NONLINEAR TIME SERIES/SYSTEM ANALYSIS (STATE-SPACE, DYNAMICS, INTERVENTION, RESILIENCE, KALMAN)

A discussion of nonlinear dynamics, demonstrated by the familiar automobile, is followed by the development of a systematic method of analysis of a possibly nonlinear time series using difference equations in the general state-space format. This format allows recursive state-dependent parameter estimation after each observation thereby revealing the dynamics inherent in the system in combination with random external perturbations.^ The one-step ahead prediction errors at each time period, transformed to have constant variance, and the estimated parametric sequences provide the information to (1) formally test whether time series observations y(,t) are some linear function of random errors (ELEM)(,s), for some t and s, or whether the series would more appropriately be described by a nonlinear model such as bilinear, exponential, threshold, etc., (2) formally test whether a statistically significant change has occurred in structure/level either historically or as it occurs, (3) forecast nonlinear system with a new and innovative (but very old numerical) technique utilizing rational functions to extrapolate individual parameters as smooth functions of time which are then combined to obtain the forecast of y and (4) suggest a measure of resilience, i.e. how much perturbation a structure/level can tolerate, whether internal or external to the system, and remain statistically unchanged. Although similar to one-step control, this provides a less rigid way to think about changes affecting social systems.^ Applications consisting of the analysis of some familiar and some simulated series demonstrate the procedure. Empirical results suggest that this state-space or modified augmented Kalman filter may provide interesting ways to identify particular kinds of nonlinearities as they occur in structural change via the state trajectory.^ A computational flow-chart detailing computations and software input and output is provided in the body of the text. IBM Advanced BASIC program listings to accomplish most of the analysis are provided in the appendix. ^

SEVERE HEAD TRAUMA, EMERGENCY TRANSPORT, AND PATIENT OUTCOME

Trauma and severe head injuries are important issues because they are prevalent, because they occur predominantly in the young, and because variations in clinical management may matter. Trauma is the leading cause of death for those under age 40. The focus of this head injury study is to determine if variations in time from the scene of accident to a trauma center hospital makes a difference in patient outcomes.^ A trauma registry is maintained in the Houston-Galveston area and includes all patients admitted to any one of three trauma center hospitals with mild or severe head injuries. A study cohort, derived from the Registry, includes 254 severe head injury cases, for 1980, with a Glasgow Coma Score of 8 or less.^ Multiple influences relate to patient outcomes from severe head injury. Two primary variables and four confounding variables are identified, including time to emergency room, time to intubation, patient age, severity of injury, type of injury and mode of transport to the emergency room. Regression analysis, analysis of variance, and chi-square analysis were the principal statistical methods utilized.^ Analysis indicates that within an urban setting, with a four-hour time span, variations in time to emergency room do not provide any strong influence or predictive value to patient outcome. However, data are suggestive that at longer time periods there is a negative influence on outcomes. Age is influential only when the older group (55-64) is included. Mode of transport (helicopter or ambulance) did not indicate any significant difference in outcome.^ In a multivariate regression model, outcomes are influenced primarily by severity of injury and age which explain 36% (R('2)) of variance. Inclusion of time to emergency room, time to intubation, transport mode and type injury add only 4% (R('2)) additional contribution to explaining variation in patient outcome.^ The research concludes that since the group most at risk to head trauma is the young adult male involved in automobile/motorcycle accidents, more may be gained by modifying driving habits and other preventive measures. Continuous clinical and evaluative research are required to provide updated clinical wisdom in patient management and trauma treatment protocols. A National Institute of Trauma may be required to develop a national public policy and evaluate the many medical, behavioral and social changes required to cope with the country's number 3 killer and the primary killer of young adults.^