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.

Endogenous parathyroid hormone is associated with reduced cartilage volume in vivo in a population-based sample of adult women

Objectives Animal and in vitro studies suggest that parathyroid hormone (PTH) may affect articular cartilage. However, little is known of the relationship between PTH and human joints in vivo.

Design Longitudinal.

Setting Barwon Statistical Division, Victoria, Australia.

Participants 101 asymptomatic women aged 35–49 years (2007–2009) and without clinical knee osteoarthritis, selected from the population-based Geelong Osteoporosis Study.

Risk factors Blood samples obtained 10 years before (1994–1997) and stored at −80°C for random batch analyses. Serum intact PTH was quantified by chemiluminescent enzyme assay. Serum 25-hydroxyvitamin D (25(OH)D) was assayed using equilibrium radioimmunoassay. Models were adjusted for age, bone area and body mass index; further adjustment was made for 25(OH)D and calcium supplementation.

Outcome Knee cartilage volume, measured by MRI.

Results A higher lnPTH was associated with reduced medial—but not lateral—cartilage volume (regression coefficient±SD, p value: −72.2±33.6 mm3, p=0.03) after adjustment for age, body mass index and bone area. Further sinusoidal adjustment (−80.8±34.4 mm3, p=0.02) and 25(OH)D with seasonal adjustment (−72.7±35.1 mm3, p=0.04), calcium supplementation and prevalent osteophytes did not affect the results.

Conclusions A higher lnPTH might be detrimental to knee cartilage in vivo. Animal studies suggest that higher PTH concentrations reduce the healing ability of cartilage following minor injury. This may be apparent in the presence of increased loading, which occurs in the medial compartment, placing the medial cartilage at higher risk for injury.

Socioeconomic status and risk factors for obesity and metabolic disorders in a population-based sample of adult females

Objectives : The association between lower socioeconomic status (SES), obesity, lifestyle choices and adverse health consequences are well documented, however to date the relationship between these variables and area-based SES (equivalised for advantage and disadvantage) has not been examined simultaneously in one population or with more than tertiary divisions of SES. We set out to examine the risk factors for obesity and metabolic disorders in the same population across quintiles of area-based SES.

Methods : We performed a descriptive cross-sectional study using existing data from a population-based random selection of women aged 20–92 years (n = 1110) recruited from the Barwon Statistical Division, South Eastern Australia.

Results : All measures of adiposity were inversely associated with SES, and remained significant after adjusting for age. Lifestyle choices associated with adiposity and poorer health, including smoking, larger serving sizes of foods, and reduced physical activity, were significantly associated with individuals from lower SES groups.

Conclusions : Greater measures of adiposity and less healthy lifestyle choices were observed in individuals from lower SES. Significant differences in body composition were identified between quintiles 1 and 5, whereas subjects in the mid quintiles had relatively similar measures. The inverse relationship between SES, obesity and less healthy lifestyle underscores the possibility that these associations may be causal and should be investigated further.

Sample subset optimization for classifying imbalanced biological data

Data in many biological problems are often compounded by imbalanced class distribution. That is, the positive examples may largely outnumbered by the negative examples. Many classification algorithms such as support vector machine (SVM) are sensitive to data with imbalanced class distribution, and result in a suboptimal classification. It is desirable to compensate the imbalance effect in model training for more accurate classification. In this study, we propose a sample subset optimization technique for classifying biological data with moderate and extremely high imbalanced class distributions. By using this optimization technique with an ensemble of SVMs, we build multiple roughly balanced SVM base classifiers, each trained on an optimized sample subset. The experimental results demonstrate that the ensemble of SVMs created by our sample subset optimization technique can achieve higher area under the ROC curve (AUC) value than popular sampling approaches such as random over-/under-sampling; SMOTE sampling, and those in widely used ensemble approaches such as bagging and boosting.

Random Subspace Two-Dimensional PCA for face recognition

The two-dimensional Principal Component Analysis (2DPCA) is a robust method in face recognition. Much recent research shows that the 2DPCA is more reliable than the well-known PCA method in recognising human face. However, in many cases, this method tends to be overfitted to sample data. In this paper, we proposed a novel method named random subspace two-dimensional PCA (RS-2DPCA), which combines the 2DPCA method with the random subspace (RS) technique. The RS-2DPCA inherits the advantages of both the 2DPCA and RS technique, thus it can avoid the overfitting problem and achieve high recognition accuracy. Experimental results in three benchmark face data sets -the ORL database, the Yale face database and the extended Yale face database B - confirm our hypothesis that the RS-2DPCA is superior to the 2DPCA itself.

Gambling participation and problem gambling severity in a stratified random survey : Findings from the second social and economic impact study of gambling in Tasmania

Demographic characteristics associated with gambling participation and problem gambling severity were investigated in a stratified random survey in Tasmania, Australia. Computer-assisted telephone interviews were conducted in March 2011 resulting in a representative sample of 4,303 Tasmanian residents aged 18 years or older. Overall, 64.8 % of Tasmanian adults reported participating in some form of gambling in the previous 12 months. The most common forms of gambling were lotteries (46.5 %), keno (24.3 %), instant scratch tickets (24.3 %), and electronic gaming machines (20.5 %). Gambling severity rates were estimated at non-gambling (34.8 %), non-problem gambling (57.4 %), low risk gambling (5.3 %), moderate risk (1.8 %), and problem gambling (.7 %). Compared to Tasmanian gamblers as a whole significantly higher annual participation rates were reported by couples with no children, those in full time paid employment, and people who did not complete secondary school. Compared to Tasmanian gamblers as a whole significantly higher gambling frequencies were reported by males, people aged 65 or older, and people who were on pensions or were unable to work. Compared to Tasmanian gamblers as a whole significantly higher gambling expenditure was reported by males. The highest average expenditure was for horse and greyhound racing ($AUD 1,556), double the next highest gambling activity electronic gaming machines ($AUD 767). Compared to Tasmanian gamblers as a whole problem gamblers were significantly younger, in paid employment, reported lower incomes, and were born in Australia. Although gambling participation rates appear to be falling, problem gambling severity rates remain stable. These changes appear to reflect a maturing gambling market and the need for population specific harm minimisation strategies. © 2014 Springer Science+Business Media New York.

Neither fixed nor random: weighted least squares meta-analysis

This study challenges two core conventional meta-analysis methods: fixed effect and random effects. We show how and explain why an unrestricted weighted least squares estimator is superior to conventional random-effects meta-analysis when there is publication (or small-sample) bias and better than a fixed-effect weighted average if there is heterogeneity. Statistical theory and simulations of effect sizes, log odds ratios and regression coefficients demonstrate that this unrestricted weighted least squares estimator provides satisfactory estimates and confidence intervals that are comparable to random effects when there is no publication (or small-sample) bias and identical to fixed-effect meta-analysis when there is no heterogeneity. When there is publication selection bias, the unrestricted weighted least squares approach dominates random effects; when there is excess heterogeneity, it is clearly superior to fixed-effect meta-analysis. In practical applications, an unrestricted weighted least squares weighted average will often provide superior estimates to both conventional fixed and random effects.

Neither fixed nor random: weighted least squares meta-regression

Our study revisits and challenges two core conventional meta-regression estimators: the prevalent use of‘mixed-effects’ or random-effects meta-regression analysis and the correction of standard errors that defines fixed-effects meta-regression analysis (FE-MRA). We show how and explain why an unrestricted weighted least squares MRA (WLS-MRA) estimator is superior to conventional random-effects (or mixed-effects) meta-regression when there is publication (or small-sample) bias that is as good as FE-MRA in all cases and better than fixed effects in most practical applications. Simulations and statistical theory show that WLS-MRA provides satisfactory estimates of meta-regression coefficients that are practically equivalent to mixed effects or random effects when there is no publication bias. When there is publication selection bias, WLS-MRA always has smaller bias than mixed effects or random effects. In practical applications, an unrestricted WLS meta-regression is likely to give practically equivalent or superior estimates to fixed-effects, random-effects, and mixed-effects meta-regression approaches. However, random-effects meta-regression remains viable and perhaps somewhat preferable if selection for statistical significance (publication bias) can be ruled out and when random, additive normal heterogeneity is known to directly affect the ‘true’ regression coefficient.