# Seminars

# Statistics Lectures: Probabilistic Models and Statistical Analysis of Event Times

Start Date: March 10, 2019

End Date: March 13, 2019

*By Prof. Edsel Penna (Department of Statistics, University of South Carolina, Columbia, USA)*The three special lectures will deal with the probabilistic modeling and statistical inference methods when dealing with lifetime data, and more generally, event-time data. Such types of data sets arise in many settings such as biomedical, public health, engineering, the physical sciences, and the social sciences. The mathematical and statistical treatment of event-time data differs from the typical statistical analysis methods since the “usual” model assuming or using the Gaussian or normal distribution is not anymore appropriate. In addition, when dealing with event times, the data accrual or the sampling process is usually constrained by right censoring, left censoring, truncation, and other types of data accrual constraints. As such the data available for statistical inferences are not all complete but some will be incomplete. Hence the question of how to utilize such incomplete data for purposes of estimating model parameters (in both parametric and nonparametric models), comparison of several groups, ascertaining effects of interventions, prediction and forecasting, and model diagnostics and validation. Lecture 1 will start with basic ideas pertaining to the probabilistic modeling of event-time variables such as hazard functions, parametric and nonparametric models, processes leading to incomplete data such as right and left censoring, truncation, etc. Classes of lifetime distributions will also be discussed and complex reliability systems will also be discussed. Models for event-time data that incorporate covariates such as the Cox proportional hazards model (Cox PHM), the accelerated failure time model (AFTM), and Aalen’s additive hazards model. Lecture 2 will deal with statistical inference methods for event-time models. The no-covariate setting but with censored data will first be treated. Likelihood-based methods for parametric estimation, hypothesis testing, and confidence interval construction in parametric models will be discussed. Some Bayesian approaches will also be touched upon. We will then proceed with inference in nonparametric models. In particular, the Kaplan-Meier or product-limit estimator of the survivor function will be discussed, together with its use in the comparison of several groups (log-rank test). Inference for regression models, such as the Cox PHM and the AFTM will then be described and illustrated. Lecture 3 will deal with the modeling and analysis of event times arising in more complex settings. We will start with statistical inference methods for the lifetime of complex reliability and engineering systems, which are systems formed from several components. In particular, we will examine if inference for the system lifetime could be improved by taking into consideration the right-censored component lifetime data. We will then proceed with the modeling and analysis of recurrent event data. Such data arise in settings where the event of interest recurs or are observed repeatedly (for example, tumor occurrence; machine failure; earthquakes; mass shootings; etc.). We will discuss some peculiarities in such settings such as size-biased sampling and the sum-quota accrual constraint, and how to deal with such phenomena in the statistical inference methods. Time, permitting, mention will be made of more recent models that we have been studying such as dynamic models incorporating competing risks and longitudinal markers. Some References: 1. Kalbfleisch, J. and Prentice, R. (2002). The Statistical Analysis of Failure Time Data. Second Edition. Wiley: New York. 2. Andersen, P., Borgan, O., Gill, R., and Keiding, N. (1993). Statistical Models Based on Counting Processes. Springer-Verlag: New York. 3. Fleming, T. and Harrington, D. (1991). Counting Processes and Survival Analysis. Wiley: New York. 4. Aalen, O., Borgan, O. and Gjessing, H. (2008). Survival and Event History Analysis: A Process Point of View. Springer-Verlag: New York. 5. Kaplan, E. and Meier, P. (1958). Nonparametric estimation from incomplete observations. JASA, 53, 457-481. 6. Cox, D. (1972). Regression models and life tables (with discussion). JRSS B, 34, 187-220. 7. Aalen, O. (1978). Nonparametric inference for a family of counting processes. Ann. Statist., 6, 701-726. 8. Andersen, P. and Gill, R. (1982). Cox’s regression model for counting processes: a large sample study. Ann. Statist., 10, 1100-1120. 9. Pena, E., Strawderman, R. and Hollander, M. (2001). Nonparametric estimation with recurrent event data. JASA, 96, 1299-1315. 10. Pena, E., Slate, E. and Gonzalez, JR (2007). Semiparametric inference for a general class of models for recurrent events. JSPI, 137, 1727-1747.

**Biography:**Dr. Edsel A. Peña is currently Professor in the Department of Statistics at the University of South Carolina. He obtained his PhD from Florida State University in 1986. He has also taught at the University of the Philippines at Los Banos, Florida State University, Bowling Green State University in Ohio, and the University of Michigan. His research expertise is in time-to-event data, including survival and recurrent event data, reliability and engineering applications, multiple testing and simultaneous inference, model validation, decision theory, Bayesian analysis and nonparametric statistics. He has published over 100 peer-reviewed articles in top tier statistics and interdisciplinary journals. He has been successful in acquiring research funding from NSF and NIH, including serving as Director of the Biometry Core of the NIH-supported University of South Carolina Center for Colon Cancer Research. He has served as associate editor for multiple statistics journals, has served on review panels for the NSF and NIH, and has chaired the Noether Award Committee for the American Statistical Association (ASA), as well as occupied positions in other sections of the ASA (Risk Analysis Section and the Nonparametric Section). He has garnered teaching and research awards at Bowling Green State University and the University of South Carolina. He is a Fellow of the American Statistical Association and an Elected Member of the International Statistical Institute (ISI). He is currently the Executive Secretary of the Institute of Mathematical Statistics (IMS). For more information, visit his website at http://www.stat.sc.edu/~pena.

### More Information:

*Prof. Hernando Ombao: email: hernando.ombao@kaust.edu.sa*

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