Recurrent events in survival analysis

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Is there any way in SPSS 19 to do a survival analysis (Cox Regression) for situations in which more than one event is analyzed? Any other accessible software?

This may include one single type of event that may happen several times to a single subject (e.g. getting ill or failing a class at school), or several different kinds of events that may or may not be competing, such as (1) repeating a given class in school after failure the previous year, and  (2) dropping out of school. Dropping out and repeating the class are competing risks; repeating one particular class is not competing with having repeated other classes before or going to repeat another class afterwards.

The specific problem I have deals with events that may hinder school progress for children of school age. They may fail to enroll at the normal age, most of which finally enroll albeit at a later age; they may have repeated one or more classes (because they failed to pass it the previous year), or may have dropped out of school.

I wish to model the chances of adverse events along the “school history” of a typical child, in terms of the age (or level of education) at which these events may happen.

To make things a little more complicated, I do not have in this case a longitudinal study, but a cross section of kids to whom the events have already  happened. The cross section information available is census data for an entire, albeit relatively small [developing] country, so statistical significance in the usual sense is not a problem (tens or hundreds of thousands of kids in each situation). Covariates include household-family variables (SES, education of adults, etc) and characteristics of the child (age, gender,  educational attainment up to the event, child work if any, etc). Some of these covariates might be treated as time-dependent, but this might be (hopefully) avoided.

Thanks in advance

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关键词：Recurrent Survival Analysis Analysi CURRENT survival events

You may want to check some nice articles by Singer and Willet. They have researched this area very well.




Fermin Ornelas, Ph.D.

Hi Fermin.  I have the Singer & Willett book, but have not yet read all of the chapters on time-to-event models--I left off somewhere in chapter 13 the last time I was reading it.  When I consult the table of contents, though, I see that they do discuss "competing risk" models in chapter 15 ("Extending the Cox Regression Model").  AFAIK, in competing risk models, each subject
still "die" only once, but it can be for different reasons.  S&W give examples of students leaving school either by graduating or quitting, employers leaving through lay-off, quitting, or getting sacked, etc.  But this is not what Hector wants.  He has a "type of event that may happen several times to a single subject".  Are you sure Singer & Willett discuss that type of model?  Thanks for clarifying.

Cheers,
Bruce Weaver Lakehead University

One book specifically discussing models for recurrent events and non competing risks is Modeling Survival Data: Extending the Cox Model, by T. M. Therneau and Patricia Grambsch (Springer, 2000). Includes S-Plus and SAS code, but no SPSS. Besides, it is 10 years old and may be somewhat dated by now. Some R code exists for similar purposes, as in the links suggested by Dale Glaser in this same thread.
All these texts assume a longitudinal data structure, in which the dates of all successive events are known for every subject; AFAIK none discusses a similar model using cross sectional data, in which you only have people of different ages (or different education levels) having or not having quitted school, or still attending school but in a class behind their age.

My own data comprise children of various ages, each belonging to one of several categories: those that never enrolled, those attending the normal or expected class for their age, others attending a class inferior to their age, dropouts, and those who have already finished senior high school (normally at about 17-18 years of age). All these groups of children (except the first and last categories) may have different levels of education attainment.

The model I wish to build may use chronological age or school attainment as the "time" variable for the survival analysis; whichever of these is chosen as the time variable, the other one may be a covariate in the model.
The events of interest are enrolling (or failing to enroll), getting one grade (or one additional grade) behind their age, and dropping out. These events may happen at any chronological age; not enrolling precludes dropping out, but if you enroll the other events are all possible, and may happen at various times.

If you fail to enroll, or after you drop out, you keep falling behind (one more grade per year). Those who finish (i.e. graduate from senior high) are censored, and are no longer at risk (as far as primary and secondary education is concerned).
A child may have fallen behind by enrolling at a late age, or for other reasons (repeating a grade, or temporarily leaving school); they can fall one (additional) grade behind more than one time, and thus may be one, two or more years below their age-adequate grade (in my dataset I got some guys in their late teens who are attending the first 1-3 grades of primary school, probably at a remedial school, and are therefore about ten years behind their age).

Altogether a very interesting problem, and possibly a real headache if I fail to get an adequate software very soon.

Hector

With regard to "a child being a grade behind his/her age", there is other noise in the measurement that you may want to keep in mind.
In different jurisdictions there are different date-of-birth criteria for entering school.  So in many analyses a child born on or before the local criterion date will be in grade n, whereas, a child born the very next day will be the same age but in grade n-1.  Without any children from the same jurisdiction being "held back" there could be something like 364 days between the birth of the oldest child and the youngest child in a class. There also would be noise due to children starting in different jurisdictions and moving.

In some jurisdictions  a child can "skip" a grade.

I don't know if it is still true, but some jurisdictions used to have half-year systems. Both halves of the grade would be going on at the same time, i.e., in September some children are entering the first half of a grade and some are entering the second half.  Systems with half-year systems had 2 criterion dates for entry.  Also a child could be "kept back" or "skip" half a grade.

In addition, within some jurisdictions the criterion date changes from year to year.


Art Kendall
Social Research Consultants

Quite true, Art, and thank you for raising the issue.
No half year regimes in the country I am analyzing, but certainly fuzziness when the age of children is measured in years. The normal enrolment age is 6, but 20% of children aged 5 are already in school, and some children aged 7 are in first grade. As no further precision exists in the data, one has to make a choice. A strict definition of being "behind" would be that the grade currently attended is lower than (age-6), but this would tend to overstate the number of  "delayed" children. A more conservative definition would be allowing for children aged 7 to be in first grade without being considered as "too old for that grade", but this risks missing some children who are 7 and are already "delayed" (same uncertainty applies to older children who are or fail to be in higher grades).
However, with any definition, the problem is that "being delayed by an additional year" is an event that may happen more than one time, along with other events such as dropping out of school (which may happen at any age and any grade). A multiple-event model is required (including recurrent events of the same type, and competing events such as dropping out --or dying, for that matter).
The R programs suggested before in this thread have a maximum number of cases (30,000 or 60,000) far below the size of my census data set, and are thus not applicable for my problem.

Hector