Hello Dr Zurakowski,

On the favourite links page of my website there is a link to an electronic statistical textbook, and there is a chapter on this topic I believe, not that I've read it, no time, I am way behind in just reading public health journals.

Thanks

Deborah Hilton Statistics Online

http://sites.google.com/site/deborahhilton/

SAS offers a solution. You can find the example at Example 66.10 Analysis of Recurrent Events Data. (http://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/viewer.htm#statug_phreg_sect055.htm). I also think the method used in example 66.11: analysis of cluster data will give you similar results by using robust sandwich covariance estimation method which accounts for within-subject correlations.

Maybe these articles can help:

Modeling repeated time-to-event health conditions with discontinuous risk intervals: an example of a longitudinal study of functional disability among older persons

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2735569/

Modelling recurrent events: comparison of statistical models with continuous and discontinuous risk intervals on recurrent malaria episodes data

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4132199/

Correlated time to event data: Modeling repeated clinical mastitis data from dairy cattle in New York State.

http://www.ncbi.nlm.nih.gov/pubmed/21035216

Empirical comparison of methods for analyzing multiple time-to-event outcomes in a non-inferiority trial: a breast cancer study.

http://www.ncbi.nlm.nih.gov/pubmed/23517401

Models for Repeated Events Data

http://www.epibiostat.ucsf.edu/dave/caps-talk.pdf

As you say, the events in a person of course are not independent,

people may vary in their intrinsic risk of an event so some people have

more events than others, there is also the effect that an event can change

your risk of a future event, for example making a person less at risk (acquired

immunity) or perhaps making them more at risk. This lack of independence is

commonly dealt with in one of two ways, either by Cox or Poisson regression with a robust standard error, (which essentially calculates the standard error directly using the mean data for each person rather than calculating it assuming a particular statistical model), or by fitting a random effect model, which models the variation in number of events per person by a statistical distribution. Often these two approaches will give very similar results. Multiple episode data should be displayed using a plot of the Nelson-Aalen cumulative hazards, this shows the timing of all the events with

the y-axis scaled to be the mean number of events per person. It has been common

to see publications where multiple events data have been analysed in terms of the

time to the first event, ignoring the other episodes, this is not recommended, and the appropriate methods are available in most statistical packages. I have looked for a very practical guide to how to do this but haven't found anything very suitable, some more technical references in addition to those given by others above, that might be useful are:

Estimation of intervention effects using first or multiple episodes in clinical trials: The Andersen-Gill model re-examined. Statistics in Medicine 29(3):328-336 Cheung YB, Xu Ying, Tan Sze Huey, Cutts F, Milligan PJM (2010)

The rate difference is a useful measure that combines efficacy with the level of incidence, for multiple episode data this method can be used:

A simple approach to estimation of incidence rate difference. American Journal of Epidemiology 172:334-343. Xu Y, Cheung YB, Lam E, Milligan PJM (2010)

http://www.stata.com/support/faqs/statistics/multiple-failure-time-data/

Dear Dr Zurakowski,

One of the most applied approaches in multiple failure-time framework are extensions of the Cox's regression model (all of them are proportional hazards models). According with Kelly and Lim (2000), there have been proposed several extensions which seek to address to the most varies particularities of each case study. For reccurent event analysis, I recommend to you apply the Prentice, Williams and Peterson (PWP) model or the Andersen and Gill (AG) model. The PWP model is suggested to be applies when the risk of occurrence of the following events is affected by the previous ones and the AG model is applies when the events reveals that they have the same risks of occurence. Read the following paper of Amorin and Cai (2015) to easily understand the implementation of this two models: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4339761/

Further information can be found on my researchgate profile: https://www.researchgate.net/profile/Ivo_Sousa-Ferreira

Best regards,

Ivo Sousa-Ferreira.