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. ^

A simulation study of the standard design, the rolling six design, the CRM, and the modified CRM in Phase I clinical trials

The Phase I clinical trial is considered the "first in human" study in medical research to examine the toxicity of a new agent. It determines the maximum tolerable dose (MTD) of a new agent, i.e., the highest dose in which toxicity is still acceptable. Several phase I clinical trial designs have been proposed in the past 30 years. The well known standard method, so called the 3+3 design, is widely accepted by clinicians since it is the easiest to implement and it does not need a statistical calculation. Continual reassessment method (CRM), a design uses Bayesian method, has been rising in popularity in the last two decades. Several variants of the CRM design have also been suggested in numerous statistical literatures. Rolling six is a new method introduced in pediatric oncology in 2008, which claims to shorten the trial duration as compared to the 3+3 design. The goal of the present research was to simulate clinical trials and compare these phase I clinical trial designs. Patient population was created by discrete event simulation (DES) method. The characteristics of the patients were generated by several distributions with the parameters derived from a historical phase I clinical trial data review. Patients were then selected and enrolled in clinical trials, each of which uses the 3+3 design, the rolling six, or the CRM design. Five scenarios of dose-toxicity relationship were used to compare the performance of the phase I clinical trial designs. One thousand trials were simulated per phase I clinical trial design per dose-toxicity scenario. The results showed the rolling six design was not superior to the 3+3 design in terms of trial duration. The time to trial completion was comparable between the rolling six and the 3+3 design. However, they both shorten the duration as compared to the two CRM designs. Both CRMs were superior to the 3+3 design and the rolling six in accuracy of MTD estimation. The 3+3 design and rolling six tended to assign more patients to undesired lower dose levels. The toxicities were slightly greater in the CRMs.^

Use of a modified delphi process for establishing occupational exposure limits in support of health surveillance for space travelers

On-orbit exposures can come from numerous factors related to the space environment as evidenced by almost 50 years of environmental samples collected for water analysis, air analysis, radiation analysis, and physiologic parameters. For astronauts and spaceflight participants the occupational exposures can be very different from those experienced by workers performing similar tasks in workplaces on Earth, because the duration of the exposure could be continuous for very long orbital, and eventually interplanetary, missions. The establishment of long-term exposure standards is vital to controlling the quality of the spacecraft environment over long periods. NASA often needs to update and revise its prior exposure standards (Spacecrafts Maximum Allowable Concentrations (SMACs)). Traditional standards-setting processes are often lengthy, so a more rapid method to review and establish standards would be a substantial advancement in this area. This project investigates use of the Delphi method for this purpose. ^ In order to achieve the objectives of this study a modified Delphi methodology was tested in three trials executed by doctoral students and a panel of experts in disciplines related to occupational safety and health. During each test/trial modifications were made to the methodology. Prior to submission of the Delphi Questionnaire to the panel of experts a pilot study/trial was conducted using five doctoral students with the goals of testing and adjusting the Delphi questionnaire to improve comprehension, work out any procedural issues and evaluate the effectiveness of the questionnaire in drawing the desired responses. The remainder of the study consisted of two trials of the Modified Delphi process using 6 chemicals that currently have the potential of causing occupational exposures to NASA astronauts or spaceflight participants. To assist in setting Occupational Exposure Limits (OEL), the expert panel was established consisting of experts from academia, government and industry. Evidence was collected and used to create close-ended questionnaires which were submitted to the Delphi panel of experts for the establishment of OEL values for three chemicals from the list of six originally selected (trial 1). Once the first Delphi trial was completed, adjustments were made to the Delphi questionnaires and the process above was repeated with the remaining 3 chemicals (trial 2). ^ Results indicate that experience in occupational safety and health and with OEL methodologies can have a positive effect in minimizing the time experts take in completing this process. Based on the results of the questionnaires and comparison of the results with the SMAC already established by NASA, we conclude that use of the Delphi methodology is appropriate for use in the decision-making process for the selection of OELs.^

Modified 3+3 design for phase I clinical trials

Phase I clinical trial is mainly designed to determine the maximum tolerated dose (MTD) of a new drug. Optimization of phase I trial design is crucial to minimize the number of enrolled patients exposed to unsafe dose levels and to provide reliable information to the later phases of clinical trials. Although it has been criticized about its inefficient MTD estimation, nowadays the traditional 3+3 method remains dominant in practice due to its simplicity and conservative estimation. There are many new designs that have been proven to generate more credible MTD estimation, such as the Continual Reassessment Method (CRM). Despite its accepted better performance, the CRM design is still not widely used in real trials. There are several factors that contribute to the difficulties of CRM adaption in practice. First, CRM is not widely accepted by the regulatory agencies such as FDA in terms of safety. It is considered to be less conservative and tend to expose more patients above the MTD level than the traditional design. Second, CRM is relatively complex and not intuitive for the clinicians to fully understand. Third, the CRM method take much more time and need statistical experts and computer programs throughout the trial. The current situation is that the clinicians still tend to follow the trial process that they are comfortable with. This situation is not likely to change in the near future. Based on this situation, we have the motivation to improve the accuracy of MTD selection while follow the procedure of the traditional design to maintain simplicity. We found that in 3+3 method, the dose transition and the MTD determination are relatively independent. Thus we proposed to separate the two stages. The dose transition rule remained the same as 3+3 method. After getting the toxicity information from the dose transition stage, we combined the isotonic transformation to ensure the monotonic increasing order before selecting the optimal MTD. To compare the operating characteristics of the proposed isotonic method and the other designs, we carried out 10,000 simulation trials under different dose setting scenarios to compare the design characteristics of the isotonic modified method with standard 3+3 method, CRM, biased coin design (BC) and k-in-a-row design (KIAW). The isotonic modified method improved MTD estimation of the standard 3+3 in 39 out of 40 scenarios. The improvement is much greater when the target is 0.3 other than 0.25. The modified design is also competitive when comparing with other selected methods. A CRM method performed better in general but was not as stable as the isotonic method throughout the different dose settings. The results demonstrated that our proposed isotonic modified method is not only easily conducted using the same procedure as 3+3 but also outperforms the conventional 3+3 design. It can also be applied to determine MTD for any given TTL. These features make the isotonic modified method of practical value in phase I clinical trials.^