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Affiliated with Universidade de Vigo, Spain

Jacobo de Uña-Álvarez

Jacobo de Uña-Álvarez is Professor in Statistics at the Universidade de Vigo since 2010. His educational background includes a BSc in Mathematics (1995) and a PhD in Mathematical Statistics (1998), both at the University of Santiago de Compostela. His main research area is nonparametric and semiparametric statistics and its application to Survival Analysis and multi-state models, including censored and truncated data. He has published more than 100 research papers. He is Associate Editor of Annals of the Institute of Statistical Mathematics (2011- ), Brazilian Journal of Probability and Statistics (2015- ) and Test (2018- ). He currently chairs the SiDOR research group and the Biostatistics and Epidemiology unit at the Biomedical Research Center in Vigo.

Course description

This course will focus on methodological and practical issues in the scope of competing risks and multi-state models. Basic concepts, models, estimation algorithms and statistical software will be reviewed. Simulation exercises and real data analyses will be provided in order to enlighten the interpretation and to facilitate the understanding. Both nonparametric methods and semiparametric approaches will be considered.

Some background in foundations of statistics and in parametric and nonparametric inference is required. Background in Survival Analysis (Kaplan-Meier estimation, Cox regression) is recommended. BSc or MSc in Statistics, Biostatistics or Mathematics is ideal.

Target audience

PhD students and postgraduates in general.


  1. Introduction: Survival function and hazard function. Right-censoring and left-truncation. Competing risks. Markov and non-Markov multi-state models. Time-homogeneity and time inhomogeneity. Motivating examples (real data).
  2. Competing risks: The competing risks multi-state model. Non-identifiability in the latent failure time model. Cause-specific hazards (transition intensities) and sub-distribution hazards. Cumulative incidence functions. Simulating competing risks data. Nonparametric estimation.
  3. Proportional hazards regression models: Proportional cause-specific hazards model. Proportional sub-distribution hazards model.

Slides and script files will be distributed well in advance. Presentation of each of the three chapters will take 35 min, followed by 15 min of practical exercises, and then a 10 min break (3 hours in total).

Required software