Course Analytical Methods for Competing Events


Time to event data with two or more types of endpoints are found in many epidemiological settings and are commonly analyzed using methods for competing risks. A competing risk is defined as an endpoint that precludes the observation of another event. The most common approach for the analysis of data with competing risks is to treat the times for one of the endpoints as censored observations for the other. This approach is closely linked to the use of semi-parametric models for the analysis of cause-specific hazards under a proportionality assumption. In this course, we will describe an application of a mixture of parametric survival distributions for the analysis of time to event data with competing risks. We treat competing events as distinct outcomes in a mixture of parametric survival distributions and use the three-parameter generalized gamma distribution to summarize the times to events. An alternative method for the analysis of competing risks is to semi-parametrically model the sub-hazards in unexposed and in exposed individuals of the cumulative incidences as proportional and to test whether they are different from 1. In this course, we will show the consequences of assuming proportionality of subhazards and indicate the limitations of that approach to appropriately describe effects of exposures on competing risks.


Alvaro Muñoz, Ph.D.
Professor of Epidemiology
Johns Hopkins Bloomberg School of Public Health
Baltimore, MD, USA


The course Analytical Methods for Competing Events is addressed to professional or academics statisticians and researchers who are interested in being introduced to the use of these methods.


It is expected that participants are familiar with survival analysis at an intermediate level including familiarity with proportional hazards regression. The laboratories will use SAS but programs to run the laboratories will be provided

SEA informs that previously there are two complementary courses: Introduction to the SAS® system on October from 24th to 27th; and Statistical Modelling with SAS® on November from 28th to 30th and December 1st.

Program of Lectures and Laboratories:

December 13

  • 10:00 – 11:50: Lecture 1
    Analytical methods for incomplete observations in cohort studies.
    Completing the missing information due to censoring and late entries.
  • 12:10 – 14:00 Lecture 2
    Measures to compare time-to-event data: relative percentiles and relative hazards; Taxonomy of hazard functions of the general gamma distribution and Parametric survival analysis based on the general gamma distribution
  • Reference: Cox C, Chu H, Schneider MF, Muñoz A. Parametric Survival Analysis and Taxonomy of Hazard Functions for the Generalized Gamma Distribution. Stat Med 2007;26:4352-74.

  • 16:00 – 18:00 Laboratory
    redistribution of right censored; right censored and late entries; competing risks with right censoring and laboratory on parametric models

December 14

  • 10:00 – 11:50: Lecture 1
    Basic concepts in competing risks: cause-specific hazard functions; sub-hazards of the cumulative incidences; mixture and conditional hazards. Proportionality of the cause-specific hazard functions and of the subhazard functions
  • 12:10 – 14:00 Lecture 2
    Inference for mutually exclusive competing events through a mixture of generalized gamma distributions.
  • References:
    Cole SR, Li R, Anastos K, Detels R, Young M, Chmiel JS, Muñoz A.Accounting for leadtime in cohort studies: evaluating when to initiate HIV therapies.Stat Med 2004;23:3351-63.
    Checkley W, Brower RG, Muñoz A. Inference for mutually exclusive competing events through a mixture of generalized gamma distributions. Epidemiology 2010;21:557-65.

  • 16:00 – 18:00 Laboratory
    Analysis of the data in Table 10.1 of Marubini et al. using mixtures of generalized gamma distributions.

December 15

  • 10:00 – 11:50: Lecture 1
    Comparison of methods for the analysis of competing risks data.
  • 12:10 – 14:00 Lecture 2
    Non-proportionality of sub-hazards in the competing events framework and tethering of the relative sub-hazards.
  • Reference:
    Muñoz A, Abraham A, Matheson M, Wada N.Non-proportionality of sub-hazards in the competing events framework. Abstract of invited presentation at conference on risk assessment and evaluation of predictions;October 12-14, 2011; Silver Spring. MD, USA.

  • 16:00 – 18:00 Laboratory
    Analysis of data using relative sub-hazards as the measure of interest in both the settings of proportional and non-proportional sub-hazards.


Servei d'Estadística Aplicada, UAB

Sponsored by:

Registration fees (2011):

Pre-registration will be formalized via the Servei d'Estadística Aplicada filling out the registration form that you will find on the web. Once we receive your form we will send an email to confirm that either you have an assigned place or you are on the waiting list.

Concept Quantity Import
    External Mixed UAB
(before November 27th)
1 assist 550,00 €  550,00 €  350,00 €
(after November 27th)
1 assist 700,00 €  700,00 €  500,00 €

UAB fee: The whole UAB Staff may benefit of this fee (administration, professors, researchers, students). Students coming from other universities who have a current course registration (They have to send a copy of the course registration). However, if an invoice is required, they will have to be registered with the standard fee.

Discounts: Not accumulative.

(*) 25% discount for morning sessions (theory) only.

(*) 25% discount for all members of Statistical Modelling Society.

If an invoice is required, you may state the name of the company in the payment receipt instead of the participant name. Once the payment of the course has been made there will be no refund except in some special circumstances.
Please wait for our confirmation before paying.

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