Pop 509 Syllabus
Week 1 (February 6, 8): Parametric Survival Models
The hazard and survival functions in continuous time. Parametric forms and the distribution of log time. The exponential, Weibull, Gompertz, Gamma, Generalized Gamma, Coale-McNeil, and generalized F distributions. The U.S. life table.
Approaches to modelling the effects of covariates. Parametric families. Proportional hazards models (PH). Accelerated failure time models (AFT). The intersection of PH and AFT. Proportional odds models (PO). The intersection of PO and AFT. Recidivism in the U.S.
Week 2 (February 13, 15): Non-Parametric Survival Models
One-sample estimation with censored data. The Kaplan-Meier estimator. Greenwood's formula. The Nelson-Aalen estimator. Expectation of life. Comparison of several groups: Mantel-Haenszel and the log-rank test.
Regression: Cox's model and partial likelihood. The score and information. The problem of ties. Tests of hypotheses. Time-varying covariates. Estimating the baseline survival. Martingale residuals.
Week 3 (February 20, 22): Models for Discrete Data and Extensions
Cox's discrete logistic model and logistic regression. Modeling grouped continuous data and the complementary log-log transformation. Piece-wise constant hazards and Poisson regression.
Current status data versus retrospective data. Open intervals and time since last event. Backward recurrence times. Interval censoring.
Week 4 (February 27, 29): Competing Risks
Modeling multiple causes of failure. Research questions of interest. Cause-specific hazards. Overall survival. Cause-specific densities. Estimation: one-sample and the generalized Kaplan-Meier and Nelson-Aalen estimators.
Regression models. Weibull regression. Cox regression and the partial likelihood. Piece-wise exponential survival and multinomial logits. The identification problem. Multivariate and marginal survival. A bivariate example.
Week 5 (March 5, 7): Unobserved Heterogenity
Heterogeneity of frailty. Frailty distributions: gamma and inverse Gaussian. Subject-specific and population-average models. Heterogeneity's ruses.
Non-parametric estimation of the mixing distribution. Relaxing assumptions about the hazard. The identification problem. Heterogeneity and time-dependence.
Week 6 (March 12, 14): Multivariate Survival
Kindred lifetimes and shared frailty. Models for husbands and wives. Sibling survival.
Event-history models. The choice of time scale. Testing goodness of fit.
Bibliography
These are a few useful texts on survival analysis. The stars indicate the two texts that come closest to our coverage.
Andersen, P.K; O. Borgan, R. Gill, N. Keiding (1991). Statistical Models Based on Counting Processes. New York: Springer-Verlag.
Blossfeld, H-P; K. Golsch, G. Rohwer (2007). Event History Analysis with Stata. New Jersey: Lawrence Erlbaum Associates.
Box-Steffensmeier, J. and B. S. Jones (2004). Event History Modeling: A Guide for Social Scientists. Cambridge, England: Cambridge University Press.
*Cleves, M.; W. G. Gould, R. G. Gutierrez and J. Marchenko(2008). An Introduction to Survival Analysis Using Stata. Second Edition. College Station, Texas: Stata Press. (First Edition 2002, Revised edition 2004).
Cox, D. and D. Oakes (1984). Analysis of Survival Data. London: Chapman-Hall.
*Kalbfleisch J. D and R. L. Prentice (2002). The Statistical Analysis of Failure Time Data. Second Edition. New York: John Wiley. (First Edition 1980).
Singer, J.D and J. B. Willett (2003) Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence. Oxford, England: Oxford University Press.
Therneau, T. M. and P. M. Grambsch (2000). Modeling Survival Data: Extending the Cox Model. New York:Springer.