Composite indices: rank robustness, statistical association, and redundancy

This article evaluates the robustness of rankings obtained from composite indices that combine information from two or more components via a weighted sum. It examines the empirical prevalence of robust comparisons using the method proposed by Foster et al. (2010). Indices examined are the Human Development Index (HDI), the Index of Economic Freedom (IEF), and the Environmental Performance Index (EPI). Key theoretical results demonstrate links between the prevalence of robust comparisons, Kendall’s tau rank correlation coefficient, and statistical association across components. Implications for redundancy among index components are also examined.

Statistical approaches to testing the relationships of the built environment with resident-level physical activity behavior and health outcomes in cross-sectional studies with cluster sampling

To achieve valid conclusions, studies exploring associations of the built environment with residents' physical activity and health-related outcomes need to employ statistical approaches accounting for clustered data. This article discusses the following main statistical approaches: analysis of covariance, regression models with robust standard errors, generalized estimating equations, and multilevel generalized linear models. The choice of a statistical method depends on the characteristics of the study and research questions. While the first three approaches are employed to account for clustering in the data, multilevel models can also help unravel more substantive issues within a social ecological theoretical framework of health behavior.

Supporting athlete selection and strategic planning in track cycling omnium: A statistical and machine learning approach

This article describes the implementation of machine learning techniques that assist cycling experts in the crucial decision-making processes for athlete selection and strategic planning in the track cycling omnium. The omnium is a multi-event competition that was included in the Olympic Games for the first time in 2012. Presently, selectors and cycling coaches make decisions based on experience and opinion. They rarely have access to knowledge that helps predict athletic performances. The omnium presents a unique and complex decision-making challenge as it is not clear what type of athlete is best suited to the omnium (e.g., sprint or endurance specialist) and tactical decisions made by the coach and athlete during the event will have significant effects on the overall performance of the athlete. In the present work, a variety of machine learning techniques were used to analyze omnium competition data from the World Championships since 2007. The analysis indicates that sprint events have slightly more influence in determining the medalists, than endurance-based events. Using a probabilistic analysis, we created a model of performance prediction that provides an unprecedented level of supporting information that assists coaches with strategic and tactical decisions during the omnium.

Modelling and analysing track cycling Omnium performances using statistical and machine learning techniques

This article describes the utilisation of an unsupervised machine learning technique and statistical approaches (e.g., the Kolmogorov-Smirnov test) that assist cycling experts in the crucial decision-making processes for athlete selection, training, and strategic planning in the track cycling Omnium. The Omnium is a multi-event competition that will be included in the summer Olympic Games for the first time in 2012. Presently, selectors and cycling coaches make decisions based on experience and intuition. They rarely have access to objective data. We analysed both the old five-event (first raced internationally in 2007) and new six-event (first raced internationally in 2011) Omniums and found that the addition of the elimination race component to the Omnium has, contrary to expectations, not favoured track endurance riders. We analysed the Omnium data and also determined the inter-relationships between different individual events as well as between those events and the final standings of riders. In further analysis, we found that there is no maximum ranking (poorest performance) in each individual event that riders can afford whilst still winning a medal. We also found the required times for riders to finish the timed components that are necessary for medal winning. The results of this study consider the scoring system of the Omnium and inform decision-making toward successful participation in future major Omnium competitions.

Examining the impact of reimbursement on referral to bone density testing for older adults: 8 years of data from the Barwon Statistical Division, Australia

Summary
In 2007, Medicare Australia revised reimbursement guidelines for dual energy X-ray absorptiometry (DXA) for Australians aged ≥70 years; we examined whether these changes increased DXA referrals in older adults. Proportions of DXA referrals doubled for men and tripled for women from 2003 to 2010; however, rates of utilization remained low.

Introduction
On April 1, 2007 Medicare Australia revised reimbursement guidelines for DXA for Australians aged ≥70 year; changes that were intended to increase the proportion of older adults being tested. We examined whether changes to reimbursement increased DXA referrals in older adults, and whether any sex differences in referrals were observed in the Barwon Statistical Division.

Methods
Proportions of DXA referrals 2003–2010 based on the population at risk ascertained from Australian Census data and annual referral rates and rate ratios stratified by sex, year of DXA, and 5-year age groups. Persons aged ≥70 years referred to the major public health service provider for DXA clinical purposes (n = 6,096; 21 % men).

Results
DXA referrals. Proportions of DXA referrals for men doubled from 0.8 % (2003) to 1.8 % (2010) and tripled from 2.0 to 6.3 % for women (all p < 0.001). For 2003–2006, referral ratios of men/women ranged between 1:1.9 and 1:3.0 and for 2007–2010 were 1:2.3 to 1:3.4. Referral ratios <2007:≥2007 were 1:1.7 for men aged 70–79 years (p < 0.001), 1:1.2 for men aged 80–84 years (p = 0.06), and 1:1.3 for men 85+ years (p = 0.16). For women, the ratios <2007:≥2007 were 1:2.1 (70–79 years), 1.1.5 (80–84 years), and 1:1.4 (85+ years) (all p < 0.001).

Conclusions
DXA referral ratios were 1:1.6 (men) and 1:1.8 (women) for 2007–2010 vs. 2003–2006; proportions of referrals doubled for men and tripled for women from 2003 to 2010. Overall, rates of DXA utilization remained low. Policy changes may have had minimal influence on referral; thus, ongoing evaluation over time is warranted.