The two major issues concerning covering arrays are explicit construction of a covering array, and exact or approximate determination of the covering array number---the minimum size of a covering array. Although these problems have been investigated extensively for the last couple of decades, in this thesis we present significant improvements on both of these questions using tools from the probabilistic method and randomized algorithms.
First, a series of improvements is developed on the previously known upper bounds on covering array numbers. An estimate for the discrete Stein-Lovász-Johnson bound is derived and the Stein- Lovász -Johnson bound is improved upon using an alteration strategy. Then group actions on the set of symbols are explored to establish two asymptotic upper bounds on covering array numbers that are tighter than any of the presently known bounds.
Second, an algorithmic paradigm, called the two-stage framework, is introduced for covering array construction. A number of concrete algorithms from this framework are analyzed, and it is shown that they outperform current methods in the range of parameter values that are of practical relevance. In some cases, a reduction in the number of tests by more than 50% is achieved.
Third, the Lovász local lemma is applied on covering perfect hash families to obtain an upper bound on covering array numbers that is tightest of all known bounds. This bound leads to a Moser-Tardos type algorithm that employs linear algebraic computation over finite fields to construct covering arrays. In some cases, this algorithm outperforms currently used methods by more than an 80% margin.
Finally, partial covering arrays are introduced to investigate a few practically relevant relaxations of the covering requirement. Using probabilistic methods, bounds are obtained on partial covering arrays that are significantly smaller than for covering arrays. Also, randomized algorithms are provided that construct such arrays in expected polynomial time.
This study answers the question, “In Adult Hispanic BMI ≥ 30 (P), how does development of a weight loss program that utilizes Motivational Interviewing (I) compared to counseling and educational materials only (C) affect weight loss over the period of three months (T).” There are limited published systematic reviews and randomized control trials to evaluate the effectiveness of Motivational Interviewing (MI), in conjunction with diet and exercise to promote weight loss. Participants (n = 5) were Latino patients of a local community health care center who were overweight and medically at risk due to unhealthy lifestyles that were determined through a screening test.
The 4-week clinical pathway program used motivational interviewing in one-on-one sessions every other week, and implemented the “Your Heart, Your Life” curriculum the other weeks. One expected outcome included lower anthropometric measurement numbers of participants’ WL, BMI, WC, and BP. Another expected outcome was an increase in physical activity. Participants were also expected to earn a higher score on a post-test about nutrition and healthy living. A paired t-test and power analyses were used to assess its effectiveness.
Results indicated significant decrease in weight loss (t [5] = 3.68, p = .0211, Cohen’s dz=1.647). For heart healthy habits, there were significant increases all three categories: weight management (t [5] = - 3.36, p = .0211), cholesterol and fat (t [5] = - 3.138, p =.035, salt and sodium (t [5] = - 4.899, p = .008). In addition, there was an increase in knowledge (t [5] = - 4.000, p = .016). Every participant showed small gains. Future implications should include more participants, including males, a control group, innovative activities that help to motivate a community of learners and more flexibility in allotted time for interventions.
Context: This project was completed at a federally qualified primary healthcare clinic in Phoenix, Arizona that served patients of all age groups, but primarily cared for the Hispanic population providing primary care, preventative services, family planning, two lab technicians, one promoter, two medical assistant supervisors, five front desk staff, one chief administrative officer, one chief financial officer, two medical directoers who were also providers at the clinic.
Problem and Analysis Assessment: During my clinical rotations, I saw the burden a missed patient appointment had not only on the patients themselves, but also on the clinic, providers, and the staff. It caused delay in treatment for patients, and it did not allow other patients that wanted to be seen to be seen. It also increased unnecessary costs and wasted provider time. Thereafter, I met with some of the leadership team and one of the medical directors to determine a solution to reduce the number of missed appointments that were occurring. An educational session was kept to discuss the findings of this problem to the providers and the staff and when surveys were handed out to the patients, providers, and staff to assess their satisfaction with the old scheduling system versus the new scheduling system, they were also provided with a cover letter discussing the project.
Intervention: In order for improvements in care to occur, a system process change including the way patients are scheduled must occur. In this case, an open-access scheduling system (OAS) was implemented. OAS allows a patient to schedule an appointment on the 'same-day' or the 'next-day' to be seen. One provider at each of the clinics, each day of the week was available for 'same-day' appointments from 1300-1600. The providers were still available for scheduled appointments using the previous scheduling method. Walk-ins were still accepted, and were scheduled based on patient provider preference; however, if an appointment was not available for their preferred provider, they were typically seen with the provider that was the 'same-day' provider for that day.
Strategy for change: Since patients were only allowed to schedule appointments one month in advance, only one month was needed to implement this process change. A recommendation for the future would be to clearly identify the patient encounter type, and label it as a same-day appointment, as this would be helpful when gathering and extracting data for this type of patient group specifically.
Measurement of Improvement: Over a three-month period, a data collection plan was used to determine the number of Mas over a three-month period before and after implementation of this change. Satisfaction scores were measured using likert scales for patients, provider, and staff, and a dichotomous scale was used to determine the likelihood of emergency room or urgent care use. A comparison was done to measure revenue during the same time frame. During the three months, a clinically significant decrease in MAs was seen (<0.52%), with an increase in revenue by 41%. Additionally, a statistically significant increase in patient, provider and staff satisfaction was also noted when compared to the old scheduling system, as >68% of all patients, providers and staff reported feeling either very satisfied or extremely satisfied with the new scheduling system. Additionally, patients also reported that they were less likely to visit an emergency room(88%) or urgent care (90%) since they were able to be seen the same-day or the next-day by a provider.
Effects of changes: An incidental finding occurred during this study - where 877 more patients were seen in the three months during the implementation of this project, compared to the three months prior; which likely resulted in a 41% increase in revenue. Additionally this project, allowed patients that wanted to be seen on the same day, to be seen, and it decreased unnecessary costs associated with emergency room or urgent care visits. Some of the limitations involved included the current political environment, appointment slots that were previously 15 minutes in length (in 2016), increased to 20 minutes in length (in 2017), a language barrier was noted for the patient surveys since English was not the first language for many of the patients who completed the survey (although documents were translated), and the surveys used were not reliable instrument given that a reliable instrument in previous studies could not be found.
Lessons learnt: In order to have accuracy of the survey results, it is best for the author of the study to hand out and provide scripture for the survey so that complete data is received from the surveyors.
Messages for others: Begin by making a small process change where only one provider allows for the open-access scheduling so that the entire office is not affected by it, and if results begin to look promising then it can be expanded. Additionally, correct labeling of patients as 'same-day' is also important so that additional data can be gathered when needed regarding the 'same-day' patients.
Patient/Family/Guardian Involvement: Patients who benefited from the new scheduling system (open-access scheduling) were asked to fill out a survey that asked them to disclose some demographic data and asked them to determine their satisfaction with the new vs old scheduling system and their likelihood of visiting an emergency room or urgent care.
Ethics Approval: Arizona State University Institutional Review Board (IRB) Received: September 2017
Over the last two decades, opioid prescription and prevalence has increased to account for over 33,000 deaths per year (Soelberg, Brown, Du Vivier, Meyer & Ramachandran, 2017). This is not only due to overdose, but misuse, abuse, and addiction. The abrupt increase in prescriptions, pills dispensed, and opioid-related deaths have encouraged the involvement of multiple entities.
In 2016, the opioid crisis gained the attention of communities that released guidelines to regulate prescription of opioid pain management. Such entities include the Center for Disease Control and Prevention (CDC), National Institute on Drug Abuse, Agency for Healthcare Research and Quality (AHRQ), Arizona Department of Health Services (AZDHS), and Substance Abuse and Mental Health Services Administration (SAMHSA). Evidence shows that prescribing practices between providers vary. It also shows that providers lack knowledge of appropriate opioid prescribing and management. To address this problem, provider education on an opioid policy is the most effective way to uniform opioid prescribing.
Methods: This project was guided by a The Rosswurm and Larrabee Model for Change to Evidence- Based Practice and Pender’s health promotion framework. IRB Approved by ASU. The instruction was implemented at an urban clinic in downtown phoenix that serves uninsured and underserved individuals. Uninsured participants were recruited (n=50). A survey pre and post registration was conducted to assess knowledge and medical portal participation in addition a random pre and post chart review was performed.
Results: Descriptive statistics was used to describe sample and outcome variables. A chi-square test of independence was calculated comparing pre and post intervention significant change was found (χ2 (1) = .002, P<0.05.), a paired sample t test was calculated to compare knowledge pre and post registration instruction the mean pre-10.187(SD = 4.422), post mean was 16.958(SD=.856). A significant increase of knowledge was found (t (47) =-9.573, p (<.001).
Outcomes: In this population both patients and providers have seen significant benefits such as increased communication and patient participation, from the implementation of evidence based educational tools such as instruction with teach back, and the usage of brochures. Potential Implication for sustainability includes the lack of a designated individual that is bilingual to register patients, making patients aware of the existence of a medical patient portal, patient’s fear of sharing immigration status.
Aim: To reduce the fear of falling in an elderly population by teaching ‘Tai Chi for Falls Prevention’ classes twice a week for 12 weeks.
Background & Significance: Falls continue to be the leading cause of injury-related deaths of Arizonans who are 65 years or older - well above the national average. It is predicted that by 2030, national medical spending for this population will total over $31 billion, yearly. Tai Chi is revered for being a beneficial form of simple, low-impact exercise, which the CDC endorses for its falls risk reduction benefits.
Methods: The intervention consisted of 60-minute classes occurring twice a week for 12 weeks. Participants were English-speaking, between 65-85 years old, and able to ambulate independently. Appropriate pre-screening tools were used before applicants consented. Their Fear of Falling (FoF) was measured using a fall risk perception tool at the beginning, middle, and the end of the project. This ordinal data was analyzed with Friedman ANOVA using SPSS 25
Outcomes/Results: After enrolling five total participants, only three completed the project. This severely limited data analysis of their FoF, resulting in a statistical significance (p = 0.68), deeming the intervention ineffective - Despite observable downwards trending FoF scores.
Conclusion: The acceptance of the null hypothesis is attributed to the low enrollment and high attrition rate. Also, the only data measured was quantifiable, subjective data. Future projects could add objective data to reinforce the benefits of Tai Chi. This might reinforce the validity of Tai Chi as a practical recommendation due to its cost-effective simple interventional design and effectiveness for prevention of accidental falls. Increased focus on improved recruitment & retainment strategies should be prioritized for similar projects in the future.
As a step in model development, statistically designed screening experiments may be used to identify the main effects and interactions most significant on a response of a system. However, traditional approaches for screening are ineffective for complex systems because of the size of the experimental design. Consequently, the factors considered are often restricted, but this automatically restricts the interactions that may be identified as well. Alternatively, the designs are restricted to only identify main effects, but this then fails to consider any possible interactions of the factors.
To address this problem, a specific combinatorial design termed a locating array is proposed as a screening design for complex systems. Locating arrays exhibit logarithmic growth in the number of factors because their focus is on identification rather than on measurement. This makes practical the consideration of an order of magnitude more factors in experimentation than traditional screening designs.
As a proof-of-concept, a locating array is applied to screen for main effects and low-order interactions on the response of average transport control protocol (TCP) throughput in a simulation model of a mobile ad hoc network (MANET). A MANET is a collection of mobile wireless nodes that self-organize without the aid of any centralized control or fixed infrastructure. The full-factorial design for the MANET considered is infeasible (with over 10^{43} design points) yet a locating array has only 421 design points.
In conjunction with the locating array, a ``heavy hitters'' algorithm is developed to identify the influential main effects and two-way interactions, correcting for the non-normal distribution of the average throughput, and uneven coverage of terms in the locating array. The significance of the identified main effects and interactions is validated independently using the statistical software JMP.
The statistical characteristics used to evaluate traditional screening designs are also applied to locating arrays.
These include the matrix of covariance, fraction of design space, and aliasing, among others. The results lend additional support to the use of locating arrays as screening designs.
The use of locating arrays as screening designs for complex engineered systems is promising as they yield useful models. This facilitates quantitative evaluation of architectures and protocols and contributes to our understanding of complex engineered networks.
Experiments were conducted to determine the performance of REACT/SALT compared to 802.11 in a streaming audio application on a physical wireless testbed, w-iLab.t. Four experiments were designed, using four different wireless node topologies, and QoS metrics were collected using Qosium. REACT performs better in these these topologies, when the mean value is calculated across each run. For the butterfly and star topology, the variance was higher for REACT even though the mean was lower. In the hidden terminal and exposed node topology, the performance of REACT was much better than 802.11 and converged more tightly, but had drops in quality occasionally.