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Flexible Parametric Survival Analysis Using Stata: Beyond the Cox Model [Pehme köide]

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(University College London and MRC Clinical Trials Unit, UK), (University of Leicester, UK)
  • Formaat: Paperback / softback, 339 pages, kõrgus x laius: 229x152 mm, kaal: 748 g
  • Ilmumisaeg: 04-Aug-2011
  • Kirjastus: Stata Press
  • ISBN-10: 1597180793
  • ISBN-13: 9781597180795
Teised raamatud teemal:
Flexible Parametric Survival Analysis Using Stata: Beyond the Cox ModelSuurem pilt
  • Formaat: Paperback / softback, 339 pages, kõrgus x laius: 229x152 mm, kaal: 748 g
  • Ilmumisaeg: 04-Aug-2011
  • Kirjastus: Stata Press
  • ISBN-10: 1597180793
  • ISBN-13: 9781597180795
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781597180795.html
Märksõnad:

Through real-world case studies, this book shows how to use Stata to estimate a class of flexible parametric survival models. It discusses the modeling of time-dependent and continuous covariates and looks at how relative survival can be used to measure mortality associated with a particular disease when the cause of death has not been recorded. The book describes simple quantification of differences between any two covariate patterns through calculation of time-dependent hazard ratios, hazard differences, and survival differences.

List of tables
xiii
List of figures
xv
Preface xxv
1 Introduction
1(22)
1.1 Goals
1(1)
1.2 A brief review of the Cox proportional hazards model
2(1)
1.3 Beyond the Cox model
2(11)
1.3.1 Estimating the baseline hazard
2(3)
1.3.2 The baseline hazard contains useful information
5(3)
1.3.3 Advantages of smooth survival functions
8(1)
1.3.4 Some requirements of a practical survival analysis
9(1)
1.3.5 When the proportional-hazards assumption is breached
10(3)
1.4 Why parametric models?
13(1)
1.4.1 Smooth baseline hazard and survival functions
13(1)
1.4.2 Time-dependent HRs
13(1)
1.4.3 Modeling on different scales
13(1)
1.4.4 Relative survival
13(1)
1.4.5 Prediction out of sample
14(1)
1.4.6 Multiple time scales
14(1)
1.5 Why not standard parametric models?
14(2)
1.6 A brief introduction to stpm2
16(1)
1.6.1 Estimation (model fitting)
16(1)
1.6.2 Postestimation facilities (prediction)
17(1)
1.7 Basic relationships in survival analysis
17(1)
1.8 Comparing models
18(1)
1.9 The delta method
19(1)
1.10 Ado-file resources
20(1)
1.11 How our book is organized
21(2)
2 Using stset and stsplit
23(14)
2.1 What is the stset command?
23(1)
2.2 Some key concepts
23(1)
2.3 Syntax of the stset command
24(1)
2.4 Variables created by the stset command
25(1)
2.5 Examples of using stset
25(8)
2.5.1 Standard survival data
26(1)
2.5.2 Using the scale() option
27(1)
2.5.3 Date of diagnosis and date of exit
27(1)
2.5.4 Date of diagnosis and date of exit with the scale() option
28(1)
2.5.5 Restricting the follow-up time
29(2)
2.5.6 Left-truncation
31(1)
2.5.7 Age as the time scale
32(1)
2.6 The stsplit command
33(2)
2.6.1 Time-dependent effects
33(1)
2.6.2 Time-varying covariates
34(1)
2.7 Conclusion
35(2)
3 Graphical introduction to the principal datasets
37(10)
3.1 Introduction
37(1)
3.2 Rotterdam breast cancer data
37(2)
3.3 England and Wales breast cancer data
39(3)
3.4 Orchiectomy data
42(3)
3.5 Conclusion
45(2)
4 Poisson models
47(44)
4.1 Introduction
47(1)
4.2 Modeling rates with the Poisson distribution
48(2)
4.3 Splitting the time scale
50(7)
4.3.1 The piecewise exponential model
53(4)
4.3.2 Time as just another covariate
57(1)
4.4 Collapsing the data to speed up computation
57(2)
4.5 Splitting at unique failure times
59(3)
4.5.1 Technical note: Why the Cox and Poisson approaches are equivalent
61(1)
4.6 Comparing a different number of intervals
62(4)
4.7 Fine splitting of the time scale
66(1)
4.8 Splines: Motivation and definition
67(14)
4.8.1 Calculating splines
69(1)
4.8.2 Restricted cubic splines
70(1)
4.8.3 Splines: Application to the Rotterdam data
71(3)
4.8.4 Varying the number of knots
74(4)
4.8.5 Varying the location of the knots
78(1)
4.8.6 Estimating the survival function
79(2)
4.9 FPs: Motivation and definition
81(9)
4.9.1 Application to Rotterdam data
83(4)
4.9.2 Higher order FP models
87(2)
4.9.3 FP function selection procedure
89(1)
4.10 Discussion
90(1)
5 Royston--Parmar models
91(34)
5.1 Motivation and introduction
92(9)
5.1.1 The exponential distribution
92(3)
5.1.2 The Weibull distribution
95(1)
5.1.3 Generalizing the Weibull
96(4)
5.1.4 Estimating the hazard function
100(1)
5.2 Proportional hazards models
101(7)
5.2.1 Generalizing the Weibull
101(2)
5.2.2 Example
103(1)
5.2.3 Comparing parameters of PH(1) and Weibull models
104(4)
5.3 Selecting a spline function
108(3)
5.3.1 Knot positions
108(1)
Example
109(1)
5.3.2 How many knots?
110(1)
5.4 PO models
111(3)
5.4.1 Introduction
111(1)
5.4.2 The loglogistic model
112(1)
5.4.3 Generalizing the loglogistic model
113(1)
5.4.4 Comparing parameters of PO(l) and loglogistic models
113(1)
Example
114(1)
5.5 Probit models
114(4)
5.5.1 Motivation
114(1)
5.5.2 Generalizing the probit model
115(1)
5.5.3 Comparing parameters of probit(l) and lognormal models
116(1)
5.5.4 Comments on probit and POs models
117(1)
5.6 Royston-Parmar (RP) models
118(6)
5.6.1 Models with 0 not equal to 0 or 1
119(1)
5.6.2 Example
119(1)
5.6.3 Likelihood function and parameter estimation
120(1)
5.6.4 Comparing regression coefficients
121(1)
5.6.5 Model selection
121(1)
5.6.6 Sensitivity to number of knots
122(1)
5.6.7 Sensitivity to location of knots
123(1)
5.7 Concluding remarks
124(1)
6 Prognostic models
125(42)
6.1 Introduction
125(1)
6.2 Developing and reporting a prognostic model
126(1)
6.3 What does the baseline hazard function mean?
127(2)
6.3.1 Example
128(1)
6.4 Model selection
129(5)
6.4.1 Choice of scale and baseline complexity
130(1)
Example
130(1)
6.4.2 Selection of variables and functional forms
131(1)
Example
132(2)
6.5 Quantitative outputs from the model
134(13)
6.5.1 Survival probabilities for individuals
134(3)
6.5.2 Survival probabilities across the risk spectrum
137(1)
6.5.3 Survival probabilities at given covariate values
138(2)
6.5.4 Survival probabilities in groups
140(2)
6.5.5 Plotting adjusted survival curves
142(1)
6.5.6 Plotting differences between survival curves
143(2)
6.5.7 Gentiles of the survival distribution
145(2)
6.6 Goodness of fit
147(2)
6.6.1 Example
148(1)
6.7 Discrimination and explained variation
149(4)
6.7.1 Example
151(1)
6.7.2 Harrell's C index of concordance
152(1)
6.8 Out-of-sample prediction: Concept and applications
153(8)
6.8.1 Extrapolation of survival functions: Basic technique
153(2)
6.8.2 Extrapolation of survival functions: Further investigations
155(2)
6.8.3 Validation of prognostic models: Basics
157(3)
6.8.4 Validation of prognostic models: Further comments
160(1)
6.9 Visualization of survival times
161(3)
6.9.1 Example
161(3)
6.10 Discussion
164(3)
7 Time-dependent effects
167(60)
7.1 Introduction
167(1)
7.2 Definitions
168(1)
7.3 What do we mean by a TD effect?
169(7)
7.4 Proportional on which scale?
176(3)
7.5 Poisson models with TD effects
179(11)
7.5.1 Piecewise models
180(4)
7.5.2 Using restricted cubic splines
184(6)
7.6 RP models with TD effects
190(15)
7.6.1 Piecewise HRs
190(3)
7.6.2 Continuous TD effects
193(8)
7.6.3 More than one TD effect
201(2)
7.6.4 Stratification is the same as including TD effects
203(2)
7.7 TD effects for continuous variables
205(6)
7.8 Attained age as the time scale
211(7)
7.8.1 The orchiectomy data
211(1)
7.8.2 Proportional hazards model
212(2)
7.8.3 TD model
214(4)
7.9 Multiple time scales
218(1)
7.10 Prognostic models with TD effects
219(5)
7.10.1 Example
220(4)
7.11 Discussion
224(3)
8 Relative survival
227(46)
8.1 Introduction
227(1)
8.2 What is relative survival?
227(1)
8.3 Excess mortality and relative survival
228(3)
8.3.1 Excess mortality
228(2)
8.3.2 Relative survival is a ratio
230(1)
8.4 Motivating example
231(2)
8.5 Life-table estimation of relative survival
233(2)
8.5.1 Using strs
234(1)
8.6 Poisson models for relative survival
235(11)
8.6.1 Piecewise models
235(6)
8.6.2 Restricted cubic splines
241(5)
8.7 RP models for relative survival
246(13)
8.7.1 Likelihood for relative survival models
247(1)
8.7.2 Proportional cumulative excess hazards
247(1)
8.7.3 RP models on other scales
248(1)
8.7.4 Application to England and Wales breast cancer data
248(2)
8.7.5 Relative survival models on other scales
250(3)
8.7.6 Time-dependent effects
253(6)
8.8 Some comments on model selection
259(8)
8.9 Age as a continuous variabl
267(5)
8.10 Concluding remarks
272(1)
9 Further topics
273(58)
9.1 Introduction
273(1)
9.2 Number needed to treat
273(2)
9.2.1 Example
274(1)
9.3 Average and adjusted survival curves
275(8)
9.3.1 Renal data
277(6)
9.4 Modeling distributions with RP models
283(13)
9.4.1 Example 1: Rotterdam breast cancer data
283(2)
9.4.2 Example 2: CD4 lymphocyte data
285(9)
9.4.3 Example 3: Prostate cancer data
294(2)
9.5 Multiple events
296(8)
9.5.1 Introduction
296(1)
9.5.2 The AG model
297(1)
9.5.3 The WLW model
298(1)
9.5.4 The PWP model
298(1)
9.5.5 Multiple events in RP models
298(6)
9.5.6 Summary
304(1)
9.6 Bayesian RP models
304(6)
9.6.1 Introduction
304(1)
9.6.2 The "zeros trick" in WinBUGS
305(1)
9.6.3 Fitting a RP model
305(5)
9.6.4 Summary
310(1)
9.7 Competing risky
310(7)
9.7.1 Summary
316(1)
9.8 Period analysis
317(5)
9.8.1 Introduction
317(1)
9.8.2 What is period analysis?
317(2)
9.8.3 Application to England and Wales breast cancer data
319(3)
9.9 Crude probability of death from relative survival models
322(7)
9.9.1 Introduction
322(1)
9.9.2 Application to England and Wales breast cancer data
323(6)
9.9.3 Conclusion
329(1)
9.10 Final remarks
329(2)
References 331(10)
Author index 341(4)
Subject index 345
Patrick Royston is a senior medical statistician at the Medical Research Council, London, UK. He has published research papers on a variety of topics in leading statistics journals. His key interests include multivariable modeling and validation, survival analysis, design and analysis of clinical trials, and statistical computing and algorithms. He is an associate editor of the Stata Journal.

Paul Lambert is a reader in medical statistics at Leicester University, UK. His main interest is in the development and application of statistical methods in population-based cancer research and related fields. He has published widely in leading statistical and medical journals.