Mathematics Calculus BC

This book gives you the tools to prepare effectively for the Advanced Placement Examination in Mathematics: Calculus BC. These tools include a concise topical review and six full-length practice tests. Our review succinctly covers areas considered most relevant to this exam. Following each of our tests is an answer key complete with detailed explanations designed to clarify the material for you.https://scholarship.richmond.edu/bookshelf/1135/thumbnail.jp

Spatial Cluster Detection for Weighted Outcomes Using Cumulative Geographic Residuals

Spatial cluster detection is an important methodology for identifying regions with excessive numbers of adverse health events without making strong model assumptions on the underlying spatial dependence structure. Previous work has focused on point or individual-level outcome data and few advances have been made when the outcome data are reported at an aggregated level, e.g. at the county- or census tract-level. This paper proposes a new class of spatial cluster detecion methods for point or aggregate data, comprising of continuous, binary, and count data. Compared with the existing spatial cluster detection methods it has the following advantages. First, it readily incorporates region-specific weights, for example, based on a region’s population or a region’s outcome variance, which is key for aggregate data. Second, the established general framework allows for area-level and individual-level covariate adjustment. A simulation study is conducted to evaluate the performance of the method. The proposed method is then applied to assess spatial clustering of high Body Mass Index in a HMO population in the Seattle, Washington USA area

Influence of body mass index on the choice of therapy for depression and follow-up care

Overweight and obese patients commonly suffer from depression and choice of depression therapy may alter weight. We conducted a cohort study to investigate whether obesity is associated with treatment choices for depression; and whether obesity is associated with appropriate duration of depression treatment and receipt of follow-up visits. Adults with a diagnosis of depression between January 1, 2006 and March 31, 2010 who had 1+ new episodes of an antidepressant medication and/or psychotherapy were eligible. Medication use, encounters, diagnoses, height, and weight were collected from health plan databases. We modeled receipt of the different therapies (medication and psychotherapy) by BMI and BMI trajectory during the 9-months prior to initiation of therapy using logistic regression models that accommodated correlation within provider and adjusted for covariates. We modeled BMI via a restricted cubic spline. Fluoxetine was the reference treatment option in the medication models. Lower BMI was associated with greater use of mirtazapine, and a declining BMI prior to treatment was associated with greater odds of initiating mirtazapine and paroxetine. Higher BMI was associated with greater odds of initiating bupropion even after adjustment for smoking status. Obese patients were less likely to receive psychotherapy and less likely to receive appropriate duration (180-days) of depression treatment compared to normal weight subjects. Our study provides evidence that BMI is considered when choosing therapy but associations were weak. Our results should prompt discussion about recommending and choosing depression treatment plans that optimize depression care and weight management concurrently. Differences in care and follow-up by BMI warrant additional research

A New Approach to Hazard Analysis for Rotorcraft

STPA is a new hazard analysis technique that can identify more hazard causes than traditional techniques. It is based on the assumption that accidents result from unsafe control rather than component failures. To demonstrate and evaluate STPA for its application to rotorcraft, it was used to analyze the UH-60MU Warning, Caution, and Advisory (WCA) system associated with the electrical and fly-by-wire flight control system (FCS). STPA results were compared with an independently conducted hazard analysis of the UH-60MU using traditional safety processes described in SAE ARP 4761 and MIL-STD-882E. STPA found the same hazard causes as the traditional techniques and also identified things not found using traditional methods, including design flaws, human behavior, and component integration and interactions. The analysis includes organizational and physical components of systems and can be used to design safety into the system from the beginning of development while being compliant with MIL-STD-882. Copyright 2016 by American Helicopter Society International All right reserved

Stakeholders\u27 views on data sharing in multicenter studies

AIM: To understand stakeholders\u27 views on data sharing in multicenter comparative effectiveness research studies and the value of privacy-protecting methods. MATERIALS and METHODS: Semistructured interviews with five US stakeholder groups. RESULTS: We completed 11 interviews, involving patients (n = 15), researchers (n = 10), Institutional Review Board and regulatory staff (n = 3), multicenter research governance experts (n = 2) and healthcare system leaders (n = 4). Perceptions of the benefits and value of research were the strongest influences toward data sharing; cost and security risks were primary influences against sharing. Privacy-protecting methods that share summary-level data were acknowledged as being appealing, but there were concerns about increased cost and potential loss of research validity. CONCLUSION: Stakeholders were open to data sharing in multicenter studies that offer value and minimize security risks

Perceived Barriers to Weight Management in Primary Care—Perspectives of Patients and Providers

BACKGROUND: Despite the consequences of overweight and obesity, effective weight management is not occurring in primary care. OBJECTIVE: To identify beliefs about obesity that act as barriers to weight management in primary care by surveying both patients and providers and comparing their responses. DESIGN: Anonymous, cross-sectional, self-administered survey of patients and providers of a Veteran’s Administration Primary Care Clinic, distributed at the clinic site. SUBJECTS: Forty-eight Internal Medicine providers and 488 patients. MEASUREMENTS: Beliefs, attitudes, and experiences with weight management as well as demographic characteristics were collected through a questionnaire. RESULTS: Providers and patients differed significantly on many beliefs about weight. Providers were more likely than patients to perceive that patients lack self-control to stay on a diet and that fattening food in society and lack of time for exercise were prime factors in weight gain. They also expressed more interest in helping patients with weight management than patients desiring this. Patients were more likely to state that weight problems should be managed on one’s own, talking to a provider is not helpful, providers blame them for their weight problem, and that appointments contain sufficient time for weight discussion. CONCLUSION: Providers and patients emphasize different barriers to weight management. Providers need to be aware of the beliefs that their patients hold to improve weight management discussions and interventions in primary care

Do Health Beliefs and Behaviors Differ According to Severity of Obesity? A Qualitative Study of Australian Adults

Public responses to obesity have focused on providing standardized messages and supports to all obese individuals, but there is limited understanding of the impact of these messages on obese adults. This descriptive qualitative study using in-depth interviews and a thematic method of analysis, compares the health beliefs and behaviors of 141 Australian adults with mild to moderate (BMI 30−39.9) and severe (BMI ≥ 40) obesity. Mildly obese individuals felt little need to change their health behaviors or to lose weight for health reasons. Most believed they could “lose weight” if they needed to, distanced themselves from the word obesity, and stigmatized those “fatter” than themselves. Severely obese individuals felt an urgent need to change their health behaviors, but felt powerless to do so. They blamed themselves for their weight, used stereotypical language to describe their health behaviors, and described being “at war” with their bodies. Further research, particularly about the role of stigma and stereotyping, is needed to fully understand the impact of obesity messaging on the health beliefs, behaviors, and wellbeing of obese and severely obese adults

Microencapsulated foods as a functional delivery vehicle for omega-3 fatty acids: a pilot study

It is well established that the ingestion of the omega-3 (N3) fatty acids docosahexaenoic acid (DHA) and eicosapentaenoic acid (EPA) positively benefit a variety of health indices. Despite these benefits the actual intake of fish derived N3 is relatively small in the United States. The primary aim of our study was to examine a technology capable of delivering omega-3 fatty acids in common foods via microencapsulation (MicroN3) in young, healthy, active participants who are at low risk for cardiovascular disease. Accordingly, we randomized 20 participants (25.4 ± 6.2 y; 73.4 ± 5.1 kg) to receive the double blind delivery of a placebo-matched breakfast meal (~2093 kJ) containing MicroN3 (450–550 mg EPA/DHA) during a 2-week pilot trial. Overall, we observed no differences in overall dietary macronutrient intake other than the N3 delivery during our treatment regimen. Post-test ANOVA analysis showed a significant elevation in mean (SE) plasma DHA (91.18 ± 9.3 vs. 125.58 ± 11.3 umol/L; P < 0.05) and a reduction in triacylglycerols (89.89 ± 12.8 vs. 80.78 ± 10.4 mg/dL; P < 0.05) accompanying the MicroN3 treatment that was significantly different from placebo (P < 0.05). In post study interviews, participants reported that the ingested food was well-tolerated, contained no fish taste, odor or gastrointestinal distress accompanying treatment. The use of MicroN3 foods provides a novel delivery system for the delivery of essential fatty acids. Our study demonstrates that MicroN3 foods promote the absorption of essential N3, demonstrate bioactivity within 2 weeks of ingestion and are well tolerated in young, active participants who are at low risk for cardiovascular disease

Examining the BMI-mortality relationship using fractional polynomials

<p>Abstract</p> <p>Background</p> <p>Many previous studies estimating the relationship between body mass index (BMI) and mortality impose assumptions regarding the functional form for BMI and result in conflicting findings. This study investigated a flexible data driven modelling approach to determine the nonlinear and asymmetric functional form for BMI used to examine the relationship between mortality and obesity. This approach was then compared against other commonly used regression models.</p> <p>Methods</p> <p>This study used data from the National Health Interview Survey, between 1997 and 2000. Respondents were linked to the National Death Index with mortality follow-up through 2005. We estimated 5-year all-cause mortality for adults over age 18 using the logistic regression model adjusting for BMI, age and smoking status. All analyses were stratified by sex. The multivariable fractional polynomials (MFP) procedure was employed to determine the best fitting functional form for BMI and evaluated against the model that includes linear and quadratic terms for BMI and the model that groups BMI into standard weight status categories using a deviance difference test. Estimated BMI-mortality curves across models were then compared graphically.</p> <p>Results</p> <p>The best fitting adjustment model contained the powers -1 and -2 for BMI. The relationship between 5-year mortality and BMI when estimated using the MFP approach exhibited a J-shaped pattern for women and a U-shaped pattern for men. A deviance difference test showed a statistically significant improvement in model fit compared to other BMI functions. We found important differences between the MFP model and other commonly used models with regard to the shape and nadir of the BMI-mortality curve and mortality estimates.</p> <p>Conclusions</p> <p>The MFP approach provides a robust alternative to categorization or conventional linear-quadratic models for BMI, which limit the number of curve shapes. The approach is potentially useful in estimating the relationship between the full spectrum of BMI values and other health outcomes, or costs.</p