Decline of serum levels of free testosterone in aging healthy Chinese men

Objective.?To investigate the age-related change of serum androgen levels in healthy men and to define a cut-off value of serum testosterone for the diagnosis of androgen deficiency in the aging male.

Method.?1080 healthy men aged 20 to ?70 years old were enrolled in Beijing, Shanghai, Xian and Chongqing. Luteinizing hormone (LH), follicle-stimulating hormone (FSH), total testosterone (T), calculated free testosterone (cFT), sex hormone binding globulin (SHBG), 17beta-oestradiol (E2), the T/LH ratio, and T/SHBG as a free testosterone index (FTI) were all determined.

Results.?Serum total T did not significantly decline, but the cFT, T/LH and FTI progressively decreased with aging. To determine androgen deficiency, the 10th percentile value of men <40 years was defined as the lower cut-off value for cFT, T/LH or FTI, which were 0.3 nmol/L, 2.8 nmol/IU, and 0.4 nmol/IU respectively. With the median value of cFT of men aged between 20 and 49 years as the criterion, the level of cFT was lower in 2.82% of men from 40 to 49 years, in 19.53% from 50 to 59 years, in 22.57% from 60 to 69 years, and in 33.19% of men ?70 years. Taking the above value of cFT as the cut-off point, the prevalence of androgen deficiency in men 40–49 years was 13.0%, 31.8% in men 50–59 years, 30.1% in men 60 to 69 years, and 46.7% in men >70 years.

Conclusions.?(i). While serum total T values do not decline with aging, the levels of cFT gradually decline with aging; (ii) when using the value of cFT of the 10th percentile of men aged 20 to 39 years as the cut-off point, the prevalence of androgen deficiency was <15% before the age of 50 years, and about 30% thereafter, approaching 45% after the age of 70 years; and (iii) in this study the values of T/LH paralleled those of cFT closely; therefore, T/LH could serve as a surrogate for cFT.     

Power and Sample Size Determination When the Alternative Hypotheses are Given in Quantiles

The power of normal-theory tests about means depends on a noncentrality parameter which is a function of the unknown parameter σ. In order to calculate power and to solve sample-size problems based on power, differences between hypothesized and alternative values of the means are frequently selected as a multiple of σ, a choice which eliminates σ from the noncentrality parameter and permits a solution. Perhaps a more natural (but equivalent) way to express alternatives is to give one or more means as the quantile of order p (say Q_p ) of a distribution with another mean. As we will demonstrate, this kind of alternative also eliminates σ from the problem.     

Comparing variances and means when distributions have non-identical shapes

The paper compares several methods for computing robust 1-α confidence intervals for σ ₁ ²-σ ₂ ², or σ ₁ ²/σ ₂ ², where σ ₁ ² and σ ₂ ² are the population variances corresponding to two independent treatment groups. The emphasis is on a Box-Scheffe approach when distributions have different shapes, and so the results reported here have implications about comparing means. The main result is that for unequal sample sizes, a Box-Scheffe approach can be considerably less robust than indicated by past investigations. Several other procedures for comparing variances, not based on a Box-Scheffe approach, were also examined and found to be highly unsatisfactory although previously published papers found them to be robust when the distributions have identical shapes. Included is a new result on why the procedures examined here are not robust, and an illustration that increasing σ ₁ ²-σ ₂ ² can reduce power in certain situations. Constants needed to apply Dunnett’s robust comparison of means are included.     

Identifying Variables Contributing to Outliers in Phase I

When a process is monitored with a T ² control chart in a Phase II setting, the MYT decomposition is a valuable diagnostic tool for interpreting signals in terms of the process variables. The decomposition splits a signaling T ² statistic into independent components that can be associated with either individual variables or groups of variables. Since these components are T ² statistics with known distributions, they can be used to determine which of the process variable(s) contribute to the signal. However, this procedure cannot be applied directly to Phase I since the distributions of the individual components are unknown. In this article, we develop the MYT decomposition procedure for a Phase I operation, when monitoring a random sample of individual observations and identifying outliers. We use a relationship between the T ² statistic in Phase I with the corresponding T ² statistic resulting when an observation is omitted from this sample to derive the distributions of these components and demonstrate the Phase I application of the MYT decomposition.     

Monitoring Variation in a Multivariate Process When the Dimension is Large Relative to the Sample Size

A control procedure is presented for monitoring changes in variation for a multivariate normal process in a Phase II operation where the subgroup size, m, is less than p, the number of variates. The methodology is based on a form of Wilk' statistic, which can be expressed as a function of the ratio of the determinants of two separate estimates of the covariance matrix. One estimate is based on the historical data set from Phase I and the other is based on an augmented data set including new data obtained in Phase II. The proposed statistic is shown to be distributed as the product of independent beta distributions that can be approximated using either a chi-square or F-distribution. An ARL study of the statistic is presented for a range of conditions for the population covariance matrix. Cases are considered where a p-variate process is being monitored using a sample of m observations per subgroup and m < p. Data from an industrial multivariate process is used to illustrate the proposed technique.     

Shrinkage Estimation Under Multivariate Elliptic Models

The estimation of the location vector of a p-variate elliptically contoured distribution (ECD) is considered using independent random samples from two multivariate elliptically contoured populations when it is apriori suspected that the location vectors of the two populations are equal. For the setting where the covariance structure of the populations is the same, we define the maximum likelihood, Stein-type shrinkage and positive-rule shrinkage estimators. The exact expressions for the bias and quadratic risk functions of the estimators are derived. The comparison of the quadratic risk functions reveals the dominance of the Stein-type estimators if p ≥ 3. A graphical illustration of the risk functions under a “typical” member of the elliptically contoured family of distributions is provided to confirm the analytical results.     

A study of the Gamma-Pareto (IV) distribution and its applications

ABSTRACT

Pareto distributions and their close relatives and generalizations provide very flexible families of heavy-tailed distributions that may be used to model income distributions as well as a wide variety of other social and economic distributions. On the other hand, gamma distribution has a wide application in various social and economic spheres such as survival analysis, to model aggregate insurance claims, and the amount of rainfall accumulated in a reservoir etc. Combining the above two heavy-tailed distributions, using the technique by Alzaatreh et al. (2012 Alzaatreh, A., Famoye, F., Lee, C. (2012). Gamma-Pareto distribution and its applications. J. Modern Appl. Stat. Methods. 11:78–94.[Crossref] , [Google Scholar]), we define a new distribution, namely Gamma-Pareto (IV) distribution, hereafter called as GPD^(IV) distribution. Various properties of the GPD^(IV) are investigated such as limiting behavior, moments, mode, and Shannon entropy. Also some characterizations of the GPD^(IV) distribution are mentioned in this paper. Maximum likelihood method is proposed for estimating the model parameters. For illustrative purposes, real data sets are considered as applications of the GPD^(IV) distribution.     

Phase I Analysis of Multiple Linear Regression Profiles

This article considers the Phase I analysis of data when the quality of a process or product is characterized by a multiple linear regression model. This is usually referred to as the analysis of linear profiles in the statistical quality control literature. The literature includes several approaches for the analysis of simple linear regression profiles. Little work, however, has been done in the analysis of multiple linear regression profiles. This article proposes a new approach for the analysis of Phase I multiple linear regression profiles. Using this approach, regardless of the number of explanatory variables used to describe it, the profile response is monitored using only three parameters, an intercept, a slope, and a variance. Using simulation, the performance of the proposed method is compared to that of the existing methods for monitoring multiple linear profiles data in terms of the probability of a signal. The advantage of the proposed method over the existing methods is greatly improved detection of changes in the process parameters of linear profiles with high-dimensional space. The article also proposes useful diagnostic aids based on F-statistics to help in identifying the source of profile variation and the locations of out-of-control samples. Finally, the use of multiple linear profile methods is illustrated by a data set from a calibration application at National Aeronautics and Space Administration (NASA) Langley Research Center.     

水处理剂ATMP测试方法探讨

现行测试ATMP活性组分方法有HG/T2841-1997(97版)和HG/T2841-2005(05本文结果05版标准操作简单,终点易判定,测试结果的精密度≥0.2%,规定了ATMP含量测试方法,有利于得到准确的检验结果。     

P．T．1047写卷卜辞与吐蕃相关史事考释

P．T．1047号敦煌古藏文写卷是一份羊肩胛骨占卜文书,现存192段落应是192次占I-的记录。其内容涉及广泛,包括王朝军政大事及民众世俗生活诸多层面。以往有拉露、石泰安、王尧、陈践等多位中外学者对该文书做过译释研究。本文在前辈研究基础上,从分析写卷卜辞入手,参证P．T．1287、P．T．1288等古藏文写卷及传统藏史典籍文献,对相关历史人物及历史事件做综合性分析研究