st: multistage survival data

[April Zeoli <zeoli@msu.edu>]

Hello,

I am working with longitudinal data which tracks the trajectory of
people with mental health disorders who are released from jail. The
events of interest are subsequent mental health treatment and
subsequent incarceration, and many participants experience multiple
incarcerations. The dataset contains dates of the events of interest,
so I believe that a survival analysis is most appropriate to answer
the question of whether subsequent mental health treatment delays the
progression of a participant back to jail.

At first I considered a recurrent event survival analysis, using Cox
proportional hazards model, because many participants experienced
multiple incarcerations. However, I struggled with how to model the
mental health treatment variable. A dichotomous variable representing
whether participants accessed mental health treatment post-jail omits
potentially valuable information regarding whether the amount of time
it takes to access treatment affects time to subsequent incarceration,
or whether the type of mental health treatment accessed (information I
also have) affects time to jail post-treatment.

I am now exploring the use of a marginal survival analysis, modeling
the data as multistage data, meaning that I am interested in numerous
stages, or events (i.e., entry into study at time released from 1st
jail, 1st mental health treatment, 2nd incarceration, 2nd mental
health treatment, 3rd jail, etc.). I believe this would allow me to
address the above questions. I would like to run a model that is a mix
of conditional and marginal estimation, and include such conditional
variables as gender and age. I discovered this type of model in
"handbook of statistics 23 - Advances in Survival Analysis" edited by
N. Balakrishnan and C.R.Rao, which states that proportional hazards
models can be used for this purpose. The problem is that I do not know
how to implement such a model in Stata 10.1 and have found no guidance
as of yet. I am looking for guidance of any sort to help me with this
analysis. Thank you for your consideration!

April

April M. Zeoli, PhD, MPH
Assistant Professor
School of Criminal Justice
Michigan State University
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