Copies of the classnotes are on the internet in PDF format as given below. The "Proofs of Theorems" files were prepared in Beamer. The "Printout of Proofs" are printable PDF files of the Beamer slides without the pauses. These notes and supplements have not been classroom tested (and so may have some typographical errors).
Survival Analysis (STAT 5750) has a formal prerequisite of Linear Algebra (MATH 2050) and permission of the advisor or the instructor. The catalog discription is: "Topics include concepts of time-to-event data, the hazard and survival functions, censoring mechanisms, non-parametric, semi-parametric, and parametric estimations and inferences, and comparison of survival curves." These descriptions are based on the ETSU 2019-20 Undergraduate Catalog.
Chapter 1. Introduction to Regression Modeling of Survival Data.
- Section 1.1. Introduction.
- Section 1.2. Typical Censoring Mehcanisms.
- Section 1.3. Example Data Sets.
- Study Guide 1.
Chapter 2. Descriptive Methods for Survival.
- Section 2.1. Introduction.
- Section 2.2. Estimation of the Surivorship Function.
- Section 2.3. Using the Estimated Survivorship Function.
- Section 2.4. Comparison of Survivorship Functions.
- Section 2.5. Other Functions of Survival Time and Their Estimators.
- Study Guide 2.
Chapter 3. Regression Models for Survival Data.
- Section 3.1. Introduction.
- Section 3.2. Semiparametric Regression Models.
- Section 3.3. Fitting the Proportional Hazards Regression Model.
- Section 3.4. Fitting the Proportional Hazards Model with Tied Survival Times.
- Section 3.5. Estimating the Survivorship Function of the Proportional Hazards Regression Model.
- Study Guide 3.
Chapter 4. Interpretation of a Fitted Proportional Hazards Regression Model.
- Section 4.1. Introduction.
- Section 4.2. Normal Scale Covariate.
- Section 4.3. Continuous Scale Covariate.
- Section 4.4. Multiple-Covariate Models.
- Section 4.5. Interpretation and use of the Covariate-Adjusted Survivorship Function.
- Section 4.6. Confidence Interval Estimation of the Covariate-Adjusted Survivorship Function.
- Study Guide 4.
Chapter 5. Model Development.
- Section 5.1. Introduction.
- Section 5.2. Purposeful Selection of Covariates.
- Section 5.3. Stepwise Selection of Covariates.
- Section 5.4. Best Subsets Selection of Covariates.
- Section 5.5. Numerical Problems.
- Study Guide 5.
Chapter 6. Assessment of Modal Adequacy.
- Section 6.1. Introduction.
- Section 6.2. Residuals.
- Section 6.3. Methods for Assessing the Proportional Hazards Assumption.
- Section 6.4. Identification of Influential and Poorly Fit Subjects.
- Section 6.5. Overall Goodness-of-Fit Tests and Measures.
- Section 6.6. Interpretation and Presentation of the Final Model.
- Study Guide 6.
Chapter 7. Extensions of the Proportional Hazards Model.
- Section 7.1. Introduction.
- Section 7.2. The Stratified Proportional Hazards Model.
- Section 7.3. Time-Varying Covariates.
- Section 7.4. Truncated, Left Censored, and Interval Censored Data.
- Study Guide 7.
Chapter 8. Parametric Regression Models.
- Section 8.1. Introduction.
- Section 8.2. The Exponential Regression Model.
- Section 8.3. The Weibull Regression Model.
- Section 8.4. The Log-Logistic Regression Model.
- Section 8.5. Other Parametric Regression Models.
- Study Guide 8.
Chapter 9. Other Models and Topics.
- Section 9.1. Introduction.
- Section 9.2. Recurrent Even Models.
- Section 9.3. Frailty Models.
- Section 9.4. Nested Case-Control Studies.
- Section 9.5. Additive Models.
- Study Guide 9.
Appendices.
- Appendix 1. The Delta Method.
- Appendix 2. An Introduction to the Counting Process Appraoch to Survival Analysis.
- Appendix 3. Percentiles for Computation of the Hall and Wellner Confidence Bands.
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