On classical and other methods of discriminant analysis and estimation of log-odds

For two multinormal populations with equal covariance matrices the likelihood ratio discriminant function, an alternative allocation rule to the sample linear discriminant function when n1 ≠ n2 ,is studied analytically. With the assumption of a known covariance matrix its distribution is derived and the expectation of its actual and apparent error rates evaluated and compared with those of the sample linear discriminant function. This comparison indicates that the likelihood ratio allocation rule is robust to unequal sample sizes. The quadratic discriminant function is studied, its distribution reviewed and evaluation of its probabilities of misclassification discussed. For known covariance matrices the distribution of the sample quadratic discriminant function is derived. When the known covariance matrices are proportional exact expressions for the expectation of its actual and apparent error rates are obtained and evaluated. The effectiveness of the sample linear discriminant function for this case is also considered. Estimation of true log-odds for two multinormal populations with equal or unequal covariance matrices is studied. The estimative, Bayesian predictive and a kernel method are compared by evaluating their biases and mean square errors. Some algebraic expressions for these quantities are derived. With equal covariance matrices the predictive method is preferable. Where it derives this superiority is investigated by considering its performance for various levels of fixed true log-odds. It is also shown that the predictive method is sensitive to n1 ≠ n2. For unequal but proportional covariance matrices the unbiased estimative method is preferred. Product Normal kernel density estimates are used to give a kernel estimator of true log-odds. The effect of correlation in the variables with product kernels is considered. With equal covariance matrices the kernel and parametric estimators are compared by simulation. For moderately correlated variables and large dimension sizes the product kernel method is a good estimator of true log-odds.

Role of the fibula in the stability of diaphyseal tibial fractures fixed by intramedullary nailing

Background: For tibial fractures, the decision to fix a concomitant fibular fracture is undertaken on a case-by-case basis. To aid in this clinical decision-making process, we investigated whether loss of integrity of the fibula significantly destabilises midshaft tibial fractures, whether fixation of the fibula restores stability to the tibia, and whether removal of the fibula and interosseous membrane for expediency in biomechanical testing significantly influences tibial interfragmentary mechanics. Methods: Tibia/fibula pairs were harvested from six cadaveric donors with the interosseous membrane intact. A tibial osteotomy fracture was fixed by reamed intramedullary (IM) nailing. Axial, torsion, bending, and shear tests were completed for four models of fibular involvement: intact fibula, osteotomy fracture, fibular plating, and resected fibula and interosseous membrane. Findings: Overall construct stiffness decreased slightly with fibular osteotomy compared to intact bone, but this change was not statistically significant. Under low loads, the influence of the fibula on construct stability was only statistically significant in torsion (large effect size). Fibular plating stiffened the construct slightly, but this change was not statistically significant compared to the fibular osteotomy case. Complete resection of the fibula and interosseous membrane significantly decreased construct torsional stiffness only (large effect size). Interpretation: These results suggest that fixation of the fibula may not contribute significantly to the stability of diaphyseal tibial fractures and should not be undertaken unless otherwise clinically indicated. For testing purposes, load-sharing through the interosseous membrane contributes significantly to overall construct mechanics, especially in torsion, and we recommend preservation of these structures when possible.

Youth-Physical Activity Towards Health: evidence and background to the development of the Y-PATH physical activity intervention for adolescents

Background: Despite known benefits of regular physical activity for health and well-being, many studies suggest that levels of physical activity in young people are low, and decline dramatically during adolescence. The purpose of the current research was to gather data on adolescent youth in order to inform the development of a targeted physical activity intervention. Methods: Cross-sectional data on physical activity levels (using self report and accelerometry), psychological correlates of physical activity, anthropometic characteristics, and the fundamental movement skill proficiency of 256 youth (53% male, 12.40 ± 0.51 years) were collected. A subsample (n = 59) participated in focus group interviews to explore their perceptions of health and identify barriers and motivators to participation in physical activity. Results: Findings indicate that the majority of youth (67%) were not accumulating the minimum 60 minutes of physical activity recommended daily for health, and that 99.5% did not achieve the fundamental movement skill proficiency expected for their age. Body mass index data showed that 25% of youth were classified as overweight or obese. Self-efficacy and physical activity attitude scores were significantly different (p < 0.05) between low, moderate and high active participants. Active and inactive youth reported differences in their perceived understanding of health and their barriers to physical activity participation, with active youth relating nutrition, exercise, energy and sports with the definition of ‘being healthy’, and inactive youth attributing primarily nutritional concepts to ‘being healthy’. Conclusions: Data show a need for targeting low levels of physical activity in youth through addressing poor health related activity knowledge and low fundamental movement skill proficiency. The Y-PATH intervention was developed in accordance with the present study findings; details of the intervention format are presented.

Adhesives for fixed orthodontic bands

Background: Orthodontic treatment involves using fixed or removable appliances (dental braces) to correct the positions of teeth. It has been shown that the quality of treatment result obtained with fixed appliances is much better than with removable appliances. Fixed appliances are, therefore, favoured by most orthodontists for treatment. The success of a fixed orthodontic appliance depends on the metal attachments (brackets and bands) being attached securely to the teeth so that they do not become loose during treatment. Brackets are usually attached to the front and side teeth, whereas bands (metal rings that go round the teeth) are more commonly used on the back teeth (molars). A number of adhesives are available to attach bands to teeth and it is important to understand which group of adhesives bond most reliably, as well as reducing or preventing dental decay during the treatment period. :Objectives: To evaluate the effectiveness of the adhesives used to attach bands to teeth during fixed appliance treatment, in terms of: (1) how often the bands come off during treatment; and (2) whether they protect the banded teeth against decay during fixed appliance treatment. Search methods: The following electronic databases were searched: Cochrane Oral Health's Trials Register (searched 2 June 2016), Cochrane Central Register of Controlled Trials (CENTRAL; 2016, Issue 5) in the Cochrane Library (searched 2 June 2016), MEDLINE Ovid (1946 to 2 June 2016) and EMBASE Ovid (1980 to 2 June 2016). We searched ClinicalTrials.gov and the World Health Organization International Clinical Trials Registry Platform for ongoing trials. No restrictions were placed on the language or date of publication when searching the electronic databases. Selection criteria: Randomised and controlled clinical trials (RCTs and CCTs) (including split-mouth studies) of adhesives used to attach orthodontic bands to molar teeth were selected. Patients with full arch fixed orthodontic appliance(s) who had bands attached to molars were included. Data collection and analysis: All review authors were involved in study selection, validity assessment and data extraction without blinding to the authors, adhesives used or results obtained. All disagreements were resolved by discussion. Main results: Five RCTs and three CCTs were identified as meeting the review's inclusion criteria. All the included trials were of split-mouth design. Four trials compared chemically cured zinc phosphate and chemically cured glass ionomer; three trials compared chemically cured glass ionomer cement with light cured compomer; one trial compared chemically cured glass ionomer with a chemically cured glass phosphonate. Data analysis was often inappropriate within the studies meeting the inclusion criteria. Authors' conclusions: There is insufficient high quality evidence with regard to the most effective adhesive for attaching orthodontic bands to molar teeth. Further RCTs are required.