The past decade has evidenced the increased prevalence of irregularly spaced longitudinal data in social sciences. Clearly lacking, however, are modeling tools that allow researchers to fit dynamic models to irregularly spaced data, particularly data that show nonlinearity and heterogeneity in dynamical structures. We consider the issue of fitting multivariate nonlinear differential equation models with random effects and unknown initial conditions to irregularly spaced data. A stochastic approximation expectation–maximization algorithm is proposed and its performance is evaluated using a benchmark nonlinear dynamical systems model, namely, the Van der Pol oscillator equations. The empirical utility of the proposed technique is illustrated using a set of 24-h ambulatory cardiovascular data from 168 men and women. Pertinent methodological challenges and unresolved issues are discussed.

Study Objectives Prior work has established associations between post-traumatic stress disorder (PTSD), disrupted sleep, and cardiovascular disease (CVD), but few studies have examined health correlates of nightmares beyond risks conferred by PTSD. This study examined associations between nightmares and CVD in military veterans. Methods Participants were veterans (N=3468; 77% male) serving since September 11, 2001, aged 38 years (SD=10.4); approximately 30% were diagnosed with PTSD. Nightmare frequency and severity was assessed using the Davidson Trauma Scale (DTS). Self-reported medical issues were assessed using the National Vietnam Veterans Readjustment Study Self-report Medical Questionnaire. Mental health disorders were established using the Structured Clinical Interview for DSM-IV. The sample was stratified by the presence or absence of PTSD. Within-group associations between nightmare frequency and severity and self-reported CVD conditions, adjusting for age, sex, race, current smoking, depression, and sleep duration. Results Frequent and severe nightmares during the past week were endorsed by 32% and 35% of participants, respectively. Those endorsing nightmares that were frequent, severe, and the combination thereof were more likely to also evidence high blood pressure (ORs 1.42, OR 1.56, and OR 1.47, respectively) and heart problems (OR 1.43, OR 1.48, and OR 1.59, respectively) after adjusting for PTSD diagnosis and other covariates. Conclusions Nightmare frequency and severity among veterans are associated with cardiovascular conditions, even after controlling for PTSD diagnosis. Study findings suggest that nightmares may be an independent risk factor for CVD. Additional research is needed to validate these findings using confirmed diagnoses and explore potential mechanisms.