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A Dynamic Model for Posttraumatic Stress Disorder Among U.S. Troops in Operation Iraqi Freedom

Department of Operations Research, Naval Postgraduate School, Monterey, California 93943
Institute for Computational and Mathematical Engineering, Stanford University, Stanford, California 94305
Graduate School of Business, Stanford University, Stanford, California 94305
mpatkins{at}nps.edu
guetz{at}stanford.edu
lwein{at}stanford.edu

We develop a dynamic model in which Operation Iraqi Freedom (OIF) servicemembers incur a random amount of combat stress during each month of deployment, develop posttraumatic stress disorder (PTSD) if their cumulative stress exceeds a servicemember-specific threshold, and then develop symptoms of PTSD after an additional time lag. Using Department of Defense deployment data and Mental Health Advisory Team PTSD survey data to calibrate the model, we predict that—because of the long time lags and the fact that some surveyed servicemembers experience additional combat after being surveyed—the fraction of Army soldiers and Marines who eventually suffer from PTSD will be approximately twice as large as in the raw survey data. We cannot put a confidence interval around this estimate, but there is considerable uncertainty (perhaps ±30%). The estimated PTSD rate translates into 300,000 PTSD cases among all Army soldiers and Marines in OIF, with 20,000 new cases each year the war is prolonged. The heterogeneity of threshold levels among servicemembers suggests that although multiple deployments raise an individual's risk of PTSD, in aggregate, multiple deployments lower the total number of PTSD cases by 30% relative to a hypothetical case in which the war was fought with many more servicemembers (i.e., a draft) deploying only once. The time lag dynamics suggest that, in aggregate, reserve servicemembers show symptoms 1–2 years before active servicemembers and predict that >75% of OIF servicemembers who self-reported symptoms during their second deployment were exposed to the PTSD-generating stress during their first deployment.

Key Words: health care; military; reliability; failure models
History: Received: October 29, 2008; accepted: April 17, 2009.