Ulrike Genschel

A Comparison of Maximum Likelihood and Median-Rank Regression for Weibull Estimation

ABSTRACT The Weibull distribution is frequently used in reliability applications. Many different methods of estimating the parameters and important functions of the parameters (e.g., quantiles and failure probabilities) have been suggested. Maximum likelihood and median-rank regression methods are most commonly used today. Largely because of conflicting results from different studies that have been conducted to investigate the properties of these estimators, there are sharp differences of opinion on which method should be used. The purpose of this article is to report on the results of our simulation study, to provide insight into the differences between the competing methods, and to resolve the differences among the previous studies.

Serum 25-hydroxyvitamin D is related to indicators of overall physical fitness in healthy postmenopausal women.

Objective: Inadequate vitamin D status is related to increased adiposity, risk of falls, and muscle weakness, particularly in older people. We hypothesized that serum 25-hydroxyvitamin D [25(OH)D] is related to physical fitness indices (androidal fat, whole body lean mass, balance, strength) in healthy postmenopausal women. Methods: Covariates for fitness indices included age or years since menopause, weight, 25(OH)D, energy expenditure, and calcium intake. Overall and regional (androidal fat mass = waist + hip fat) body composition was assessed (N = 242) via dual-energy x-ray absorptiometry. Results: Regression analyses revealed that 71% of variability (P ≤ 0.0001) in androidal fat mass was accounted for by weight (53.0%, P ≤ 0.0001), white blood cell (WBC) count (2.0%, P ≤ 0.0001), supplemental calcium (1.7%, P = 0.0004), years since menopause (1.1%, P = 0.0034), 25(OH)D (1.0%, P = 0.0051), and vegetable servings (0.6%, P = 0.027); 64% of variability (P ≤ 0.0001) in lean mass was accounted for by weight (63.1.%, P ≤ 0.0001), WBC count (1.4%, P = 0.0038), and 25(OH)D (1.0%, P = 0.013); 12% of variability (P ≤ 0.0001) in balance (right + left leg) was accounted for by age (3.8%, P = 0.0019), 25(OH)D (2.0%, P = 0.025), and WBC count (1.8%, P = 0.032); 14% of variability (P ≤ 0.0001) in handgrip strength (right + left) was accounted for by weight (9.3%, P ≤ 0.0001), 25(OH)D (2.4%, P = 0.013), WBC count (2.1%, P = 0.019), and age (1.6%, P = 0.044); and 22% of variability (P ≤ 0.0001) in torso strength was accounted for by site (15.0%, P ≤ 0.0001) and weight (4.6%, P = 0.0003). Conclusions: Serum 25(OH)D was the common contributor to physical fitness indices (androidal fat mass, lean mass, balance, handgrip strength) in healthy postmenopausal women.

Association of Oxidative Stress, Iron, and Centralized Fat Mass in Healthy Postmenopausal Women

OBJECTIVE Centralized adiposity, insulin resistance, excess iron, and elevated oxidative stress place postmenopausal women at risk for atherosclerotic cardiovascular disease (CVD). The objective of this study was to determine the relationship among excess iron, oxidative stress, and centralized fat mass in healthy postmenopausal women. METHODS The parent project recruited healthy women for a randomized, double-blind, clinical trial designed to examine the effect of soy isoflavones on bone. At baseline (n = 122), we measured three antioxidant enzymes, iron status indices (serum ferritin among others), oxidative stress indices (oxidized low-density lipoprotein [oxLDL], urinary isoprostanes [PGF(2alpha)], protein carbonyls, DNA damage), and waist, hip, and thigh fat mass using dual-energy x-ray absorptiometry (DXA). We calculated insulin resistance using the homeostasis model assessment (HOMA). Multiple regression analysis was used to determine the CVD risk factors that contributed to oxidative stress and centralized fat mass (waist + hip/thigh = AndGynFM ratio). RESULTS Almost 14% (p < 0.0005) of the variability in oxLDL was accounted for by AndGynFM ratio (6.1%, p < 0.0005), age (4.0%, p = 0.012), and serum iron (2.8%, p = 0.053). Similarly, 16% (p < 0.0001) of the variability in PGF(2alpha) was accounted for by the AndGynFM ratio (4.8%, p = 0.011), HOMA (3.9%, p = 0.021), and serum iron (2.7%, p = 0.054). We accounted for 33% (p </= 0.0001) of the variability in AndGynFM ratio by high-density lipoprotein cholesterol (HDL-C) (4.3%, p = 0.008), ferritin (4.9%, p = 0.005), HOMA (4.5%, p = 0.006), oxLDL (2.6%, p = 0.04), and PGF(2alpha) (3.0%, p = 0.025). CONCLUSIONS Our study suggests that reducing centralized fat mass and maintaining a favorable lipid profile, antioxidant status, and iron status all may be important in protecting postmenopausal women from atherosclerotic CVD.

Centrally located body fat is related to inflammatory markers in healthy postmenopausal women

Objective:C-reactive protein and fibrinogen are established atherosclerotic cardiovascular disease risk factors. These acute-phase proteins and the proinflammatory cytokines tumor necrosis factor &agr;, interleukin-6, and interleukin-1&bgr; may be elevated in obesity and with menopause. The purpose of this multicenter study was to identify whether centrally located fat and/or overall adiposity were related to these inflammatory markers in healthy postmenopausal women. Design:We used dual-energy x-ray absorptiometry to assess overall and regional body composition (fat mass in particular) in 242 postmenopausal women in relation to plasma fibrinogen, serum C-reactive protein, and these proinflammatory cytokines. Results:Multiple regression analyses revealed that 36% of the variability in C-reactive protein (F = 32.4, P ≤ 0.0001) was accounted for by androidal fat mass (16.1%, P ≤ 0.0001), white blood cells (5.6%, P ≤ 0.0001), and age (2.3%, P = 0.0045). Regression analyses revealed that 30% of the variability in fibrinogen (F = 24.5, P ≤ 0.0001) was accounted for by white blood cells (3.1%, P = 0.0015), hip fat mass (2.2%, P = 0.0081), years since menopause (0.9%, P = 0.082), and geographic site (P ≤ 0.0001). Our results indicated that androidal fat mass and hip fat mass contributed to C-reactive protein and fibrinogen, respectively, whereas we found no association between whole-body or regional fat measures and cytokines. Conclusion:Further study is warranted to determine the responsiveness of these acute-phase proteins and cytokines to loss of body fat through exercise and dietary intervention in postmenopausal women.

Centrally located body fat is related to appetitive hormones in healthy postmenopausal women

OBJECTIVE Body composition and energy homeostasis are thought to affect the appetitive hormones: adiponectin, leptin, insulin, and ghrelin. This study examined whether centrally located fat and/or overall adiposity were related to these appetitive hormones in healthy postmenopausal women. DESIGN Overall and regional body composition was assessed by dual-energy X ray absorptiometry in relation to plasma adiponectin, serum leptin, serum insulin, and plasma ghrelin in 242 postmenopausal women. RESULTS Regression analyses revealed that the androidal-to-gynoidal fat mass ratio (18.0%), age (3.2%), and white blood cell count (1.8%) accounted for 28% of the variability in adiponectin (F=22.2; P<0.0001); androidal (waist+hip) fat mass (66.0%), androidal fat mass(2) (6.2%), whole-body lean mass (2.2%), and age (0.8%) accounted for 69% of the variability in leptin (F=102.5; P<0.0001). Regression analyses revealed that sagittal abdominal diameter (8.4%), glucose (5.4%), white blood cell count (2.6%), and dietary omega-3 fatty acids (2.0%) accounted for 32% of the variability in insulin (F=20.8; P<0.0001); waist circumference (12.7%), hip lean mass (2.0%), and white blood cell count (1.9%) accounted for 26% of the variability in ghrelin (F=20.7; P<0.0001). Our results indicated that centralized fat mass was the primary contributor to these appetitive hormones in healthy postmenopausal women. CONCLUSION Since central adiposity in postmenopausal women was related to appetitive hormones, minimizing weight gain during the menopausal transition may optimize appetitive hormones, thereby facilitating appetite control and weight maintenance.

Soy Isoflavones for Reducing Bone Loss Study: Effects of a 3-year trial on hormones, adverse events, and endometrial thickness in postmenopausal women

ObjectiveThis study aims to assess the overall safety and potential endometrium-stimulating effects of soy isoflavone tablets consumed (3 y) by postmenopausal women and to determine endometrial thickness response to treatment among compliant women, taking into account hormone concentrations and other hypothesized modifying factors. MethodsWe randomized healthy postmenopausal women (aged 45.8-65.0 y) to placebo control or two doses (80 or 120 mg/d) of soy isoflavones at two sites. We used intent-to-treat analysis (N = 224) and compliant analysis (>95%; N = 208) to assess circulating hormone concentrations, adverse events, and endometrial thickness (via transvaginal ultrasound). ResultsMedian values for endometrial thickness (mm) declined from baseline through 36 months. Nonparametric analysis of variance for treatment differences among groups showed no differences in absolute (or percentage of change) endometrial thickness (&khgr;2 P ranged from 0.12 to 0.69) or in circulating hormones at any time point. A greater number of adverse events in the genitourinary system (P = 0.005) were noted in the 80 mg/day group compared with the 120 mg/day group, whereas other systems showed no treatment effects. The model predicting endometrial thickness response (using natural logarithm) to treatment among compliant women across time points was significant (P ⩽ 0.0001), indicating that estrogen exposure (P = 0.0013), plasma 17&bgr;-estradiol (P = 0.0086), and alcohol intake (P = 0.023) contributed significantly to the response. Neither the 80 mg/day dose (P = 0.57) nor the 120 mg/day dose (P = 0.43) exerted an effect on endometrial thickness across time. ConclusionsOur randomized controlled trial verifies the long-term overall safety of soy isoflavone tablet intake by postmenopausal women who display excellent compliance. We find no evidence of treatment effects on endometrial thickness, adverse events, or circulating hormone concentrations, most notably thyroid function, across a 3-year period.

Appetitive Hormones, but Not Isoflavone Tablets, Influence Overall and Central Adiposity in Healthy Postmenopausal Women

Objective: One of the multiple health benefits of soy protein or its isoflavones may be their purported favorable effect on body composition. We examined the effect of isoflavones extracted from soy protein on overall and regional body composition, taking into account appetitive hormones as potential mediators, as well as the direct effect on appetitive hormones. Methods: This randomized, double-blind, placebo-controlled multicenter trial included 229 healthy postmenopausal women (age, 45.8-65 y; body mass index, 24.9 ± 3.0 kg/m2) who consumed placebo or soy isoflavone (80 or 120 mg/d) tablets for 12 months. We used intent-to-treat analysis to examine changes in body composition (whole-body lean mass, whole-body fat mass, androidal fat mass, and androidal-to-gynoidal fat mass ratio) and appetitive hormones (insulin, leptin, ghrelin, and adiponectin) in response to treatment. Results: Repeated-measures analysis of variance indicated that soy isoflavone treatment did not exert a significant effect on body composition measures (P value from 0.36 to 0.79) or appetitive hormone concentrations; the inclusion of covariates in statistical models did not alter these results. Independently of treatment, leptin and ghrelin related inversely to each body composition measure (P values from 0.044 to ≤0.0001). Adiponectin related inversely to all fat measures (P values from 0.0004 to <0.0001). Time since last menstrual period related directly to all fat measures (P values from 0.06 to 0.0055). Dietary fat contributed to whole-body (P = 0.028) and androidal (P = 0.017) fat mass. Conclusions: Our findings do not support a favorable effect of soy isoflavone tablets on body composition in healthy postmenopausal women.

Nonparametric confidence regions for the central orientation of random rotations

Three-dimensional orientation data, with observations as 3×3 rotation matrices, have applications in areas such as computer science, kinematics and materials sciences, where it is often of interest to estimate a central orientation parameter S represented by a 3×3 rotation matrix. A well-known estimator of this parameter is the projected arithmetic mean and, based on this statistic, two nonparametric methods for setting confidence regions for S exist. Both of these methods involve large-sample normal theory, with one approach based on a data-transformation of rotations to directions (four-dimensional unit vectors) prior to analysis. However, both of these nonparametric methods may result in poor coverage accuracy in small samples. As a remedy, we consider two bootstrap methods for approximating the sampling distribution of the projected mean statistic and calibrating nonparametric confidence regions for the central orientation parameter S. As with normal approximations, one bootstrap method is based on the rotation data directly while the other bootstrap approach involves a data-transformation of rotations into directions. Both bootstraps are shown to be valid for approximating sampling distributions and calibrating confidence regions based on the projected mean statistic. A simulation study compares the performance of the normal theory and proposed bootstrap confidence regions for S, based on common data-generating models for symmetric orientations. The bootstrap methods are shown to exhibit good coverage accuracies, thus providing an improvement over normal theory approximations especially for small sample sizes. The bootstrap methods are also illustrated with a real data example from materials science.

Point Estimation of the Central Orientation of Random Rotations.

Data as three-dimensional rotations have application in computer science, kinematics, and materials sciences, among other areas. Estimating the central orientation from a sample of such data is an important problem, which is complicated by the fact that several different approaches exist for this, motivated by various geometrical and decision-theoretical considerations. However, little is known about how such estimators compare, especially on common distributions for location models with random rotations. We examine four location estimators, three of which are commonly found in different literatures and the fourth estimator (a projected median) is newly introduced. Our study unifies existing literature and provides a detailed numerical investigation of location estimators for three commonly used rotation distributions in statistics and materials science. While the data-generating model influences the best choice of an estimator, the proposed projected median emerges as an overall good performer, which can be suggested without particular distributional assumptions. We illustrate the estimators and our findings with data from a materials science study by approximating the central orientation of cubic crystals on the microsurface of a metal. Accompanying supplementary materials are available online.

A Permutation Test for Correlated Errors in Adjacent Questionnaire Items

Response patterns are of importance to survey researchers because of the insight they provide into the thought processes respondents use to answer survey questions. In this article we propose the use of structural equation modeling to examine response patterns and develop a permutation test to quantify the likelihood of observing a specific response pattern. Of interest is a response pattern where the response to the current item is conditioned on the respondents answer to the immediately preceding item. This pattern manifests itself in the error structure of the survey items by resulting in larger correlations of the errors for adjacent items than for nonadjacent items. We illustrate the proposed method using data from the 2002 Oregon Survey of Roads and Highways and report SAS code that can be easily modified to examine other response patterns of interest.