Applied Survival Analysis Using R (Use R!) 1st ed. 2016 Edition

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by Dirk F. Moore

Dirk F. Moore is Associate Professor ofBiostatistics at the Rutgers School of Public Health and the Rutgers CancerInstitute of New Jersey. He received a Ph.D. in biostatistics from theUniversity of Washington in Seattle and, prior to joining Rutgers, was afaculty member in the Statistics Department at Temple University. He haspublished numerous papers on the theory and application of survival analysisand other biostatistics methods to clinical trials and epidemiology studies.

·      Series: Use R!

·      Paperback: 226 pages

·      Publisher: Springer; 1st ed. 2016 edition(June 17, 2016)

Applied Survival Analysis Using R covers themain principles of survival analysis, gives examples of how it is applied, andteaches how to put those principles to use to analyze data using R as avehicle. Survival data, where the primary outcome is time to a specific event,arise in many areas of biomedical research, including clinical trials,epidemiological studies, and studies of animals. Many survival methods areextensions of techniques used in linear regression and categorical data, whileother aspects of this field are unique to survival data. This text employsnumerous actual examples to illustrate survival curve estimation, comparison ofsurvivals of different groups, proper accounting for censoring and truncation,model variable selection, and residual analysis.

Because explaining survival analysisrequires more advanced mathematics than many other statistical topics, thisbook is organized with basic concepts and most frequently used procedurescovered in earlier chapters, with more advanced topics near the end and in theappendices. A background in basic linear regression and categorical dataanalysis, as well as a basic knowledge of calculus and the R system, will helpthe reader to fully appreciate the information presented. Examples aresimple and straightforward while still illustrating key points, shedding lighton the application of survival analysis in a way that is useful for graduatestudents, researchers, and practitioners in biostatistics.

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关键词：Survival Analysis Edition Analysi Applied University clinical received survival methods

Contents
1 Introduction .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 What Is Survival Analysis? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 What You Need to Know to Use This Book . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Survival Data and Censoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Some Examples of Survival Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Additional Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Basic Principles of Survival Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1 The Hazard and Survival Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Other Representations of a Survival Distribution .. . . . . . . . . . . . . . . . . . 13
2.3 Mean and Median Survival Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 Parametric Survival Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5 Computing the Survival Function from the Hazard Function .. . . . . 19
2.6 A Brief Introduction to Maximum Likelihood Estimation . . . . . . . . . 20
2.7 Additional Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Nonparametric Survival Curve Estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1 Nonparametric Estimation of the Survival Function . . . . . . . . . . . . . . . 25
3.2 Finding the Median Survival and a Confidence Interval
for the Median .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3 Median Follow-Up Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4 Obtaining a Smoothed Hazard and Survival Function Estimate . . . 32
3.5 Left Truncation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.6 Additional Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4 Nonparametric Comparison of Survival Distributions . . . . . . . . . . . . . . . . . 43
4.1 Comparing Two Groups of Survival Times . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2 Stratified Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.3 Additional Note . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5 Regression Analysis Using the Proportional Hazards Model . . . . . . . . . . 55
5.1 Covariates and Nonparametric Survival Models . . . . . . . . . . . . . . . . . . . . 55
5.2 Comparing Two Survival Distributions Using
a Partial Likelihood Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.3 Partial Likelihood Hypothesis Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.3.1 The Wald Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.3.2 The Score Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.3.3 The Likelihood Ratio Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.4 The Partial Likelihood with Multiple Covariates . . . . . . . . . . . . . . . . . . . 63
5.5 Estimating the Baseline Survival Function.. . . . . . . . . . . . . . . . . . . . . . . . . 64
5.6 Handling of Tied Survival Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.7 Left Truncation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.8 Additional Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6 Model Selection and Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.1 Covariate Adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.2 Categorical and Continuous Covariates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.3 Hypothesis Testing for Nested Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.4 The Akaike Information Criterion for Comparing
Non-nested Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.5 Including Smooth Estimates of Continuous Covariates
in a Survival Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.6 Additional Note . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
7 Model Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
7.1 Assessing Goodness of Fit Using Residuals . . . . . . . . . . . . . . . . . . . . . . . . 87
7.1.1 Martingale and Deviance Residuals . . . . . . . . . . . . . . . . . . . . . . . 87
7.1.2 Case Deletion Residuals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.2 Checking the Proportion Hazards Assumption . . . . . . . . . . . . . . . . . . . . . 94
7.2.1 Log Cumulative Hazard Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
7.2.2 Schoenfeld Residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
7.3 Additional Note . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
8 Time Dependent Covariates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
8.1 Introduction.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
8.2 Predictable Time Dependent Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
8.2.1 Using the Time Transfer Function . . . . . . . . . . . . . . . . . . . . . . . . . 107
8.2.2 Time Dependent Variables That Increase
Linearly with Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
8.3 Additional Note . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
9 Multiple Survival Outcomes and Competing Risks. . . . . . . . . . . . . . . . . . . . . 113
9.1 Clustered Survival Times and Frailty Models. . . . . . . . . . . . . . . . . . . . . . . 113
9.1.1 Marginal Survival Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
9.1.2 Frailty Survival Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
9.1.3 Accounting for Family-Based Clusters
in the “ashkenazi” Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
9.1.4 Accounting for Within-Person Pairing of Eye
Observations in the Diabetes Data . . . . . . . . . . . . . . . . . . . . . . . . . 120
9.2 Cause-Specific Hazards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
9.2.1 Kaplan-Meier Estimation with Competing Risks . . . . . . . . . 121
9.2.2 Cause-Specific Hazards and Cumulative
Incidence Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
9.2.3 Cumulative Incidence Functions for Prostate
Cancer Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
9.2.4 Regression Methods for Cause-Specific Hazards . . . . . . . . . 128
9.2.5 Comparing the Effects of Covariates on
Different Causes of Death . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
9.3 Additional Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
10 Parametric Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
10.1 Introduction.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
10.2 The Exponential Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
10.3 The Weibull Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
10.3.1 Assessing theWeibull Distribution as a Model
for Survival Data in a Single Sample . . . . . . . . . . . . . . . . . . . . . . 138
10.3.2 Maximum Likelihood Estimation of Weibull
Parameters for a Single Group of Survival Data . . . . . . . . . . 141
10.3.3 Profile Weibull Likelihood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
10.3.4 Selecting a Weibull Distribution to Model
Survival Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
10.3.5 Comparing Two Weibull Distributions Using
the Accelerated Failure Time and Proportional
Hazards Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
10.3.6 A Regression Approach to the Weibull Model .. . . . . . . . . . . 148
10.3.7 Using the Weibull Distribution to Model
Survival Data with Multiple Covariates . . . . . . . . . . . . . . . . . . . 149
10.3.8 Model Selection and Residual Analysis with
Weibull Survival Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
10.4 Other Parametric Survival Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
10.5 Additional Note . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
11 Sample Size Determination for Survival Studies . . . . . . . . . . . . . . . . . . . . . . . . 157
11.1 Power and Sample Size for a Single Arm Study. . . . . . . . . . . . . . . . . . . . 157
11.2 Determining the Probability of Death in a Clinical Trial . . . . . . . . . . . 161
11.3 Sample Size for Comparing Two Exponential Survival
Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
11.4 Sample Size for Comparing Two Survival Distributions
Using the Log-Rank Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
11.5 Determining the Probability of Death
from a Non-parametric Survival Curve Estimate . . . . . . . . . . . . . . . . . . . 166
11.6 Example: Calculating the Required Number of Patients
for a Randomized Study of Advanced Gastric Cancer Patients . . . . 169
11.7 Example: Calculating the Required Number of Patients
for a Randomized Study of Patients with Metastatic
Colorectal Cancer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
11.8 Using Simulations to Estimate Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
11.9 Additional Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
12 Additional Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
12.1 Using Piecewise Constant Hazards to Model Survival Data . . . . . . . 177
12.2 Interval Censoring .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
12.3 The Lasso Method for Selecting Predictive Biomarkers . . . . . . . . . . . 192
A A Basic Guide to Using R for Survival Analysis . . . . . . . . . . . . . . . . . . . . . . . . 201
A.1 The R System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
A.1.1 A First R Session . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
A.1.2 Scatterplots and Fitting Linear Regression Models . . . . . . . 204
A.1.3 Accommodating Non-linear Relationships . . . . . . . . . . . . . . . . 207
A.1.4 Data Frames and the Search Path for Variable Names . . . . 209
A.1.5 Defining Variables Within a Data Frame . . . . . . . . . . . . . . . . . . 211
A.1.6 Importing and Exporting Data Frames . . . . . . . . . . . . . . . . . . . . 211
A.2 Working with Dates in R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
A.2.1 Dates and Leap Years. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
A.2.2 Using the “as.date” Function .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
A.3 Presenting Coefficient Estimates Using Forest Plots . . . . . . . . . . . . . . . 215
A.4 Extracting the Log Partial Likelihood and Coefficient
Estimates from a coxph Object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .223
R Package Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .225

mittie 发表于 2016-6-27 09:36
by Dirk F. Moore
Dirk F. Moore is Associate Professor ofBiostatistics at the Rutgers School of Pub ...

非常好

谢谢楼主    R语言类应用

Thanks

非常及时的资源，目前正在研究这些方面。很感谢楼主的分享

mittie 发表于 2016-6-27 09:36
by Dirk F. Moore
Dirk F. Moore is Associate Professor ofBiostatistics at the Rutgers School of Pub ...

好的好的

想问一下第二个附件下载后用什么程序打开？

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