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I am creating a model to identify which factors predict two different recidivism outcomes (A)new arrest, or (B) return to prison in a group of people who parole, with equal time at risk (2 years). The outcomes of interest are A) arrested within two years or not, or B) returned to prison within two years, or not. Each outcome of interest occurs in about 25% of cases and individuals can experience both outcomes of interest during the two year period.

I am using multinomial logistic regression to build two different models for the two outcomes of interest. However, when people are returned to prison (i.e. experience outcome B), they are not able to experience outcome A (arrest) for at least 6 months. I understand this is biasing my results when I am building a model for outcome A, but I am unsure of how to correct for this. I have seen other scholars simply extend the time they are tracking individuals who pause their time at risk (i.e. individuals who experience outcome B are tracked for 2.5 years, instead of 2 years to account for the 6 months they were unable to experience outcome A), but this strikes me as not particularly sophisticated. Is there a model better suited for this type of issue?

kjetil b halvorsen
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Julia
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  • Do you have access to event dates? What about a survival model for time spent without returning to prison? There are many papers on joint modeling of survival and ..., for example [this one](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4454429/), but I cannot find posts on this site ... – kjetil b halvorsen Nov 03 '20 at 16:39
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    @kjetilbhalvorsen yes I do have event dates. I am not particularly concerned with estimating time to event, so I had not fully considered survival analysis until now. I have never heard of the joint model mentioned. If I use it to estimate time spent without a new arrest, would it account for competing risk from the prison return? Thanks for your suggestions. – Julia Nov 03 '20 at 18:01

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This would work better as a competing risks model, which is a specialized form of a survival model. Competing risks is based on the Cox Proportional Hazards model, which uses a lot of the same underlying principles as a logistic regression model.

Competing risks uses the concept of a group being "at risk" for all events until one event occurs. The people who can experience the event are known as the "risk set." Usually, when someone experiences an event, they are removed from the risk set for the rest of the follow-up.

Use this kind of time to event model should give you a better sense of which effects are important. Probably, someone who goes to prison again immediately after release is different from someone who has the same outcome at the end of your two-year follow up. Competing risks will account for that.

In your case it sounds like some people can experience a certain event that removes them from the risk set for a period of time, but they also become "at risk" for the other event again after a period of time. You can account for that, too, if you think it's biasing your results.

This R vignette shows how you might implement in R and gives a deeper explanation on the concepts. https://cran.r-project.org/web/packages/survival/vignettes/compete.pdf

This whitepaper has a good description of competing risks in general: https://data.princeton.edu/pop509/CompetingRisks.pdf

Melinda Thielbar PhD
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    Can you explain what a competing risks model is ? This site works best when users don't have to go to an external site for their answers/ – LeelaSella Nov 03 '20 at 20:49