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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010069361 | QA276.4 T32 2004 | Open Access Book | Book | Searching... |
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Summary
Summary
Survival Analysis Using S: Analysis of Time-to-Event Data is designed as a text for a one-semester or one-quarter course in survival analysis for upper-level or graduate students in statistics, biostatistics, and epidemiology. Prerequisites are a standard pre-calculus first course in probability and statistics, and a course in applied linear regression models. No prior knowledge of S or R is assumed. A wide choice of exercises is included, some intended for more advanced students with a first course in mathematical statistics.
The authors emphasize parametric log-linear models, while also detailing nonparametric procedures along with model building and data diagnostics. Medical and public health researchers will find the discussion of cut point analysis with bootstrap validation, competing risks and the cumulative incidence estimator, and the analysis of left-truncated and right-censored data invaluable. The bootstrap procedure checks robustness of cut point analysis and determines cut point(s).
In a chapter written by Stephen Portnoy, censored regression quantiles - a new nonparametric regression methodology (2003) - is developed to identify important forms of population heterogeneity and to detect departures from traditional Cox models. By generalizing the Kaplan-Meier estimator to regression models for conditional quantiles, this methods provides a valuable complement to traditional Cox proportional hazards approaches.
Author Notes
Mara Tableman is an Associate Professor in the Department of Mathematics & Statistics at Portland State University, Lecturer in the Seminar fuer Statistik at the Swiss Federal Institute of Technology, and Adjunct Associate Professor at the Oregon Health & Sciences University
Jong-Sung Kim is an Assistant Professor in the Department of Mathematics & Statistics at Portland State University, Oregon, USA
Table of Contents
| Preface | p. xiii |
| 1 Introduction | p. 1 |
| 1.1 Motivation - two examples | p. 2 |
| 1.2 Basic definitions | p. 5 |
| 1.3 Censoring and truncation models | p. 9 |
| 1.4 Course objectives | p. 18 |
| 1.5 Data entry and import/export of data files | p. 20 |
| 1.6 Exercises | p. 21 |
| 2 Nonparametric Methods | p. 25 |
| 2.1 Kaplan-Meier estimator of survival | p. 25 |
| Redistribute-to-the-right algorithm | p. 30 |
| Empirical estimates of variance, hazard, quantiles, truncated mean survival, and truncated mean residual life | p. 32 |
| 2.2 Comparison of survivor curves: two-sample problem | p. 39 |
| Fisher's exact test | p. 41 |
| Mantel-Haenszel/log-rank test | p. 41 |
| Hazard ratio as a measure of effect | p. 45 |
| Stratifying on a covariate | p. 46 |
| Example of Simpson's paradox | p. 49 |
| 2.3 Exercises | p. 51 |
| 3 Parametric Methods | p. 55 |
| 3.1 Frequently used (continuous) models | p. 56 |
| Summary | p. 62 |
| Construction of the Quantile-quantile (Q-Q) plot | p. 63 |
| 3.2 Maximum likelihood estimation (MLE) | p. 64 |
| Delta method | p. 66 |
| 3.3 Confidence intervals and tests | p. 66 |
| 3.4 One-sample problem | p. 68 |
| 3.4.1 Fitting data to the exponential model | p. 68 |
| 3.4.2 Fitting data to the Weibull and log-logistic models | p. 77 |
| 3.5 Two-sample problem | p. 80 |
| Fitting data to the Weibull, log-logistic, and log-normal models | p. 81 |
| Quantiles | p. 84 |
| Prelude to parametric regression models | p. 88 |
| 3.6 A bivariate version of the delta method | p. 89 |
| 3.7 The delta method for a bivariate vector field | p. 89 |
| 3.8 General version of the likelihood ratio test | p. 91 |
| 3.9 Exercises | p. 92 |
| 4 Regression Models | p. 95 |
| 4.1 Exponential regression model | p. 96 |
| 4.2 Weibull regression model | p. 98 |
| 4.3 Cox proportional hazards (PH) model | p. 100 |
| 4.4 Accelerated failure time model | p. 101 |
| 4.5 Summary | p. 105 |
| 4.6 AIC procedure for variable selection | p. 106 |
| Motorette data example | p. 107 |
| 4.7 Exercises | p. 117 |
| 5 The Cox Proportional Hazards Model | p. 121 |
| CNS lymphoma example | p. 121 |
| 5.1 AIC procedure for variable selection | p. 124 |
| 5.2 Stratified Cox PH regression | p. 133 |
| 5.3 Exercises | p. 137 |
| 5.4 Review of first five chapters: self-evaluation | p. 139 |
| 6 Model Checking: Data Diagnostics | p. 143 |
| 6.1 Basic graphical methods | p. 144 |
| 6.2 Weibull regression model | p. 147 |
| Graphical checks of overall model adequacy | p. 147 |
| Deviance, Cox-Snell, martingale, and deviance residuals | p. 148 |
| dfbeta | p. 152 |
| Motorette example | p. 152 |
| 6.3 Cox proportional hazards model | p. 157 |
| 6.3.1 Cox-Snell residuals for assessing the overall fit of a PH model | p. 159 |
| 6.3.2 Martingale residuals for identifying the best functional form of a covariate | p. 160 |
| 6.3.3 Deviance residuals to detect possible outliers | p. 161 |
| 6.3.4 Schoenfeld residuals to examine fit and detect outlying covariate values | p. 162 |
| 6.3.5 Grambsch and Therneau's test for PH assumption | p. 164 |
| 6.3.6 dfbetas to assess influence of each observation | p. 164 |
| 6.3.7 CNS lymphoma example: checking the adequacy of the PH model | p. 166 |
| 6.3.8 Cut point analysis with bootstrap validation | p. 172 |
| 6.4 Exercises | p. 179 |
| 7 Additional Topics | p. 181 |
| 7.1 Extended Cox model | p. 181 |
| Treatment of heroin addicts example | p. 186 |
| 7.2 Competing risks: cumulative incidence estimator | p. 195 |
| 7.3 Analysis of left-truncated and right-censored data | p. 202 |
| 7.3.1 Modified Kaplan-Meier (K-M) estimator of the survivor function for LTRC data | p. 205 |
| Psychiatric inpatients example | p. 206 |
| 7.3.2 Cox PH model for LTRC data | p. 209 |
| 7.4 Exercises | p. 212 |
| 8 Censored Regression Quantiles | p. 213 |
| 8.1 Introduction | p. 213 |
| 8.2 What are regression quantiles? | p. 214 |
| 8.2.1 Definition of regression quantiles | p. 215 |
| 8.2.2 A regression quantile example | p. 217 |
| 8.3 Doing regression quantile | p. 220 |
| 8.4 Censored regression quantile model and Cox model | p. 224 |
| 8.5 Computation of censored regression quantiles | p. 227 |
| 8.5.1 The new Kaplan-Meier weights | p. 227 |
| 8.5.2 The single-sample algorithm | p. 228 |
| 8.5.3 The general censored regression quantile algorithm | p. 230 |
| 8.6 Examples of censored regression quantile | p. 232 |
| 8.6.1 Software for censored regression quantiles | p. 233 |
| 8.6.2 CNS lymphoma example | p. 234 |
| 8.6.3 UMARU impact study (UIS) example | p. 239 |
| 8.7 Exercises | p. 242 |
| References | p. 247 |
| Index | p. 251 |
