Sequential fixed-width confidence bands for kernel regression estimation

We consider a random design model based on independent and identically distributed (iid) pairs of observations (Xi, Yi), where the regression function m(x) is given by m(x) = E(Yi|Xi = x) with one independent variable. In a nonparametric setting the aim is to produce a reasonable approximation to the unknown function m(x) when we have no precise information about the form of the true density, f(x) of X. We describe an estimation procedure of non-parametric regression model at a given point by some appropriately constructed fixed-width (2d) confidence interval with the confidence coefficient of at least 1−. Here, d(> 0) and 2 (0, 1) are two preassigned values. Fixed-width confidence intervals are developed using both Nadaraya-Watson and local linear kernel estimators of nonparametric regression with data-driven bandwidths.

The sample size was optimized using the purely and two-stage sequential procedure together with asymptotic properties of the Nadaraya-Watson and local linear estimators. A large scale simulation study was performed to compare their coverage accuracy. The numerical results indicate that the confidence bands based on the local linear estimator have the best performance than those constructed by using Nadaraya-Watson estimator. However both estimators are shown to have asymptotically correct coverage properties.

Sample size determination for kernel regression estimation using sequential fixed-width confidence bands

We consider a random design model based on independent and identically distributed pairs of observations (Xi, Yi), where the regression function m(x) is given by m(x) = E(Yi|Xi = x) with one independent variable. In a nonparametric setting the aim is to produce a reasonable approximation to the unknown function m(x) when we have no precise information about the form of the true density, f(x) of X. We describe an estimation procedure of non-parametric regression model at a given point by some appropriately constructed fixed-width (2d) confidence interval with the confidence coefficient of at least 1−. Here, d(> 0) and 2 (0, 1) are two preassigned values. Fixed-width confidence intervals are developed using both Nadaraya-Watson and local linear kernel estimators of nonparametric regression with data-driven bandwidths. The sample size was optimized using the purely and two-stage sequential procedures together with asymptotic properties of the Nadaraya-Watson and local linear estimators. A large scale simulation study was performed to compare their coverage accuracy. The numerical results indicate that the confi dence bands based on the local linear estimator have the better performance than those constructed by using Nadaraya-Watson estimator. However both estimators are shown to have asymptotically correct coverage properties.

Association between changes in habitual physical activity and changes in bone density, muscle strength, and functional performance in elderly men and women

OBJECTIVES: To investigate the long-term effects of habitual physical activity on changes in musculoskeletal health, functional performance, and fracture risk in elderly men and women.

DESIGN: Ten-year prospective population-based study.

SETTING: Malmö-Sjöbo Prospective Study, Sweden.

PARTICIPANTS: Participants were 152 men and 206 women aged 50, 60, 70, and 80 who were followed for 10 years.

MEASUREMENTS: Distal radius bone mineral density (BMD) (single photon absorptiometry), upper limb muscle (grip) strength, balance, gait velocity, occupational and leisure-time activity, and fractures (interview-administered questionnaire) were reassessed after 10 years. Annual changes for all measures were compared between participants with varying habitual physical activity histories at baseline and follow-up: inactive–inactive (n=202), active–inactive (n=47), inactive–active (n=49), and active–active (n=60). Data for men and women were pooled, because there were no sex-by-activity group interactions. To detect possible differences in fracture incidence between the varying habitual activity groups, participants were classified into two activity groups based on their activity classification at baseline and follow-up: inactive:less active versus active:more active.

RESULTS: The annual rate of bone loss was 0.6% per year less in individuals classified as active at both time points than in those classified as inactive at both time points (P<.01). Similar results were observed for balance, but there was no effect of varying habitual activity on changes in muscle strength or gait velocity. There were also no differences in fracture incidence between individuals categorized as active:more active and those categorized as inactive:less active during the follow-up (adjusted hazard ratio=0.90, 95% confidence interval (CI)=0.42–1.90).

CONCLUSION: This study showed that elderly men and women who maintained a habitually active lifestyle over 10 years had lower bone loss and retained better balance than those who remained habitually inactive.

Statin use, bone mineral density, and fracture risk: Geelong Osteoporosis Study

Background Recent data suggest that 3-hydroxy-3-methylglutaryl coenzyme A reductase inhibitors (statins) decrease fracture risk and increase bone mineral density (BMD).

Methods This cross-sectional study is set in southeastern Australia. We evaluated the association between statin use, fracture risk, and BMD in 1375 women (573 with incident fractures and 802 without incident fracture, all drawn from the same community). Fractures were identified radiologically. Medication use and lifestyle factors were documented by questionnaire.

Results Unadjusted odds ratio for fracture associated with statin use was 0.40 (95% confidence interval [CI], 0.23-0.71). Adjusting for BMD at the femoral neck, spine, and whole body increased the odds ratio to 0.45 (95% CI, 0.25-0.80), 0.42 (95% CI, 0.24-0.75), and 0.43 (95% CI, 0.24-0.78), respectively. Adjusting for age, weight, concurrent medications, and lifestyle factors had no substantial effect on the odds ratio for fracture. Statin use was associated with a 3% greater adjusted BMD at the femoral neck (P = .08), and BMD tended to be greater at the spine and whole body but did not achieve statistical significance.

Conclusion The substantial 60% reduction in fracture risk associated with statin use is greater than would be expected from increases in BMD alone.

Evaluation of three field monitoring-density estimation protocols and their relevance to Komodo dragon conservation

Finding practical ways to robustly estimate abundance or density trends in threatened species is a key facet for effective conservation management. Further identifying less expensive monitoring methods that provide adequate data for robust population density estimates can facilitate increased investment into other conservation initiatives needed for species recovery. Here we evaluated and compared inference-and cost-effectiveness criteria for three field monitoring-density estimation protocols to improve conservation activities for the threatened Komodo dragon (Varanus komodoensis). We undertook line-transect counts, cage trapping and camera monitoring surveys for Komodo dragons at 11 sites within protected areas in Eastern Indonesia to collect data to estimate density using distance sampling methods or the Royle-Nichols abundance induced heterogeneity model. Distance sampling estimates were considered poor due to large confidence intervals, a high coefficient of variation and that false absences were obtained in 45 % of sites where other monitoring methods detected lizards present. The Royle-Nichols model using presence/absence data obtained from cage trapping and camera monitoring produced highly correlated density estimates, obtained similar measures of precision and recorded no false absences in data collation. However because costs associated with camera monitoring were considerably less than cage trapping methods, albeit marginally more expensive than distance sampling, better inference from this method is advocated for ongoing population monitoring of Komodo dragons. Further the cost-savings achieved by adopting this field monitoring method could facilitate increased expenditure on alternative management strategies that could help address current declines in two Komodo dragon populations.

The association between alcohol outlet density and alcohol use among urban and regional Australian adolescents

AIMS: While recent evidence suggests that higher alcohol outlet density is associated with greater alcohol use among adolescents, influence of the four main outlet types on youth drinking within urban and regional communities is unknown. This study provides the first investigation of this relationship. DESIGN: Repeated cross-sectional surveys with random samples of secondary students clustered by school. Mixed-effects logistic regression analyses examined the association between each outlet type and the drinking outcomes, with interaction terms used to test urban/regional differences. SETTING: Australia, 2002-11. PARTICIPANTS: Respondents participating in a triennial survey (aged 12-17 years); 44 897 from urban settings, 23 311 from regional settings. MEASUREMENTS: The key outcome measures were past month alcohol use, risky drinking among all students and risky drinking among past week drinkers. For each survey year, students were assigned a postcode-level outlet density (number of licences per 1000 population) for each outlet type (general, on-premise, off-premise, clubs). FINDINGS: Interaction terms revealed a significant association between off-premises outlet density and risky drinking among all adolescents in urban (odds ratio = 1.36, 95% confidence interval CI = 1.05-1.75, P < 0.05) but not regional areas. Similarly, club density was associated with the drinking outcomes in urban communities only. General and on-premises density was associated with alcohol use and risky drinking among all adolescents. CONCLUSIONS: Higher densities of general, on- and off-premises outlets in an adolescent's immediate neighbourhood are related to increased likelihood of alcohol consumption among all adolescents. The density of licensed clubs is associated more strongly with drinking for urban than for regional adolescents.