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<p>Subjects enrolled in a clinical trial may experience a competing risk event which alters the risk of the primary event of interest. This differs from when subject information is censored, which is non-informative. In order to calculate the cumulative incidence function (CIF) for the event of interest, competing risks and censoring must be treated appropriately; otherwise estimates will be biased. There are two commonly used methods of calculating a confidence interval (CI) for the CIF for the event of interest which account for censoring and competing risk: the Kalbfleisch-Prentice (KP) method and the Counting Process (CP) method. The goal of this paper is to understand the variances associated with the two methods to improve our understanding of the CI. This will allow for appropriate estimation of the CIF CI for a single-arm cohort study that is currently being conducted. Previous work has failed to address this question because researchers typically focus on comparing two treatment arms using statistical tests that compare cause-specific hazard functions and do not require a CI for the CIF. The two methods were compared by calculating CIs for the CIF using data from a previous related study, using bootstrapping, and a simulation study with varying event rates and competing risk rates. The KP method usually estimated a larger CIF and variance than the CP method. When event rates were low (5%), the CP method is recommended as it yields more consistent results than the KP method. The CP method is recommended for the proposed study since event rates are expected to be moderate (5-10%).</p> / Master of Science (MS)

In robust parameter design it is often possible to set the levels of the controllable factors to produce a zero gradient for the transmission of variability from the noise variables. If the number of control variables is greater than the number of noise variables, a continuum of zero-gradient solutions exists. This situation is useful as it provides the experimenter with multiple conditions under which to configure a zero gradient for noise variable transmission. However, this situation requires a confidence region for the multiple-solution factor levels that provides proper simultaneous coverage. This requirement has not been previously recognized in the literature. In the case where the number of control variables is greater than the number of noise variables, we show how to construct critical values needed to maintain the simultaneous coverage rate. Two examples are provided as a demonstration of the practical need to adjust the critical values for simultaneous coverage. The zero-gradient confidence region only focuses on the variance, and there are in fact many such situations in which focus is or could be placed entirely on the process variance. In the situation where both mean and variance need to be considered, a general confidence region in control variables is developed by minimizing weighted mean square error. This general method is applicable to many situations including mixture experiments which have an inherit constraint on the control factors. It also gives the user the flexibility to put different weights on the mean and variance parts for simultaneous optimization. It turns out that the same computational algorithm can be used to compute the dual confidence region in both control factors and the response variable. / Statistics

This was an investigation of students’ mathematics confidence and how it is shaped by their accumulated experiences in mathematics education, and informs their view of the purpose of mathematics in their current and envisioned lives. There is no shortage of studies on black students’ poor performance in mathematics education and its seeming persistence in spite of reform initiatives and policy changes. Conversely, there is a dearth of studies in the field on high achieving black students and the construction of their mathematics identities. Some scholars have argued that the plenitude of data on the failure of black students in mathematics education has contributed to mainstream beliefs of a racial hierarchy of mathematics ability in America. This perception has not only shaped attitudes and behaviors of educational scholars, policymakers, practitioners, but it has contributed to the alienation of many students from the community of “doers of mathematics.” In an effort to combat the pervasiveness of race-based beliefs of math ability, some researchers in the field of mathematics have advocated for the need to refocus research on better understanding students’ mathematics identity and its relationship to their performance. In light of this, this study, using ethnographic methods, examined the mathematics confidence—a subset of mathematics identity—of a group of seniors enrolled in honor’s pre-calculus at an under resourced urban comprehensive high school. Data collected and analyzed for this study showed that participants, in spite of a history of mostly success in math and despite being socialized to view the classroom as opportunity to challenge disparaging views of African Americans, refused to seek or claim membership to the community of math people. This study provides new insights into black students’ perception of and sense of belongingness to mathematics, and its potential impact on their academic and economic prospects. / Urban Education

This qualitative study investigated how confidence chats affect how students with disabilities (SWD) position themselves during mathematics discourse and the impact the confidence chats had on a student’s mathematical identity. A critical discourse analysis was conducted over a three-month period using transcripts from classroom observations, student-teacher confidence chats, and teacher interview debriefs. Findings revealed that following the confidence chats, SWD participated in discourse, and students were able to adjust their positioning in relation to others. Over the course of the study, student collaboration increased and their reliance on teacher support decreased. In addition, the findings indicated that confidence chats provided a window into students’ macro-identities which the teacher was not seeing during classroom interactions. Students were positioned in relation to tests and grades and were not seeing the relevance of how mathematics is preparing them for college or career readiness. The implications of this study suggest that students may not know what collaboration looks and sounds like. Taking time to set norms and expectations is a critical element when providing opportunities for discourse in the classroom. Additionally, student strengths need to be affirmed, so students build confidence in their mathematical abilities and connect their mathematics identities to positive experiences and the real-world.

The objective of this thesis is to estimate, for a distribution network, confidence intervals containing the values of nodal hourly power consumption and nodal maximum power consumption per customer where they are not measured. The values of nodal hourly power consumption are needed in operational as well as in planning stages to carry out load flow studies. As for the values of nodal maximum power consumption per customer, they are used to solve planning problems such as transformer sizing. Confidence interval estimation was preferred to point estimation because it takes into consideration the large variability of the consumption values. A computationally intensive statistical technique, namely the bootstrap method, is utilized to estimate these intervals. It allows us to replace idealized model assumptions for the load distributions by model free analyses. Two studies have been executed. The first one is based on the original nonparametric bootstrap method to calculate a 95% confidence interval for nodal hourly power consumption. This estimation is carried out for a given node and a given hour of the year. The second one makes use of the parametric bootstrap method in order to infer a 95% confidence interval for nodal maximum power consumption per customer. This estimation is realized for a given node and a given month. Simulation results carried out on a real data set are presented and discussed. / Master of Science

Yes / Near-peer teaching is becoming increasingly popular as a learning methodology. We report the development of a novel near-peer biological sciences revision course and its acceptability and impact on student confidence and exam performance. A cross-sectional analysis of tutee-completed evaluation forms before and after each session was performed, providing demographic details, quality scores, and self-rating of confidence in the topic taught on a 0 to 100 mm visual analogue scale (VAS). The confidence data was examined using analysis of means. Exam performance was examined by analysis of variance and canonical correlation analysis. Thirty-eight sessions were delivered to an average of 69.9 (±27.1) years 1 and 2 medical students per session generating 2656 adequately completed forms. There was a mean VAS gain of 19.1 (5.3 to 27.3) in self-reported confidence. Looking at relationship between attendance and exam scores, only two topics showed significant association between number of sessions attended and exam performance, fewer than hypothesised. The present study demonstrates that near-peer teaching for biological sciences is feasible and is associated with improved self-reported confidence in the sessions taught. The outcome data, showing significant effect for only a small number of items, demonstrates the difficulty of outcome related research.

Yes / The Royal College of Midwives (RCM) reports that between 5–10% of newly qualified midwives (NQM) leave the profession in the UK within a year of registration, with similar losses reported internationally (RCM 2010). NQMs are in a position of vulnerability and are highly susceptible to workplace adversity that subsequently may affect their emotional well-being. This literature review explores the experiences of NQMs surrounding their emotional well-being within the first 12 months of transition. Following a thorough search and appraisal of the literature, four papers were reviewed. Two key themes were identified consisting of factors that challenge NQMs’ resilience causing negative emotional well-being, and factors that enhance resilience, promoting positive emotional well-being. The findings of this review demonstrate that there is a need for the consistent implementation of protective mechanisms such as structured preceptorship and supportive mentorship. Such interventions may improve physical and emotional well-being, increase retention and better prepare NQMs for the journey ahead; ultimately also improving quality of care for women and patient safety.

Yes / The aim of this study was to establish the impact of dementia education and training on the knowledge, attitudes and confidence of health and social care staff. The study also aimed to identify the most effective features (content and pedagogical) of dementia education and training. Cross-sectional survey study. Data collection occurred in 2017. Health and social care staff in the UK including acute care, mental health community care trusts, primary care and care homes. All health and social care staff who had completed dementia education and training meeting the minimal standards as set by Health Education England, within the past 5 years were invited to participate in an online survey. A total of 668 health and social care staff provided informed consent and completed an online survey, and responses from 553 participants were included in this study. The majority of the respondents were of white British ethnicity (94.4%) and identified as women (88.4%). Knowledge, attitude and confidence of health and social care staff. Hierarchical multiple regression analysis was conducted. Staff characteristics, education and training content variables and pedagogical factors were found to account for 29% of variance in staff confidence (F=4.13, p<0.001), 22% of variance in attitude (knowledge) (F=3.80, p<001), 18% of the variance in staff knowledge (F=2.77, p<0.01) and 14% of variance in staff comfort (attitude) (F=2.11, p<0.01). The results suggest that dementia education and training has limited impact on health and social care staff learning outcomes. While training content variables were important when attempting to improve staff knowledge, more consideration should be given to pedagogical factors when training is aiming to improve staff attitude and confidence. / NIHR Policy Research Programme (Understanding Effective Dementia Workforce Education and Training: A Formative Evaluation (DeWET Evaluation), PR-R10–0514-12006).