# Course detail

### LCE5809 - Analysis of Survival

__Credit hours__

In-class work per week |
Practice per week |
Credits |
Duration |
Total |

3 |
1 |
8 |
15 weeks |
120 hours |

__Instructor__

Edwin Moises Marcos Ortega

__Objective__

The set of techniques and statistical models for the analysis of data whose response variable is the time until the occurrence of an event (for example, the death of an individual) is called survival analysis. These data are often censured, i.e. the comments are incomplete in that, for some reason it was not possible to observe the occurrence of the event. In this sense, will be developed and applied techniques of analysis of survival in agronomic experiments and related areas, showing the estimation techniques, verification of adjustment of the models, analysis of waste and diagnostics, as well as inference and obtaining the confidence intervals. The specific objectives are: (i). To study and to determine the distribution of the times of failure; ii) compare the times of failure for different groups. (iii) study the prognostic value of possible risk factors.

__Content__

1 Introduction 2. Basic concepts: time of failure, types of censorship, data representation of survival. 3. Functions of interest: Function of survival, function of risk, relationship between the functions. 4. Non-parametric methods for the analysis of data on survival: the Kaplan-Meier analysis, actuarial estimator or ironing board of life, Nelson-Aalen estimator, the comparison of survival curves. 5. Proportional Hazards Model: Cox regression model, pets of physical, checking the assumption of the Cox proportional hazards and analysis of waste. 6. Parametric methods for the analysis of data on survival: basic distributions in survival analysis (Exponential, Weibull, Log-normal, extreme value, generalized Range, Weibull Multiple, Weibull-exponenciado), pets of parameters, confidence interval of parameters, choose the appropriate distribution. 7. Models of regression in the analysis of survival: the logistic regression models, exponential, Weibull widespread range, inference in logistic regression models and analysis of waste and diagnosis. 8. Regression models with cure fraction. 9. Regression models bivariates with censored data.

__Bibliography__

Allison, Paul D. Survival Analysis Using SAS: A Practical Guide. 2010. 2ed. Cary, NC: SAS Institute Inc.

Collet, A. Modelling Survival Data in Medical Research. Chapman and Hall, London. 2003.

Cordeiro, G. M. A Teoria de Verossimilhança. Associação Brasileira de Estatística, Rio de Janeiro, 10º SINAPE. 1992.

Cox, D. R. e Oakes, D. Analysis of Survival Data. Chapman and Hall, London. 1984.

Hosmer, D. W. e Lemeshow, J. F. Applied Survival Analysis. John Wiley and Sons, New York. 1992.

Ibrahim, J. G., Chen, M, H., e Sinha, D. Bayesian Survival Analysis. Springer -Verlag, New York. 2001.

Kalbfleisch, J. D. e Prentice, R. L. The Statistical Analysis of Failure Time Data. John Wiley and Sons, New York. 1980.

Kleinbaum, David G.e Mitchel Klein. Survival Analysis a Self-Learning Tex. 2005 - 2ed.Springer, USA.

Kaplan, E. L. e Meier, P. Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53, 457-481. 1958

Klein, J. P. e Moeschberger, M. L. Survival Analysis Techniques for censored anf Truncated Data. Springer -Verlag, New York. 1997.

Lawless, J. F. Statistical Models and Methods for Lifetime Data. John Wiley and Sons, New York. 2003.

Tableman, M. and Kim, J.S. Survival Analysis using S. Anlaysis of Time-to-Event Data. Chapmann and Hall. New York. 2003.

Mudholkar, G. S., Srivastava, D. K., and Friemer, M. The exponentiated Weibull family: A reanalysis of the bus-motor-failure data. Technometrics 37, 436-445. 1995.

Nelson, W. Accelerated Life Testing: Statistical Models, Data Analysis and Test Plans. John Wiley and Sons, New York. 1990

Ortega, E. M. M. Análise de Influência Local e Resíduos nos Modelos de Regressão Log-gama Generalizados. São Paulo: Tese de Doutorado. 2001.

VENABLES, W.N. e RIPLEY, B.D. Statistics and Computing. Springer-Verlag. 2002. 495p.