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. ^

Factors associated with HPV16 status and survival among patients with squamous cell carcinoma of the oropharynx

Background: Squamous cell carcinoma of the oropharynx (SCCOP) is characterized by local tumor aggressiveness, high recurrence rates, a high incidence of second primary tumors, and medical comorbidities. Significant trends in demographic and clinical characteristics as well as survival among SCCOP patients have been observed over time, likely owing to the changing etiology of the disease. Human papillomavirus type 16 (HPV16) infection is associated with a significant proportion of these cancers. Biomarkers that may aid in identifying patients that are at higher risk of recurrence and death are important so that these patients may be followed more closely to improve their quality of life. ^ Study population and methods: The retrospective review (Specific Aim 2) included 3891 newly diagnosed, previously untreated patients presenting to our institution between 1955 and 2004. A total of 2299 patients treated at our institution were included in survival and recursive partitioning analysis. The prospective cohort study (Specific Aim 3) included 266 patients presenting to our institution between January 2006 and September 2009. ^ Results: The results from the retrospective review showed that over time, patients presented at younger ages and were more likely to have base of tongue/tonsil tumors and to be never/former smokers and moreover survival improved significantly over time. In survival and recursive partitioning analyses, the TNM staging system was efficient in prognosticating patients prior to 1995. However, in the recent decade, the TNM staging system was completely inadequate. The factors having the greatest positive effect on overall survival since 1995 were those common to HPV-associated SCCOP. The results from the prospective cohort study indicate that patients with high nodal stage and those with late stage disease have increased levels of pretreatment serum HPV DNA. ^ Conclusions: We saw a distinct improvement in survival among SCCOP patients over the past 50 years at our institution. The main factors contributing to this were changes in clinical characteristics, in particular surrogates for HPV status. The current TNM staging system for SCCOP is inadequate and incorporation of HPV status (and perhaps smoking status) is encouraged. Furthermore, although pretreatment circulating levels of HPV DNA was associated with higher N category and overall disease stage, it has limited utility as a marker for recurrence among SCCOP patients.^