Exploration Of Distributions Of Ratio Of Partial Sum Of Sample Eigenvalues When All Population Eigenvalues Are The Same

This paper explores empirically the first two moments of ratio of the partial sum of the first two sample eigenvalues to the sum of all eigenvalues when the population eigenvalues of a covariance matrix are all the same. Estimation of the first two moments can be practically crucial in assessing non-randomness of observed patterns on planar graphical displays based on lower rank approximations of data matrices. For derivation of the moments, exact and large sample asymptotic distributions of the sample ratios are reviewed but neither can be applicable to derivation of the moments. Therefore, I rely on simulations, where data matrices X with order n×m element-wise independent normal distribution with mean 0 and variance σ2 are assumed, that is, X ~ N(0,σ2Inm), and then derive formulas for estimates of means and standard deviations of the sample ratios within a range of order of the data matrix. The derivations are based on the biplot graphical diagnostic methods proposed by Bradu and Gabriel (1976)

Utility of Weights for Weighted Kappa as a Measure of Interrater Agreement on Ordinal Scale

Kappa statistics, unweighted or weighted, are widely used for assessing interrater agreement. The weights of the weighted kappa statistics in particular are defined in terms of absolute and squared distances in ratings between raters. It is proposed that those weights can be used for assessment of interrater agreements. A closed form expectations and variances of the agreement statistics referred to as AI1 and AI2, functions of absolute and squared distances in ratings between two raters, respectively, are obtained. AI1 and AI2 are compared with the weighted and unweighted kappa statistics in terms of Type I Error rate, bias, and statistical power using Monte Carlo simulations. The AI1 agreement statistic performs better than the other agreement statistics

Comparison of Post Hoc Multiple Pairwise Testing Procedures as Applied to Small k-Group Logrank Tests

Abstract: The logrank test is widely used to compare groups on distribution of survival time in the presence of censoring. There is no convention for post hoc pairwise comparisons after a significant omnibus k-group logrank test. This simulation study compares four post hoc pairwise testing procedures: Bonferroni, Dunn-Šidák, Hochberg, and unadjusted post hoc logrank test procedure. Evaluation criteria include, familywise type I error rate, correct decision rate, number of correctly rejected pairs, and false discovery rate. We demonstrated that when conditioned upon rejection of the omnibus test, multiplicity adjustments may be unnecessary and can be overly conservative when k is at most 4, or number of comparisons is no greater than 6. This is supported by the results that the performance of the unadjusted post hoc logrank test procedure is preferred over the others on all criteria except for the false discovery rate. The Hochberg procedure appears to be superior among the adjustments examined. Data from a clinical trial for suicide prevention illustrate these approaches where number of comparison groups is often limited

Overweight, obesity, and colorectal cancer screening: Disparity between men and women

BACKGROUND: To estimate the association between body-mass index (BMI: kg/m(2)) and colorectal cancer (CRC) screening among US adults aged ≥ 50 years. METHODS: Population-based data from the 2001 Behavioral Risk Factor Surveillance Survey. Adults (N = 84,284) aged ≥ 50 years were classified by BMI as normal weight (18.5–<25), overweight (25–<30), obesity class I (30–<35), obesity class II (35–<40), and obesity class III (≥ 40). Interval since most recent screening fecal occult blood test (FOBT): (0 = >1 year since last screening vs. 1 = screened within the past year), and screening sigmoidoscopy (SIG): (0 = > 5 years since last screening vs. 1 = within the past 5 years) were the outcomes. RESULTS: Results differed between men and women. After adjusting for age, health insurance, race, and smoking, we found that, compared to normal weight men, men in the overweight (odds ratio [OR] 1.25, 95% CI = 1.05–1.51) and obesity class I (OR = 1.21, 95% CI = 1.03–1.75) categories were more likely to have obtained a screening SIG within the previous 5 years, while women in the obesity class I (OR = 0.86, 95%CI = 0.78–0.94) and II (OR = 0.88, 95%CI = 0.79–0.99) categories were less likely to have obtained a screening SIG compared to normal weight women. BMI was not associated with FOBT. CONCLUSION: Weight may be a correlate of CRC screening behavior but in a different way between men and women

Simple Skeletal Muscle Mass Estimation Formulas: What We Can Learn From Them

One century ago Harris and Benedict published a short report critically examining the relations between body size, body shape, age, and basal metabolic rate. At the time, basal metabolic rate was a vital measurement in diagnosing diseases such as hypothyroidism. Their conclusions and basal metabolic rate prediction formulas still resonate today. Using the Harris-Benedict approach as a template, we systematically examined the relations between body size, body shape, age, and skeletal muscle mass (SM), the main anatomic feature of sarcopenia. The sample consisted of 12,330 non-Hispanic (NH) white and NH black participants in the US National Health and Nutrition Survey who had complete weight, height, waist circumference, age, and dual-energy X-ray (DXA) absorptiometry data. A conversion formula was used to derive SM from DXA-measured appendicular lean soft tissue mass. Weight, height, waist circumference, and age alone and in combination were significantly correlated with SM (all, p &lt; 0.001). Advancing analyses through the aforementioned sequence of predictor variables allowed us to establish how at the anatomic level these body size, body shape, and age measures relate to SM much in the same way the Harris-Benedict equations provide insights into the structural origins of basal heat production. Our composite series of SM prediction equations should prove useful in modeling efforts and in generating hypotheses aimed at understanding how SM relates to body size and shape across the adult lifespa

Statistical power as a function of Cronbach alpha of instrument questionnaire items

Abstract Background In countless number of clinical trials, measurements of outcomes rely on instrument questionnaire items which however often suffer measurement error problems which in turn affect statistical power of study designs. The Cronbach alpha or coefficient alpha, here denoted by C α , can be used as a measure of internal consistency of parallel instrument items that are developed to measure a target unidimensional outcome construct. Scale score for the target construct is often represented by the sum of the item scores. However, power functions based on C α have been lacking for various study designs. Methods We formulate a statistical model for parallel items to derive power functions as a function of C α under several study designs. To this end, we assume fixed true score variance assumption as opposed to usual fixed total variance assumption. That assumption is critical and practically relevant to show that smaller measurement errors are inversely associated with higher inter-item correlations, and thus that greater C α is associated with greater statistical power. We compare the derived theoretical statistical power with empirical power obtained through Monte Carlo simulations for the following comparisons: one-sample comparison of pre- and post-treatment mean differences, two-sample comparison of pre-post mean differences between groups, and two-sample comparison of mean differences between groups. Results It is shown that C α is the same as a test-retest correlation of the scale scores of parallel items, which enables testing significance of C α . Closed-form power functions and samples size determination formulas are derived in terms of C α , for all of the aforementioned comparisons. Power functions are shown to be an increasing function of C α , regardless of comparison of interest. The derived power functions are well validated by simulation studies that show that the magnitudes of theoretical power are virtually identical to those of the empirical power. Conclusion Regardless of research designs or settings, in order to increase statistical power, development and use of instruments with greater C α , or equivalently with greater inter-item correlations, is crucial for trials that intend to use questionnaire items for measuring research outcomes. Discussion Further development of the power functions for binary or ordinal item scores and under more general item correlation strutures reflecting more real world situations would be a valuable future study

Effects of COVID-19 Lockdown on Lifestyle Behaviors in Children with Obesity Living in Verona, Italy: A Longitudinal Study

Objective: The aim of this study was to test the hypothesis that youths with obesity, when removed from structured school activities and confined to their homes during the coronavirus disease 2019 pandemic, will display unfavorable trends in lifestyle behaviors. Methods: The sample included 41 children and adolescents with obesity participating in a longitudinal observational study located in Verona, Italy. Lifestyle information including diet, activity, and sleep behaviors was collected at baseline and 3 weeks into the national lockdown during which home confinement was mandatory. Changes in outcomes over the two study time points were evaluated for significance using paired t tests. Results: There were no changes in reported vegetable intake; fruit intake increased (P = 0.055) during the lockdown. By contrast, potato chip, red meat, and sugary drink intakes increased significantly during the lockdown (P value range, 0.005 to &lt; 0.001). Time spent in sports activities decreased by 2.30 (SD 4.60) h/wk (P = 0.003), and sleep time increased by 0.65 (SD 1.29) h/d (P = 0.003). Screen time increased by 4.85 (SD 2.40) h/d (P &lt; 0.001). Conclusions: Recognizing these adverse collateral effects of the coronavirus disease 2019 pandemic lockdown is critical in avoiding depreciation of weight control efforts among youths afflicted with excess adiposity. Depending on duration, these untoward lockdown effects may have a lasting impact on a child's or adolescent's adult adiposity level

Development, Calibration, and Validation of a U.S. White Male Population-Based Simulation Model of Esophageal Adenocarcinoma

The incidence of esophageal adenocarcinoma (EAC) has risen rapidly in the U.S. and western world. The aim of the study was to begin the investigation of this rapid rise by developing, calibrating, and validating a mathematical disease simulation model of EAC using available epidemiologic data.The model represents the natural history of EAC, including the essential biologic health states from normal mucosa to detected cancer. Progression rates between health states were estimated via calibration, which identified distinct parameter sets producing model outputs that fit epidemiologic data; specifically, the prevalence of pre-cancerous lesions and EAC cancer incidence from the published literature and Surveillance, Epidemiology, and End Results (SEER) data. As an illustrative example of a clinical and policy application, the calibrated and validated model retrospectively analyzed the potential benefit of an aspirin chemoprevention program.Model outcomes approximated calibration targets; results of the model's fit and validation are presented. Approximately 7,000 cases of EAC could have been prevented over a 30-year period if all white males started aspirin chemoprevention at age 40 in 1965.The model serves as the foundation for future analyses to determine a cost-effective screening and management strategy to prevent EAC morbidity and mortality

Trial Characteristics and Appropriateness of Statistical Methods Applied for Design and Analysis of Randomized School-Based Studies Addressing Weight-Related Issues: A Literature Review

Objective. To evaluate whether clustering effects, often quantified by the intracluster correlation coefficient (ICC), were appropriately accounted for in design and analysis of school-based trials. Methods. We searched PubMed and extracted variables concerning study characteristics, power analysis, ICC use for power analysis, applied statistical models, and the report of the ICC estimated from the observed data. Results. N = 263 papers were identified, and N = 121 papers were included for evaluation. Overall, only a minority (21.5%) of studies incorporated ICC values for power analysis, fewer studies (8.3%) reported the estimated ICC, and 68.6% of studies applied appropriate multilevel models. A greater proportion of studies applied the appropriate models during the past five years (2013-2017) compared to the prior years (74.1% versus 63.5%, p = 0.176). Significantly associated with application of appropriate models were a larger number of schools (p = 0.030), a larger sample size (p = 0.002), longer follow-up (p = 0.014), and randomization at a cluster level (p &lt; 0.001) and so were studies that incorporated the ICC into power analysis (p = 0.016) and reported the estimated ICC (p = 0.030). Conclusion. Although application of appropriate models has increased over the years, consideration of clustering effects in power analysis has been inadequate, as has report of estimated ICC. To increase rigor, future school-based trials should address these issues at both the design and analysis stages

Effects of COVID-19 lockdown on lifestyle behaviors in children with obesity: Longitudinal study update

Objective: A previous report from our group identified directionally unfavorable dietary and lifestyle behavior trends in longitudinally monitored children and adolescents with obesity early in the COVID-19 pandemic lockdown. The current study aimed at extending these previous observations in youths with obesity on the dietary and lifestyle behavioral consequences of the extended COVID-19 lockdown in Verona, Italy.Methods: The sample included 32 children and adolescents with obesity participating in the longitudinal OBELIX study. Diet and lifestyle information were collected pre-pandemic, 3 weeks into the national lockdown, and 9 months later when home confinement continued to be mandatory. Changes in outcomes over the study time points were evaluated for significance using repeated-measures ANOVA and post-hoc pairwise t-tests with Bonferroni corrections.Results: As previously reported, meals/day, fried potato intake, and red meat ingestion increased significantly (p &lt; 0.001) during the initial lockdown. Sleep time and screen time increased and sports participation decreased significantly (p &lt; 0.001) during the initial lockdown. These changes in health behaviors remained significantly different from baseline at the second lockdown assessment, with the exception sleep time returned to baseline levels.Conclusions: Unfavorable diet and lifestyle behavioral changes in response to the initial COVID-19 lockdown in children and adolescents with obesity have largely been sustained over the course of the pandemic. There is an urgent need to intervene on these behaviors to prevent further deleterious effects on long-term child health; access to weight management care is critically important for these children. In addition to intervening on these behaviors, our findings should help to inform ongoing lockdown policies