Thyroid function in the elderly and sex hormones in elderly men: reference intervals and associations with health

Aims: The aims were to create clinically feasible reference intervals for thyroidstimulating hormone (TSH) and free thyroxine (FT4) and to analyze associations between thyroid function and self-rated health, neuropsychiatric symptoms, depression and dementia in the elderly. The second aim was also to establish reference intervals for sex hormones and to analyze associations between sex hormone levels and self-rated health, symptoms, depression and dementia in elderly men. Subjects and methods: The study population comprised 1252 subjects aged 65 years or over, living in the municipality of Lieto, south-western Finland. Self-rated health, life satisfaction, symptoms, depression, and dementia were assessed with specific questions, clinical examination and tools such as the Zung Self-report Depression Scale and the Mini-Mental State Examination. Independent variables were dichotomized, and associations of these variables with TSH, FT4 or sex hormone levels were assessed. Levels of TSH and FT4 in thyroid disease–free women and women treated with thyroxine were also compared. Results: Elevated concentrations of thyroid peroxidase antibodies (TPOAb) or thyroglobulin antibodies (TgAb) were found to have a marked effect on the upper reference limit for TSH among women, who were thyroid antibody positive more higher than suggested in several recent guidelines. After age adjustment, there were no associations between TSH levels and self-rated health, life satisfaction, or most neuropsychiatric symptoms in the thyroid disease-free population. Although women with thyroxine treatment for primary hypothyroidism had far higher TSH levels than thyroid disease-free women, there were no differences between thyroid-disease free women and women with stable thyroxine treatment regarding self-rated health, life satisfaction or symptoms. Age had a significant positive association with luteinizing hormone (LH), follicle 2 practice, one range in men aged 65 years or over can be used for T, E2 and FSH measured with the AutoDelfia method, but two separate reference intervals should be used for fT, LH and SHBG. After adjustment for age, higher levels of T and fT were associated with better self-rated health (SRH) in the reference population. After adjustment for age and body mass index (BMI), there were no associations between sex hormone concentrations and self-rated health, life satisfaction or most symptoms in concentration. Conclusion: Age-specific reference intervals were derived for thyroid function and sex hormones based on comprehensive data from a community-dwelling population with a high participation rate. The results do not support the need to decrease the upper reference limit for TSH or to lower the optimal TSH target in levothyroxine treatment in older adults, as recommended in recent guidelines. Older age or being overweight symptoms among elderly men. The associations of single symptoms with T levels were inconsistent among elderly men, although the association of low T level with diagnosed depression might be clinically significant.

Reference intervals for 24 laboratory parameters determined in 24-hour urine collections.

BACKGROUND: Reference intervals for many laboratory parameters determined in 24-h urine collections are either not publicly available or based on small numbers, not sex specific or not from a representative sample. METHODS: Osmolality and concentrations or enzymatic activities of sodium, potassium, chloride, glucose, creatinine, citrate, cortisol, pancreatic α-amylase, total protein, albumin, transferrin, immunoglobulin G, α1-microglobulin, α2-macroglobulin, as well as porphyrins and their precursors (δ-aminolevulinic acid and porphobilinogen) were determined in 241 24-h urine samples of a population-based cohort of asymptomatic adults (121 men and 120 women). For 16 of these 24 parameters creatinine-normalized ratios were calculated based on 24-h urine creatinine. The reference intervals for these parameters were calculated according to the CLSI C28-A3 statistical guidelines. RESULTS: By contrast to most published reference intervals, which do not stratify for sex, reference intervals of 12 of 24 laboratory parameters in 24-h urine collections and of eight of 16 parameters as creatinine-normalized ratios differed significantly between men and women. For six parameters calculated as 24-h urine excretion and four parameters calculated as creatinine-normalized ratios no reference intervals had been published before. For some parameters we found significant and relevant deviations from previously reported reference intervals, most notably for 24-h urine cortisol in women. Ten 24-h urine parameters showed weak or moderate sex-specific correlations with age. CONCLUSIONS: By applying up-to-date analytical methods and clinical chemistry analyzers to 24-h urine collections from a large population-based cohort we provide as yet the most comprehensive set of sex-specific reference intervals calculated according to CLSI guidelines for parameters determined in 24-h urine collections.

Intervals between response choices on a single-item measure of quality of life.

BACKGROUND: A single overall rating of quality of life (QoL) is a sensitive method that is often used in population surveys. However, the exact meaning of response choices is unclear. In particular, uneven spacing may affect the way QoL ratings should be analyzed and interpreted. This study aimed to determine the intervals between response choices to a single-item QoL assessment. METHODS: A secondary analysis was conducted on data from the Lc65+ cohort study and two additional, population-based, stratified random samples of older people (N = 5,300). Overall QoL was rated as excellent, very good, good, fair or poor. A QoL score (range 0-100) was derived from participants' answers to a 28-item QoL assessment tool. A transformed QoL score ranging from 1 (poor) to 5 (excellent) was calculated. The same procedure was repeated to compute seven domain-specific QoL subscores (Feeling of safety; Health and mobility; Autonomy; Close entourage; Material resources; Esteem and recognition; Social and cultural life). RESULTS: Mean (95 % confidence intervals) QoL scores were 96.23 (95.81-96.65) for excellent, 93.09 (92.74-93.45) for very good, 81.45 (80.63-82.27) for good, 65.44 (62.67-68.20) for fair and 54.52 (45.31-63.73) for poor overall QoL, corresponding to transformed QoL scores of respectively 5.00, 4.70, 3.58, 2.05, and 1.00. Ordinality of the categories excellent to poor was preserved in all seven QoL subscores. CONCLUSIONS: The excellent-to-poor rating scale provides an ordinal measure of overall QoL. The intervals between response choices are unequal, but an interval scale can be obtained after adequate recoding of excellent, very good, good, fair and poor.

Strings of congruent primes in short intervals

Soit $p_1 = 2, p_2 = 3, p_3 = 5,\ldots$ la suite des nombres premiers, et soient $q \ge 3$ et $a$ des entiers premiers entre eux. R\'ecemment, Daniel Shiu a d\'emontr\'e une ancienne conjecture de Sarvadaman Chowla. Ce dernier a conjectur\'e qu'il existe une infinit\'e de couples $p_n,p_{n+1}$ de premiers cons\'ecutifs tels que $p_n \equiv p_{n+1} \equiv a \bmod q$. Fixons $\epsilon > 0$. Une r\'ecente perc\'ee majeure, de Daniel Goldston, J\`anos Pintz et Cem Y{\i}ld{\i}r{\i}m, a \'et\'e de d\'emontrer qu'il existe une suite de nombres r\'eels $x$ tendant vers l'infini, tels que l'intervalle $(x,x+\epsilon\log x]$ contienne au moins deux nombres premiers $\equiv a \bmod q$. \'Etant donn\'e un couple de nombres premiers $\equiv a \bmod q$ dans un tel intervalle, il pourrait exister un nombre premier compris entre les deux qui n'est pas $\equiv a \bmod q$. On peut d\'eduire que soit il existe une suite de r\'eels $x$ tendant vers l'infini, telle que $(x,x+\epsilon\log x]$ contienne un triplet $p_n,p_{n+1},p_{n+2}$ de nombres premiers cons\'ecutifs, soit il existe une suite de r\'eels $x$, tendant vers l'infini telle que l'intervalle $(x,x+\epsilon\log x]$ contienne un couple $p_n,p_{n+1}$ de nombres premiers tel que $p_n \equiv p_{n+1} \equiv a \bmod q$. On pense que les deux \'enonc\'es sont vrais, toutefois on peut seulement d\'eduire que l'un d'entre eux est vrai, sans savoir lequel. Dans la premi\`ere partie de cette th\`ese, nous d\'emontrons que le deuxi\`eme \'enonc\'e est vrai, ce qui fournit une nouvelle d\'emonstration de la conjecture de Chowla. La preuve combine des id\'ees de Shiu et de Goldston-Pintz-Y{\i}ld{\i}r{\i}m, donc on peut consid\'erer que ce r\'esultat est une application de leurs m\'thodes. Ensuite, nous fournirons des bornes inf\'erieures pour le nombre de couples $p_n,p_{n+1}$ tels que $p_n \equiv p_{n+1} \equiv a \bmod q$, $p_{n+1} - p_n < \epsilon\log p_n$, avec $p_{n+1} \le Y$. Sous l'hypoth\`ese que $\theta$, le \og niveau de distribution \fg{} des nombres premiers, est plus grand que $1/2$, Goldston-Pintz-Y{\i}ld{\i}r{\i}m ont r\'eussi \`a d\'emontrer que $p_{n+1} - p_n \ll_{\theta} 1$ pour une infinit\'e de couples $p_n,p_{n+1}$. Sous la meme hypoth\`ese, nous d\'emontrerons que $p_{n+1} - p_n \ll_{q,\theta} 1$ et $p_n \equiv p_{n+1} \equiv a \bmod q$ pour une infinit\'e de couples $p_n,p_{n+1}$, et nous prouverons \'egalement un r\'esultat quantitatif. Dans la deuxi\`eme partie, nous allons utiliser les techniques de Goldston-Pintz-Y{\i}ld{\i}r{\i}m pour d\'emontrer qu'il existe une infinit\'e de couples de nombres premiers $p,p'$ tels que $(p-1)(p'-1)$ est une carr\'e parfait. Ce resultat est une version approximative d'une ancienne conjecture qui stipule qu'il existe une infinit\'e de nombres premiers $p$ tels que $p-1$ est une carr\'e parfait. En effet, nous d\'emontrerons une borne inf\'erieure sur le nombre d'entiers naturels $n \le Y$ tels que $n = \ell_1\cdots \ell_r$, avec $\ell_1,\ldots,\ell_r$ des premiers distincts, et tels que $(\ell_1-1)\cdots (\ell_r-1)$ est une puissance $r$-i\`eme, avec $r \ge 2$ quelconque. \'Egalement, nous d\'emontrerons une borne inf\'erieure sur le nombre d'entiers naturels $n = \ell_1\cdots \ell_r \le Y$ tels que $(\ell_1+1)\cdots (\ell_r+1)$ est une puissance $r$-i\`eme. Finalement, \'etant donn\'e $A$ un ensemble fini d'entiers non-nuls, nous d\'emontrerons une borne inf\'erieure sur le nombre d'entiers naturels $n \le Y$ tels que $\prod_{p \mid n} (p+a)$ est une puissance $r$-i\`eme, simultan\'ement pour chaque $a \in A$.

Computationally Efficient Bootstrap Prediction Intervals for Returns and Volatilities in ARCH and GARCH Processes

We propose a novel, simple, efficient and distribution-free re-sampling technique for developing prediction intervals for returns and volatilities following ARCH/GARCH models. In particular, our key idea is to employ a Box–Jenkins linear representation of an ARCH/GARCH equation and then to adapt a sieve bootstrap procedure to the nonlinear GARCH framework. Our simulation studies indicate that the new re-sampling method provides sharp and well calibrated prediction intervals for both returns and volatilities while reducing computational costs by up to 100 times, compared to other available re-sampling techniques for ARCH/GARCH models. The proposed procedure is illustrated by an application to Yen/U.S. dollar daily exchange rate data.

Error estimates for approximate approximations on compact intervals

The aim of this paper is the investigation of the error which results from the method of approximate approximations applied to functions defined on compact in- tervals, only. This method, which is based on an approximate partition of unity, was introduced by V. Mazya in 1991 and has mainly been used for functions defied on the whole space up to now. For the treatment of differential equations and boundary integral equations, however, an efficient approximation procedure on compact intervals is needed. In the present paper we apply the method of approximate approximations to functions which are defined on compact intervals. In contrast to the whole space case here a truncation error has to be controlled in addition. For the resulting total error pointwise estimates and L1-estimates are given, where all the constants are determined explicitly.

Necessary and sufficient conditions for robust stability using modal intervals

In this paper, robustness of parametric systems is analyzed using a new approach to interval mathematics called Modal Interval Analysis. Modal Intervals are an interval extension that, instead of classic intervals, recovers some of the properties required by a numerical system. Modal Interval Analysis not only simplifies the computation of interval functions but allows semantic interpretation of their results. Necessary, sufficient and, in some cases, necessary and sufficient conditions for robust performance are presented

Confidence Intervals

PowerPoint slides for Confidence Intervals. Examples are taken from the Medical Literature

Normal distribution and confidence intervals

lecture for COMP6235

Working memory in school-aged children: Exhibition intervals and distracters effects in Memonum computerized test

This study assessed visual working memory through Memonum computerized test in schoolchildren. The effects of three exposure times (1, 4 and 8 seconds) have been evaluated, and the presentation of a distractor on the mnemonic performance in the test Memonum in 72 children from a college in the metropolitan area of Bucaramanga, Colombia, aged between 8 and 11 in grades third, fourth and fifth grade. It has been found significant difference regarding the exposure time in the variables number of hits and successes accumulated, showing a better mnemonic performance in participants who took the test during 8 seconds compared to children who took the test during 1 second; in addition, the presence of a distractor showed a significant difference regarding the strengths and successes accumulated. Such distractor is considered a stimulus generator interference that disrupts the storage capacity of working memory in children. Additionally, a significant difference was found with respect to the use of mental rehearsal strategy, indicating that participants who took the test in 4 and 8 seconds, respectively, assigned higher scores than children who took the test in 1 second. A long exposure time to stimuli during Memonum test increases the holding capacity. Also, the use of a distractor affects the storage capacity and this, at the same time, increases the school progression due to the use of mnemonic strategies that children use to ensure the memory of the numerical series

Quantified real constraint solving using modal intervals with applications to control

Les restriccions reals quantificades (QRC) formen un formalisme matemàtic utilitzat per modelar un gran nombre de problemes físics dins els quals intervenen sistemes d'equacions no-lineals sobre variables reals, algunes de les quals podent ésser quantificades. Els QRCs apareixen en nombrosos contextos, com l'Enginyeria de Control o la Biologia. La resolució de QRCs és un domini de recerca molt actiu dins el qual es proposen dos enfocaments diferents: l'eliminació simbòlica de quantificadors i els mètodes aproximatius. Tot i això, la resolució de problemes de grans dimensions i del cas general, resten encara problemes oberts. Aquesta tesi proposa una nova metodologia aproximativa basada en l'Anàlisi Intervalar Modal, una teoria matemàtica que permet resoldre problemes en els quals intervenen quantificadors lògics sobre variables reals. Finalment, dues aplicacions a l'Enginyeria de Control són presentades. La primera fa referència al problema de detecció de fallades i la segona consisteix en un controlador per a un vaixell a vela.

Evaluation of suitable spectral intervals for near-IR laboratory detection of water vapour continuum absorption

The water vapour continuum absorption is an important component of molecular absorption of radiation in atmosphere. However, uncertainty in knowledge of the value of the continuum absorption at present can achieve 100% in different spectral regions leading to an error in flux calculation up to 3-5 W/m2 global mean. This work uses line-by-line calculations to reveal the best spectral intervals for experimental verification of the CKD water vapour continuum models in the currently least studied near-infrared spectral region. Possible sources of errors in continuum retrieval taken into account in the simulation include the sensitivity of laboratory spectrometers and uncertainties in the spectral line parameters in HITRAN-2004 and Schwenke-Partridge database. It is shown that a number of micro-windows in near-IR can be used at present for laboratory detection of the water vapour continuum with estimated accuracy from 30 to 5%.

Bootstrapping prediction intervals for autoregressive models

Methods of improving the coverage of Box–Jenkins prediction intervals for linear autoregressive models are explored. These methods use bootstrap techniques to allow for parameter estimation uncertainty and to reduce the small-sample bias in the estimator of the models’ parameters. In addition, we also consider a method of bias-correcting the non-linear functions of the parameter estimates that are used to generate conditional multi-step predictions.

Bootstrap prediction intervals for autoregressive time series

The calculation of interval forecasts for highly persistent autoregressive (AR) time series based on the bootstrap is considered. Three methods are considered for countering the small-sample bias of least-squares estimation for processes which have roots close to the unit circle: a bootstrap bias-corrected OLS estimator; the use of the Roy–Fuller estimator in place of OLS; and the use of the Andrews–Chen estimator in place of OLS. All three methods of bias correction yield superior results to the bootstrap in the absence of bias correction. Of the three correction methods, the bootstrap prediction intervals based on the Roy–Fuller estimator are generally superior to the other two. The small-sample performance of bootstrap prediction intervals based on the Roy–Fuller estimator are investigated when the order of the AR model is unknown, and has to be determined using an information criterion.