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. ^

Extended kalman filter for estimation of parameters in nonlinear state-space models of biochemical networks.

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.

A comparative state policy analysis of the adoption of birth defects surveillance legislation

Birth defects are the leading cause of infant mortality in the United States and are a major cause of lifetime disability. However, efforts to understand their causes have been hampered by a lack of population-specific data. During 1990–2004, 22 state legislatures responded to this need by proposing birth defects surveillance legislation (BDSL). The contrast between these states and those that did not pass BDSL provides an opportunity to better understand conditions associated with US public health policy diffusion. ^ This study identifies key state-specific determinants that predict: (1) the introduction of birth defects surveillance legislation (BDSL) onto states' formal legislative agenda, and (2) the successful adoption of these laws. Secondary aims were to interpret these findings in a theoretically sound framework and to incorporate evidence from three analytical approaches. ^ The study begins with a comparative case study of Texas and Oregon (states with divergent BDSL outcomes), including a review of historical documentation and content analysis of key informant interviews. After selecting and operationalizing explanatory variables suggested by the case study, Qualitative Comparative Analysis (QCA) was applied to publically available data to describe important patterns of variation among 37 states. Results from logistic regression were compared to determine whether the two methods produced consistent findings. ^ Themes emerging from the comparative case study included differing budgetary conditions and the significance of relationships within policy issue networks. However, the QCA and statistical analysis pointed to the importance of political parties and contrasting societal contexts. Notably, state policies that allow greater access to citizen-driven ballot initiatives were consistently associated with lower likelihood of introducing BDSL. ^ Methodologically, these results indicate that a case study approach, while important for eliciting valuable context-specific detail, may fail to detect the influence of overarching, systemic variables, such as party competition. However, QCA and statistical analyses were limited by a lack of existing data to operationalize policy issue networks, and thus may have downplayed the impact of personal interactions. ^ This study contributes to the field of health policy studies in three ways. First, it emphasizes the importance of collegial and consistent relationships among policy issue network members. Second, it calls attention to political party systems in predicting policy outcomes. Finally, a novel approach to interpreting state data in a theoretically significant manner (QCA) has been demonstrated.^

Differential dynamic properties of scleroderma fibroblasts in response to perturbation of environmental stimuli.

Diseases are believed to arise from dysregulation of biological systems (pathways) perturbed by environmental triggers. Biological systems as a whole are not just the sum of their components, rather ever-changing, complex and dynamic systems over time in response to internal and external perturbation. In the past, biologists have mainly focused on studying either functions of isolated genes or steady-states of small biological pathways. However, it is systems dynamics that play an essential role in giving rise to cellular function/dysfunction which cause diseases, such as growth, differentiation, division and apoptosis. Biological phenomena of the entire organism are not only determined by steady-state characteristics of the biological systems, but also by intrinsic dynamic properties of biological systems, including stability, transient-response, and controllability, which determine how the systems maintain their functions and performance under a broad range of random internal and external perturbations. As a proof of principle, we examine signal transduction pathways and genetic regulatory pathways as biological systems. We employ widely used state-space equations in systems science to model biological systems, and use expectation-maximization (EM) algorithms and Kalman filter to estimate the parameters in the models. We apply the developed state-space models to human fibroblasts obtained from the autoimmune fibrosing disease, scleroderma, and then perform dynamic analysis of partial TGF-beta pathway in both normal and scleroderma fibroblasts stimulated by silica. We find that TGF-beta pathway under perturbation of silica shows significant differences in dynamic properties between normal and scleroderma fibroblasts. Our findings may open a new avenue in exploring the functions of cells and mechanism operative in disease development.

Differential dynamic properties of scleroderma fibroblasts in response to perturbation of environmental stimuli.

Diseases are believed to arise from dysregulation of biological systems (pathways) perturbed by environmental triggers. Biological systems as a whole are not just the sum of their components, rather ever-changing, complex and dynamic systems over time in response to internal and external perturbation. In the past, biologists have mainly focused on studying either functions of isolated genes or steady-states of small biological pathways. However, it is systems dynamics that play an essential role in giving rise to cellular function/dysfunction which cause diseases, such as growth, differentiation, division and apoptosis. Biological phenomena of the entire organism are not only determined by steady-state characteristics of the biological systems, but also by intrinsic dynamic properties of biological systems, including stability, transient-response, and controllability, which determine how the systems maintain their functions and performance under a broad range of random internal and external perturbations. As a proof of principle, we examine signal transduction pathways and genetic regulatory pathways as biological systems. We employ widely used state-space equations in systems science to model biological systems, and use expectation-maximization (EM) algorithms and Kalman filter to estimate the parameters in the models. We apply the developed state-space models to human fibroblasts obtained from the autoimmune fibrosing disease, scleroderma, and then perform dynamic analysis of partial TGF-beta pathway in both normal and scleroderma fibroblasts stimulated by silica. We find that TGF-beta pathway under perturbation of silica shows significant differences in dynamic properties between normal and scleroderma fibroblasts. Our findings may open a new avenue in exploring the functions of cells and mechanism operative in disease development.

Bifurcation and singularity analysis of a molecular network for the induction of long-term memory.

Withdrawal reflexes of the mollusk Aplysia exhibit sensitization, a simple form of long-term memory (LTM). Sensitization is due, in part, to long-term facilitation (LTF) of sensorimotor neuron synapses. LTF is induced by the modulatory actions of serotonin (5-HT). Pettigrew et al. developed a computational model of the nonlinear intracellular signaling and gene network that underlies the induction of 5-HT-induced LTF. The model simulated empirical observations that repeated applications of 5-HT induce persistent activation of protein kinase A (PKA) and that this persistent activation requires a suprathreshold exposure of 5-HT. This study extends the analysis of the Pettigrew model by applying bifurcation analysis, singularity theory, and numerical simulation. Using singularity theory, classification diagrams of parameter space were constructed, identifying regions with qualitatively different steady-state behaviors. The graphical representation of these regions illustrates the robustness of these regions to changes in model parameters. Because persistent protein kinase A (PKA) activity correlates with Aplysia LTM, the analysis focuses on a positive feedback loop in the model that tends to maintain PKA activity. In this loop, PKA phosphorylates a transcription factor (TF-1), thereby increasing the expression of an ubiquitin hydrolase (Ap-Uch). Ap-Uch then acts to increase PKA activity, closing the loop. This positive feedback loop manifests multiple, coexisting steady states, or multiplicity, which provides a mechanism for a bistable switch in PKA activity. After the removal of 5-HT, the PKA activity either returns to its basal level (reversible switch) or remains at a high level (irreversible switch). Such an irreversible switch might be a mechanism that contributes to the persistence of LTM. The classification diagrams also identify parameters and processes that might be manipulated, perhaps pharmacologically, to enhance the induction of memory. Rational drug design, to affect complex processes such as memory formation, can benefit from this type of analysis.

State health care reform: An analysis of strategies

The United States health care system faces significant challenges, particularly with problems of the uninsured and with the rising costs of care. These problems lead many to study and discuss strategies for reforming the health care system. Four different plans for ideal health care reform, set forth by notable scholars or organizations, are explained herein. Then, states within the United States are examined in terms of their recent efforts at health care reform. Those states proposing significant changes to their health care systems are analyzed—namely, Maine, Massachusetts, and Vermont. The strategies used in these three states are compared to the strategies laid out by the experts in order to determine which strategies are the most popular in current health care reform efforts among the states studied here. These strategies are totaled to find which organization's plan for ideal reform seems to be the most popular. The strategies of managed competition are shown to be the most popular strategies among these three state health care reforms, while the strategies of the single-payer plan discussed herein were the least popular. All three states seem to utilize strategies that build upon their previous health care system, rather than implementing strategies that completely replace the previous system. ^

A space-time analysis of reported shigellosis and salmonellosis cases in Texas from 2000 to 2004

Background. The purpose of this study was to describe the risk factors and demographics of persons with salmonellosis and shigellosis and to investigate both seasonal and spatial variations in the occurrence of these infections in Texas from 2000 to 2004, utilizing time series analyses and the geographic information system digital mapping methods. ^ Methods. Spatial Analysis: MapInfo software was used to map the distribution of age-adjusted rates of reported shigellosis and salmonellosis in Texas from 2000–2004 by zip codes. Census data on above or below poverty level, household income, highest level of educational attainment, race, ethnicity, and urban/rural community status was obtained from the 2000 Decennial Census for each zip code. The zip codes with the upper 10% and lower 10% were compared using t-tests and logistic regression to determine whether there were any potential risk factors. ^ Temporal analysis. Seasonal patterns in the prevalence of infections in Texas from 2000 to 2003 were determined by performing time-series analysis on the numbers of cases of salmonellosis and shigellosis. A linear regression was also performed to assess for trends in the incidence of each disease, along with auto-correlation and multi-component cosinor analysis. ^ Results. Spatial analysis: Analysis by general linear model showed a significant association between infection rates and age, with young children aged less than 5 and those aged 5–9 years having increased risk of infection for both disease conditions. The data demonstrated that those populations with high percentages of people who attained a higher than high school education were less likely to be represented in zip codes with high rates of shigellosis. However, for salmonellosis, logistic regression models indicated that when compared to populations with high percentages of non-high school graduates, having a high school diploma or equivalent increased the odds of having a high rate of infection. ^ Temporal analysis. For shigellosis, multi-component cosinor analyses were used to determine the approximated cosine curve which represented a statistically significant representation of the time series data for all age groups by sex. The shigellosis results show 2 peaks, with a major peak occurring in June and a secondary peak appearing around October. Salmonellosis results showed a single peak and trough in all age groups with the peak occurring in August and the trough occurring in February. ^ Conclusion. The results from this study can be used by public health agencies to determine the timing of public health awareness programs and interventions in order to prevent salmonellosis and shigellosis from occurring. Because young children depend on adults for their meals, it is important to increase the awareness of day-care workers and new parents about modes of transmission and hygienic methods of food preparation and storage. ^

Analysis of Mycobacterium tuberculosis in the state of Texas for rifampin resistance using molecular beacons

Mycobacterium tuberculosis, a bacillus known to cause disease in humans since ancient times, is the etiological agent of tuberculosis (TB). The infection is primarily pulmonary, although other organs may also be affected. The prevalence of pulmonary TB disease in the US is highest along the US-Mexico border, and of the four US states bordering Mexico, Texas had the second highest percentage of cases of TB disease among Mexico-born individuals in 1999 (CDC, 2001). Between the years of 1993 and 1998, the prevalence of drug-resistant (DR) TB was 9.1% among Mexican-born individuals and 4.4% among US-born individuals (CDC, 2001). In the same time period, the prevalence of multi-drug resistant (MDR) TB was 1.4% among Mexican-born individuals and 0.6% among US-born individuals (CDC, 2001). There is a renewed urgency in the quest for faster and more effective screening, diagnosis, and treatment methods for TB due to the resurgence of tuberculosis in the US during the mid-1980s and early 1990s (CDC, 2007a), and the emergence of drug-resistant, multidrug-resistant, and extremely drug-resistant tuberculosis worldwide. Failure to identify DR and MDR-TB quickly leads to poorer treatment outcomes (CDC, 2007b). The recent rise in TB/HIV comorbidity further complicates TB control efforts. The gold standard for identification of DR-TB requires mycobacterial growth in culture, a technique taking up to three weeks, during which time DR/MDR-TB individuals harboring resistant organisms may be receiving inappropriate treatment. The goal of this study was to determine the sensitivity and specificity of real-time quantitative polymerase chain reaction (qPCR) using molecular beacons in the Texas population. qPCR using molecular beacons is a novel approach to detect mycobacterial mutations conferring drug resistance. This technique is time-efficient and has been shown to have high sensitivity and specificity in several populations worldwide. Rifampin (RIF) susceptibility was chosen as the test parameter because strains of M. tuberculosis which are resistant to RIF are likely to also be MDR. Due to its status as a point of entry for many immigrants into the US, control efforts against TB and drug-resistant TB in Texas is a vital component of prevention efforts in the US as a whole. We show that qPCR using molecular beacons has high sensitivity and specificity when compared with culture (94% and 87%, respectively) and DNA sequencing (90% and 96%, respectively). We also used receiver operator curve analysis to calculate cutoff values for the objective determination of results obtained by qPCR using molecular beacons. ^

THE IMPLEMENTATION OF FEDERAL FAMILY PLANNING POLICY: AN ANALYSIS OF FACTORS AFFECTING STATE EXPENDITURES, FISCAL YEARS 1976-1981 (WOMEN, BUDGET, POPULATION)

The purpose of this study was to analyze the implementation of national family planning policy in the United States, which was embedded in four separate statutes during the period of study, Fiscal Years 1976-81. The design of the study utilized a modification of the Sabatier and Mazmanian framework for policy analysis, which defined implementation as the carrying out of statutory policy. The study was divided into two phases. The first part of the study compared the implementation of family planning policy by each of the pertinent statutes. The second part of the study identified factors that were associated with implementation of federal family planning policy within the context of block grants.^ Implemention was measured here by federal dollars spent for family planning, adjusted for the size of the respective state target populations. Expenditure data were collected from the Alan Guttmacher Institute and from each of the federal agencies having administrative authority for the four pertinent statutes, respectively. Data from the former were used for most of the analysis because they were more complete and more reliable.^ The first phase of the study tested the hypothesis that the coherence of a statute is directly related to effective implementation. Equity in the distribution of funds to the states was used to operationalize effective implementation. To a large extent, the results of the analysis supported the hypothesis. In addition to their theoretical significance, these findings were also significant for policymakers insofar they demonstrated the effectiveness of categorical legislation in implementing desired health policy.^ Given the current and historically intermittent emphasis on more state and less federal decision-making in health and human serives, the second phase of the study focused on state level factors that were associated with expenditures of social service block grant funds for family planning. Using the Sabatier-Mazmanian implementation model as a framework, many factors were tested. Those factors showing the strongest conceptual and statistical relationship to the dependent variable were used to construct a statistical model. Using multivariable regression analysis, this model was applied cross-sectionally to each of the years of the study. The most striking finding here was that the dominant determinants of the state spending varied for each year of the study (Fiscal Years 1976-1981). The significance of these results was that they provided empirical support of current implementation theory, showing that the dominant determinants of implementation vary greatly over time. ^

Policy analysis of shifting to the state-run Texas women's health program

During the 82nd Texas legislature, state leaders passed a provision stating that healthcare providers, who perform, promote, or affiliate with providers who perform or promote elective abortion services may not be eligible to participate in the Texas Medicaid Women's Health Program (WHP). The federal government reacted to this new provision by vowing to eliminate its 90% share of program support on the grounds that the provision violated a patient's freedom to choose a provider; a right protected by the Social Security Act. Texas leaders stated that the Women's Health Program would continue without federal support, financed exclusively with state funds.^ The following policy analysis compares the projected impact of the current Medicaid Women's Health Program to the proposed state-run program using the criteria-alternative matrix framework. The criteria used to evaluate the program alternatives include population affected, unintended pregnancy and abortion impact, impact on cervical cancer rate, and state-level government expenditures. Each criterion was defined by selected measures. The population affected was measured by the number of women served in the programs. Government expenditures were measured in terms of payments for program costs, Medicaid delivery costs, and cervical cancer diagnostic costs. Unintended pregnancy impact was measured by the number of projected unplanned pregnancies and abortions under each alternative. The impact on cervical cancer was projected in terms of the number of new cervical cancer cases under each alternative. Differences in the projections with respect to each criterion were compared to assess the impact of shifting to the state-only policy.^ After examining program alternatives, it is highly recommended that Texas retain the Medicaid WHP. If the state does decide to move forward with the state-run WHP, it is recommended that the program run at its previous capacity. Furthermore, for the purpose of addressing the relatively high cervical cancer incidence rate in Texas, incorporating HPV vaccination coverage for women ages 18-26 as part of the Women's Health Program is recommended.^