
Preface……Page 1
Table of contents……Page 3
Contributors……Page 16
Measures of predictive accuracy……Page 21
Discrimination index in logistic regression……Page 22
Extension of C statistics to survival analysis……Page 23
A chi-square statistic for the survival time model with censored observations……Page 26
Poisson approximation to survival time model……Page 27
Chi-square statistic based on the Poisson approximation……Page 30
The asymptotic null distribution of K2 and Kt2……Page 37
Algorithms for generating numerical examples……Page 38
Comparison of the proposed statistic (2) and Kt2……Page 39
References……Page 45
Introduction……Page 46
Martingale residuals……Page 47
Estimation of the threshold parameter……Page 49
Inference for beta……Page 51
Comparison of test procedures……Page 53
Accelerated failure time models with a single covariate……Page 56
Adjustment for other covariates……Page 59
Discussion……Page 60
References……Page 61
Introduction……Page 62
Degree of separation index……Page 63
Estimation and inference procedures……Page 67
Distribution property of test statistics under the null hypothesis……Page 71
Application examples……Page 74
Discussion and conclusion……Page 75
References……Page 77
Time-varying effects in survival analysis……Page 79
Estimation for proportional or additive models……Page 85
Cox’s proportional regression model……Page 86
Aalen’s additive model……Page 89
Additive-multiplicative intensity models……Page 90
Testing in proportional and additive hazards models……Page 92
Non-parametric model and testing……Page 93
Semi-parametric model……Page 94
Test for time-dependent effects in semi-parametric model……Page 96
Survival with malignant melanoma……Page 97
References……Page 101
Introduction……Page 104
The SLLN……Page 108
The CLT……Page 110
Bias……Page 112
The jackknife……Page 114
Censored correlation and regression……Page 117
Conclusions……Page 119
References……Page 120
Introduction……Page 122
Estimation without truncation……Page 124
Estimation with truncation……Page 127
Semiparametric regression analysis……Page 131
Nonparametric comparison of survival functions……Page 134
Discussion and future researches……Page 136
References……Page 138
Introduction……Page 140
The (nonparametric) KME……Page 144
Estimators of S(t) under MCAR……Page 145
Estimators of S(t) under MAR (CAR)……Page 147
Information bound for estimating S(t)……Page 148
Information bound for estimating H1(t)……Page 150
Semiparametric estimation in the MCI model……Page 151
Comparison of asymptotic variances……Page 155
Conclusion……Page 156
References……Page 157
Introduction……Page 159
Modeling the censoring mechanism……Page 160
Estimating functions in the observed data model……Page 163
Initial mappings that correspond with a specified RAL estimator……Page 164
Generalized Dabrowska’s estimator……Page 167
Orthogonalized estimating function and corresponding estimator……Page 169
Estimation of Q1(FX,G) by Monte Carlo simulations……Page 173
Simulations……Page 175
Comparison of µn0 with µnDab……Page 176
Comparison of µn0, µnDab and µn1……Page 177
Discussion……Page 178
References……Page 188
Introduction……Page 190
Definition of the estimators……Page 191
Asymptotic distribution of the estimators……Page 196
Generalization to models with covariates……Page 204
Discussion……Page 208
References……Page 209
Introduction……Page 210
Estimation of the bivariate distribution function……Page 212
An alternative estimator……Page 215
Doubly truncated data……Page 216
Estimation of bivariate hazard……Page 217
Reverse hazard with right truncation……Page 219
Bivariate density estimation……Page 220
References……Page 221
Introduction……Page 223
Framework……Page 224
Kullback information and Hellinger distances based on hazards……Page 227
A general device to derive lower bounds for estimating a function……Page 229
Lower bound for F={h>=0: ||h(s)||22