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.

The Integrated Model of Sport Confidence: A Canonical Correlation and Mediational Analysis

The main purpose of the study was to examine crucial parts of Vealey’s (2001) integrated framework hypothesizing that sport confidence is a mediating variable between sources of sport confidence (including achievement, self-regulation, and social climate) and athletes’ affect in competition. The sample consisted of 386 athletes, who completed the Sources of Sport Confidence Questionnaire, Trait Sport Confidence Inventory, and Dispositional Flow Scale-2. Canonical correlation analysis revealed a confidence-achievement dimension underlying flow. Bias-corrected bootstrap confidence intervals in AMOS 20.0 were used in examining mediation effects between source domains and dispositional flow. Results showed that sport confidence partially mediated the relationship between achievement and  self-regulation domains and flow, whereas no significant mediation was found for social climate. On a subscale level, full mediation models emerged for achievement and flow dimensions of challenge–skills balance, clear goals, and concentration on the task at hand.

Power, effects, confidence, and significance: an investigation of statistical practices in nursing research

Objectives: To (a) assess the statistical power of nursing research to detect small, medium, and large effect sizes; (b) estimate the experiment-wise Type I error rate in these studies; and (c) assess the extent to which (i) a priori power analyses, (ii) effect sizes (and interpretations thereof), and (iii) confidence intervals were reported. Design: Statistical review. Data sources: Papers published in the 2011 volumes of the 10 highest ranked nursing journals, based on their 5-year impact factors. Review methods: Papers were assessed for statistical power, control of experiment-wise Type I error, reporting of a priori power analyses, reporting and interpretation of effect sizes, and reporting of confidence intervals. The analyses were based on 333 papers, from which 10,337 inferential statistics were identified. Results: The median power to detect small, medium, and large effect sizes was .40 (interquartile range [. IQR]. = .24-.71), .98 (IQR= .85-1.00), and 1.00 (IQR= 1.00-1.00), respectively. The median experiment-wise Type I error rate was .54 (IQR= .26-.80). A priori power analyses were reported in 28% of papers. Effect sizes were routinely reported for Spearman's rank correlations (100% of papers in which this test was used), Poisson regressions (100%), odds ratios (100%), Kendall's tau correlations (100%), Pearson's correlations (99%), logistic regressions (98%), structural equation modelling/confirmatory factor analyses/path analyses (97%), and linear regressions (83%), but were reported less often for two-proportion z tests (50%), analyses of variance/analyses of covariance/multivariate analyses of variance (18%), t tests (8%), Wilcoxon's tests (8%), Chi-squared tests (8%), and Fisher's exact tests (7%), and not reported for sign tests, Friedman's tests, McNemar's tests, multi-level models, and Kruskal-Wallis tests. Effect sizes were infrequently interpreted. Confidence intervals were reported in 28% of papers. Conclusion: The use, reporting, and interpretation of inferential statistics in nursing research need substantial improvement. Most importantly, researchers should abandon the misleading practice of interpreting the results from inferential tests based solely on whether they are statistically significant (or not) and, instead, focus on reporting and interpreting effect sizes, confidence intervals, and significance levels. Nursing researchers also need to conduct and report a priori power analyses, and to address the issue of Type I experiment-wise error inflation in their studies. © 2013 .

Statistical evaluation of time-dependent metabolite concentrations: estimation of post-mortem intervals based on in situ 1H-MRS of the brain

Knowledge of the time interval from death (post-mortem interval, PMI) has an enormous legal, criminological and psychological impact. Aiming to find an objective method for the determination of PMIs in forensic medicine, 1H-MR spectroscopy (1H-MRS) was used in a sheep head model to follow changes in brain metabolite concentrations after death. Following the characterization of newly observed metabolites (Ith et al., Magn. Reson. Med. 2002; 5: 915-920), the full set of acquired spectra was analyzed statistically to provide a quantitative estimation of PMIs with their respective confidence limits. In a first step, analytical mathematical functions are proposed to describe the time courses of 10 metabolites in the decomposing brain up to 3 weeks post-mortem. Subsequently, the inverted functions are used to predict PMIs based on the measured metabolite concentrations. Individual PMIs calculated from five different metabolites are then pooled, being weighted by their inverse variances. The predicted PMIs from all individual examinations in the sheep model are compared with known true times. In addition, four human cases with forensically estimated PMIs are compared with predictions based on single in situ MRS measurements. Interpretation of the individual sheep examinations gave a good correlation up to 250 h post-mortem, demonstrating that the predicted PMIs are consistent with the data used to generate the model. Comparison of the estimated PMIs with the forensically determined PMIs in the four human cases shows an adequate correlation. Current PMI estimations based on forensic methods typically suffer from uncertainties in the order of days to weeks without mathematically defined confidence information. In turn, a single 1H-MRS measurement of brain tissue in situ results in PMIs with defined and favorable confidence intervals in the range of hours, thus offering a quantitative and objective method for the determination of PMIs.

DISTRIBUTION FUNCTIONS, MEAN SQUARED ERRORS, AND CONFIDENCE LIMITS FOR RIDGE REGRESSION ESTIMATORS

A large number of ridge regression estimators have been proposed and used with little knowledge of their true distributions. Because of this lack of knowledge, these estimators cannot be used to test hypotheses or to form confidence intervals.^ This paper presents a basic technique for deriving the exact distribution functions for a class of generalized ridge estimators. The technique is applied to five prominent generalized ridge estimators. Graphs of the resulting distribution functions are presented. The actual behavior of these estimators is found to be considerably different than the behavior which is generally assumed for ridge estimators.^ This paper also uses the derived distributions to examine the mean squared error properties of the estimators. A technique for developing confidence intervals based on the generalized ridge estimators is also presented. ^

Birth-to-pregnancy intervals and adverse perinatal outcomes among African-born black women in Washington State.

Thesis (Master's)--University of Washington, 2016-06

Point-wise confidence interval estimation by neural networks: A comparative study based on automotive engine calibration.

In developing neural network techniques for real world applications it is still very rare to see estimates of confidence placed on the neural network predictions. This is a major deficiency, especially in safety-critical systems. In this paper we explore three distinct methods of producing point-wise confidence intervals using neural networks. We compare and contrast Bayesian, Gaussian Process and Predictive error bars evaluated on real data. The problem domain is concerned with the calibration of a real automotive engine management system for both air-fuel ratio determination and on-line ignition timing. This problem requires real-time control and is a good candidate for exploring the use of confidence predictions due to its safety-critical nature.

Does psychological stress mediate social deprivation in tooth loss?

It is unclear which theoretical dimension of psychological stress affects health status. We hypothesized that both distress and coping mediate the relationship between socio-economic position and tooth loss. Cross-sectional data from 2915 middle-aged adults evaluated retention of < 20 teeth, behaviors, psychological stress, and sociodemographic characteristics. Principal components analysis of the Perceived Stress Scale (PSS) extracted 'distress' (a = 0.85) and 'coping' (a =0.83) factors, consistent with theory. Hierarchical entry of explanatory variables into age- and sex-adjusted logistic regression models estimated odds ratios (OR) and 95% confidence intervals [95% CI] for retention of < 20 teeth. Analysis of the separate contributions of distress and coping revealed a significant main effect of coping (OR = 0.7 [95% CI = 0.7-0.8]), but no effect for distress (OR = 1.0 [95% CI = 0.9-1.1]) or for the interaction of coping and distress. Behavior and psychological stress only modestly attenuated socio-economic inequality in retention of < 20 teeth, providing evidence to support a mediating role of coping.

Bayesian versus frequentist statistical inference for investi gating a one-off cancer cluster reported to a health department

Background The problem of silent multiple comparisons is one of the most difficult statistical problems faced by scientists. It is a particular problem for investigating a one-off cancer cluster reported to a health department because any one of hundreds, or possibly thousands, of neighbourhoods, schools, or workplaces could have reported a cluster, which could have been for any one of several types of cancer or any one of several time periods. Methods This paper contrasts the frequentist approach with a Bayesian approach for dealing with silent multiple comparisons in the context of a one-off cluster reported to a health department. Two published cluster investigations were re-analysed using the Dunn-Sidak method to adjust frequentist p-values and confidence intervals for silent multiple comparisons. Bayesian methods were based on the Gamma distribution. Results Bayesian analysis with non-informative priors produced results similar to the frequentist analysis, and suggested that both clusters represented a statistical excess. In the frequentist framework, the statistical significance of both clusters was extremely sensitive to the number of silent multiple comparisons, which can only ever be a subjective "guesstimate". The Bayesian approach is also subjective: whether there is an apparent statistical excess depends on the specified prior. Conclusion In cluster investigations, the frequentist approach is just as subjective as the Bayesian approach, but the Bayesian approach is less ambitious in that it treats the analysis as a synthesis of data and personal judgements (possibly poor ones), rather than objective reality. Bayesian analysis is (arguably) a useful tool to support complicated decision-making, because it makes the uncertainty associated with silent multiple comparisons explicit.

Incomplete pregnancy and risk of ovarian cancer : results from two Australian case-control studies and systematic review

Although full-term pregnancies reduce the risk of ovarian cancer, it has not been conclusively established whether incomplete pregnancies also influence risk. We investigated the relationship between a history of incomplete pregnancy and incident epithelial ovarian cancer among over 4,500 women who participated in two large Australian population-based case-control studies in 1990-1993 and 2002-2005. They provided responses to detailed questions about their reproductive histories and other personal factors. Summary odds ratios (OR) and confidence intervals (CI) derived from each study using the same covariates were aggregated. We found no significant associations between the number of incomplete pregnancies and ovarian cancer, for parous (OR = 0.98, 95% CI: 0.89, 1.08) or nulliparous (OR = 1.06, 95% CI: 0.75, 1.48) women, nor for the number of spontaneous or induced abortions and ovarian cancer for parous women (OR = 0.95, 95% CI 0.82, 1.09; OR = 1.08, 95% CI: 0.86, 1.36) or nulliparous women (OR = 1.2, 95% CI: 0.6, 2.4; OR = 0.8, 95% CI: 0.47, 1.38), respectively. A systematic review of 37 previous studies of the topic confirmed our findings that a history of incomplete pregnancy does not influence a woman’s risk of epithelial ovarian cancer.

The prognostic significance of quality of life following breast cancer [Conference Abstract]

Introduction: Evidence suggests a positive association between quality of life (QOL). and overall survival(OS). among metastatic breast cancer (BC). patients, although the relationship in early-stage BC is unclear. This work examines the association between QOL and OS following a diagnosis of early-stage BC. ----- Methods: A population-based sample of Queensland women (n=287). with early-stage, invasive, unilateral BC, were prospectively observed for a median of 6.6 years. QOL was assessed at six and 18 months post-diagnosis using the Functional Assessment of Cancer Therapy, Breast FACT-B+4. questionnaire. Raw scores for the FACT-B+4 scales were computed and individuals were categorised according to whether QOL declined, remained stable or improved over time. OS was measured from the date of diagnosis to the date of death or was censored at the date of last follow-up. Risk ratios (RR) and 95% confidence intervals (CI). for the association between QOL and OS were obtained using Cox proportional hazards survival models adjusted for confounding characteristics. ----- Results: A total of 27 (9.4%). women died during the follow-up period. Three baseline QOL scales (emotional, general and overall QOL) were significantly associated with OS, with RRs ranging between 0.89 95% CI: 0.81, 0.98; P=0.01. and 0.98 (95% CI: 0.96, 0.99; P=0.03),indicating a 2%-11% reduced risk of death for every one unit increase in QOL. When QOL was categorised according to changes between six and 18 months post-diagnosis, analyses showed that for those who experienced declines in functional and physical QOL, risk of death increased by two- (95% CI: 1.43, 12.52; P<0.01) and four-fold (95% CI: 1.15, 7.19; P=0.02), respectively. Conclusions: This work indicates that specific QOL scales at six months post-diagnosis, and changes in certain QOL scales over the subsequent 12-month period (as measured by the FACT-B+4), are associated with overall survival in women with early-stage breast cancer.

Patterns of reporting to child protection services in Canada by healthcare and nonhealthcare professionals

Background: All Canadian jurisdictions require certain professionals to report suspected or observed child maltreatment. This study examined the types of maltreatment, level of harm and child functioning issues, controlling for family socioeconomic status, age and gender of the child reported by healthcare and non-healthcare professionals. Methods: We conducted chi-square analyses and logistic regression on a national child welfare sample from the 2003 Canadian Incidence Study of Reported Child Abuse and Neglect (CIS-2003) and compared the differences in professional reporting with its previous cycle (CIS-1998) using Bonferroni-corrected confidence intervals. Results: Our analysis of CIS-2003 data revealed that the majority of substantiated child maltreatment is reported to service agencies by non-healthcare professionals (57%), followed by non-professionals (33%) and healthcare professionals (10%). The number of professional reports increased 2.5 times between CIS-1998 and CIS-2003, while non-professionals’ increased 1.7 times. Of the total investigations, professional reports represented 59% in CIS-1998 and 67% in CIS-2003 (p<0.001). Compared to non-healthcare professionals, healthcare professionals more often reported younger children, children who experienced neglect and emotional maltreatment and those assessed as suffering harm and child functioning issues, but less often exposure to domestic violence. Conclusion: The results indicate that healthcare professionals played an important role in identifying children in need of protection considering harm and other child functioning issues. The authors discuss the reasons why underreporting is likely to remain an issue.

Using samples to estimate the sensitivity and specificity of a surveillance process

Determining sensitivity and specificity of a postoperative infection surveillance process is a difficult undertaking. Because postoperative infections are rare, vast numbers of negative results exist, and it is often not reasonable to assess them all. This study gives a methodological framework for estimating sensitivity and specificity by taking only a small sample of the number of patients who test negative and comparing their findings to the reference or “gold standard” rather than comparing the findings of all patients to the gold standard. It provides a formula for deriving confidence intervals for these estimates and a guide to minimum requirements for sampling results.