Sample size considerations using mathematical models: an example with Chlamydia trachomatis infection and its sequelae pelvic inflammatory disease.

BACKGROUND The success of an intervention to prevent the complications of an infection is influenced by the natural history of the infection. Assumptions about the temporal relationship between infection and the development of sequelae can affect the predicted effect size of an intervention and the sample size calculation. This study investigates how a mathematical model can be used to inform sample size calculations for a randomised controlled trial (RCT) using the example of Chlamydia trachomatis infection and pelvic inflammatory disease (PID). METHODS We used a compartmental model to imitate the structure of a published RCT. We considered three different processes for the timing of PID development, in relation to the initial C. trachomatis infection: immediate, constant throughout, or at the end of the infectious period. For each process we assumed that, of all women infected, the same fraction would develop PID in the absence of an intervention. We examined two sets of assumptions used to calculate the sample size in a published RCT that investigated the effect of chlamydia screening on PID incidence. We also investigated the influence of the natural history parameters of chlamydia on the required sample size. RESULTS The assumed event rates and effect sizes used for the sample size calculation implicitly determined the temporal relationship between chlamydia infection and PID in the model. Even small changes in the assumed PID incidence and relative risk (RR) led to considerable differences in the hypothesised mechanism of PID development. The RR and the sample size needed per group also depend on the natural history parameters of chlamydia. CONCLUSIONS Mathematical modelling helps to understand the temporal relationship between an infection and its sequelae and can show how uncertainties about natural history parameters affect sample size calculations when planning a RCT.

Seasonal variation of high-molecular-weight compounds in the water-soluble fraction of organic urban aerosols

Aerosol samples were collected in Zurich, Switzerland, at an urban background site and were analyzed with size exclusion chromatography (SEC) and laser/desorption ionization mass spectrometry (LDI-MS) for water-soluble organic compounds with high molecular weight. Daily samples were collected during two campaigns in winter and summer, for 1 month each. The concentration of high-molecular-weight compounds (humic-like substances (HULIS)) was between 0.4 and 4 μg/m3 in winter and summer. The most intense signals in the LDI-MS mass spectra were measured between m/z150 and 500, comparing well with the mode of the two main high mass peaks determined with SEC corresponding to masses between 200 and 600 Da. For the maximum molecular weight, however, different results were obtained by the two techniques: whereas a maximum molecular weight between 1300 and 3300 Da was found with SEC, hardly any peaks above m/z700 were measured with LDI-MS. During summer the maximum molecular weight of HULIS (determined with SEC) correlates positively with several parameters such as ozone and increased temperature indicative of enhanced atmospheric photo-oxidation. The HULIS concentration also correlates positively with the oxalic acid concentration in the particles. This suggests that HULIS are generated by secondary processes in summer. The lack of such correlations during winter suggests that other sources and processes might be important during colder seasons.

Das Ministerium Brandenburg und die Fraction Unruh, und Eiserner Bestand an Regierungs-Rechten, ohne welche ein Staat überhaupt nicht lebensfähig ist

Boberach: Weil Völker nicht selten an ihren politischen Ideen zugrundegehen, war auch Preußen durch die Politik der Linken bedroht und das Ministerium hat die dem Staat gebührenden Regierungsfunktionen mit Recht in Anspruch genommen

Hepatocellular Carcinoma Screening With Computed Tomography Using the Arterial Enhancement Fraction With Radiologic-Pathologic Correlation.

OBJECTIVE The aim of this study was to investigate the performance of the arterial enhancement fraction (AEF) in multiphasic computed tomography (CT) acquisitions to detect hepatocellular carcinoma (HCC) in liver transplant recipients in correlation with the pathologic analysis of the corresponding liver explants. MATERIALS AND METHODS Fifty-five transplant recipients were analyzed: 35 patients with 108 histologically proven HCC lesions and 20 patients with end-stage liver disease without HCC. Six radiologists looked at the triphasic CT acquisitions with the AEF maps in a first readout. For the second readout without the AEF maps, 3 radiologists analyzed triphasic CT acquisitions (group 1), whereas the other 3 readers had 4 contrast acquisitions available (group 2). A jackknife free-response reader receiver operating characteristic analysis was used to compare the readout performance of the readers. Receiver operating characteristic analysis was used to determine the optimal cutoff value of the AEF. RESULTS The figure of merit (θ = 0.6935) for the conventional triphasic readout was significantly inferior compared with the triphasic readout with additional use of the AEF (θ = 0.7478, P < 0.0001) in group 1. There was no significant difference between the fourphasic conventional readout (θ = 0.7569) and the triphasic readout (θ = 0.7615, P = 0.7541) with the AEF in group 2. Without the AEF, HCC lesions were detected with a sensitivity of 30.7% (95% confidence interval [CI], 25.5%-36.4%) and a specificity of 97.1% (96.0%-98.0%) by group 1 looking at 3 CT acquisition phases and with a sensitivity of 42.1% (36.2%-48.1%) and a specificity of 97.5% (96.4%-98.3%) in group 2 looking at 4 CT acquisition phases. Using the AEF maps, both groups looking at the same 3 acquisition phases, the sensitivity was 47.7% (95% CI, 41.9%-53.5%) with a specificity of 97.4% (96.4%-98.3%) in group 1 and 49.8% (95% CI, 43.9%-55.8%)/97.6% (96.6%-98.4%) in group 2. The optimal cutoff for the AEF was 50%. CONCLUSION The AEF is a helpful tool to screen for HCC with CT. The use of the AEF maps may significantly improve HCC detection, which allows omitting the fourth CT acquisition phase and thus making a 25% reduction of radiation dose possible.

Inhalation anesthesia of rats: influence of the fraction of inspired oxygen on limb ischemia/reperfusion injury

Inhalation anesthesia with isoflurane is a well-established and safe method used in small laboratory animals. In most cases oxygen is used as a carrier gas for isoflurane, but room air or mixtures of oxygen with air or nitrous oxide are also being used. Anesthesia is therefore administered using different fractions of inspired oxygen (FiO2), and this may have consequences for the outcome of experiments. The aim of the present study was to investigate the influence of FiO2 on rat hind limb ischemia/reperfusion injury and to refine the used inhalation anesthesia. Male Wistar rats were subjected to 3.5 h of ischemia and 2 h of reperfusion, and divided into three groups according to FiO2 in the O2/air/isoflurane anesthesia gas mixture: 40%, 60%, and 100% O2. Normal, healthy rats were used as controls. Muscle edema and creatine kinase MM, a marker for myocyte necrosis, were significantly increased with 40% FiO2 as compared with 100% FiO2 (P<0.05). Partial pressure of oxygen, oxygen saturation, and oxyhemoglobin were significantly higher in the 100% O2 group as compared with 40% O2. No significant differences were detected for other parameters, such as the oxidative stress markers malondialdehyde and superoxide dismutase. We conclude that a refined inhalation anesthesia setting using 40% FiO2, reflecting more or less the clinical situation, leads to a more severe and more physiologically relevant reperfusion injury than higher FiO2. Oxidative stress did not correlate with FiO2 and seemed to have no influence on reperfusion injury.

Fibroblast Growth Factor 23 Is an Independent and Specific Predictor of Mortality in Patients With Heart Failure and Reduced Ejection Fraction

BACKGROUND Strategies to improve risk prediction are of major importance in patients with heart failure (HF). Fibroblast growth factor 23 (FGF-23) is an endocrine regulator of phosphate and vitamin D homeostasis associated with an increased cardiovascular risk. We aimed to assess the prognostic effect of FGF-23 on mortality in HF patients with a particular focus on differences between patients with HF with preserved ejection fraction and patients with HF with reduced ejection fraction (HFrEF). METHODS AND RESULTS FGF-23 levels were measured in 980 patients with HF enrolled in the Ludwigshafen Risk and Cardiovascular Health (LURIC) study including 511 patients with HFrEF and 469 patients with HF with preserved ejection fraction and a median follow-up time of 8.6 years. FGF-23 was additionally measured in a second cohort comprising 320 patients with advanced HFrEF. FGF-23 was independently associated with mortality with an adjusted hazard ratio per 1-SD increase of 1.30 (95% confidence interval, 1.14-1.48; P<0.001) in patients with HFrEF, whereas no such association was found in patients with HF with preserved ejection fraction (for interaction, P=0.043). External validation confirmed the significant association with mortality with an adjusted hazard ratio per 1 SD of 1.23 (95% confidence interval, 1.02-1.60; P=0.027). FGF-23 demonstrated an increased discriminatory power for mortality in addition to N-terminal pro-B-type natriuretic peptide (C-statistic: 0.59 versus 0.63) and an improvement in net reclassification index (39.6%; P<0.001). CONCLUSIONS FGF-23 is independently associated with an increased risk of mortality in patients with HFrEF but not in those with HF with preserved ejection fraction, suggesting a different pathophysiologic role for both entities.

Organisation of the equine immunoglobulin constant heavy chain genes. II. Equine cgamma genes.

The number of immunoglobulin G constant heavy chain genes (cgamma genes) varies broadly among mammalian species, reflecting structural and functional differences between expressed immunoglobulin G (IgG) isotypes and allotypes. Up to now equine IgG isotypes have been defined only at the biochemical and serological level. It is still not clear how many IgG isotypes exist in horses and whether there are any allotypes. Here, we describe the isolation and characterisation of equine cgamma genes. An equine genomic lambda phage library was screened with a human cgamma4 probe. Cross-hybridising equine cgamma sequences were cloned twice and characterised by restriction mapping with the human cgamma4 and a murine sgamma1 probe. Genomic equine DNA probes for both, cgamma genes and corresponding switch regions (sgamma), were isolated and used for a more detailed BamHI restriction analysis, comparing genomic DNA of various horses. This analysis reveals the existence of at least five, or probably six cgamma genes in the equine haploid genome. Beside the porcine system, this is the highest number of cgamma genes described for any mammalian species. Moreover, for two of these cgamma genes, BamHI restriction fragment length polymorphism became evident.

Organization of the equine immunoglobulin heavy chain constant region genes; III. Alignment of c mu, c gamma, c epsilon and c alpha genes.

Previous restriction analysis of cloned equine DNA and genomic DNA of equine peripheral blood mononuclear cells had indicated the existence of one c epsilon, one c alpha and up to six c gamma genes in the haploid equine genome. The c epsilon and c alpha genes have been aligned on a 30 kb DNA fragment in the order 5' c epsilon-c alpha 3'. Here we describe the alignment of the equine c mu and c gamma genes by deletion analysis of one IgM, four IgG and two equine light chain expressing heterohybridomas. This analysis establishes the existence of six c gamma genes per haploid genome. The genomic alignment of the cH-genes is 5' c mu/(/) c gamma 1/(/) c gamma 2/(/) c gamma 3/(/) c gamma 4/(/) c gamma 5/(/) c gamma 6/(/) c epsilon-c alpha 3', naming the c gamma genes according to their position relative to c mu. For three of the c gamma genes the corresponding IgG isotypes could be identified as IgGa for c gamma 1, IgG(T) for c gamma 3 and IgGb for c gamma 4.

Dimensions of projections of sets on Riemannian surfaces of constant curvature

We apply the theory of Peres and Schlag to obtain generic lower bounds for Hausdorff dimension of images of sets by orthogonal projections on simply connected two-dimensional Riemannian manifolds of constant curvature. As a conclusion we obtain appropriate versions of Marstrand's theorem, Kaufman's theorem, and Falconer's theorem in the above geometrical settings.

THE EQUILIBRIUM CONSTANT FOR THE GLYCINE SYNTHASE REACTION (ONE-CARBON, METABOLISM, FOLATE)

The equilibrium constant (K(,c)) under physiological conditions (38(DEGREES)C, 0.25 M ionic strength (I), pH 7.0) for the glycine synthase (GS) reaction (E C 2.1.2.1.0) (Equation 1) has been determined. (UNFORMATTED TABLE FOLLOWS)^ 5,10-CH(,2)-H(,4)Folate NADH NH (,4)+ CO(,2) ^ K(,c) = Eq. 1^ H(,4)Folate NAD('+) GLY ^(TABLE ENDS)^ The enzymatic instability of the GS enzyme complex itself has made it necessary to determine the overall K(,c) from the product of constants for the partial reactions of GS determined separately under the same conditions. The partial reactions are the H(,4)Folate-formaldehyde (CH(,2)(OH)(,2)) condensation reaction (Reaction 1) the K(,c) for which has been reported by this laboratory (3.0 x 10('4)), the lipoate (LipS(,2)) dehydrogenase reaction (LipDH) (Reaction 2) and the Gly-Lip^ decarboxylase reaction (Reaction 3) forming reduced lipoate (Lip(SH)(,2)), NH(,4)('+), CO(,2) and CH(,2)(OH)(,2.) (UNFORMATTED TABLE FOLLOWS)(,)^ H(,4)Fote + CH(,2)(OH)(,2) 5,10-CH(,2)-H(,4)Folate (1)^ Lip(SH)(,2) + NAD('+) LipS(,2) + NADH + H('+) (2)^ H('+) + Gly + LipS(,2) Lip(SH)(,2) + NH(,4)('+) CO(,2) + CH(,2)(OH)(,2) (3)^(TABLE ENDS)^ In this work the K(,c) for Reactions 2 and 3 are reported.^ The K(,c)' for the LipDH reaction described by other authors was reported with unexplainable conclusions regarding the pH depend- ence for the reaction. These conclusions would imply otherwise unexpected acid dissociation constants for reduced and oxidized lipoate. The pK(,a)',s for these compounds have been determined to resolve discrepancy. The conclusions are as follows: (1) The K(,c) for the LipDH reaction is 2.08 x 10('-8); (2) The pK(,a)',s for Lip(SH)(,2) are 4.77(-COOH), 9.91(-SH), 11.59(-SH); for LipS(,2) the carboxyl pK(,a)' is 4.77; (3) Contrary to previous literature, the log K(,c)' for the LipDH reaction is a linear function of the pH, a conclusion supported by the values for the dissociation constants.^ The K(,c) for Reaction 3 is the product of constants for Reactions 4-7. (UNFORMATTED TABLE FOLLOWS)^ LipSHSCH(,2)OH + H(,2)O Lip(SH)(,2) + CH(,2)(OH)(,2) (4)^ H(,2)O + LipSHSCH(,2)NH(,3)('+) LipSHSCH(,2)OH + NH(,4)('+) (5)^ LipSHSCH(,2)NH(,2) + H('+) LipSHSCH(,2)NH(,3)('+) (6)^ Gly + LipS(,2) LipSHSCH(,2)NH(,2) + CO(,2) (7)^(TABLE ENDS)^ Reactions 4-6 are non-enzymatic reactions whose constants were determined spectrophotometrically. Reaction 7 was catalyzed by the partially purified P-protein of GS with equilibrium approached from both directions. The value for K(,c) for this reaction is 8.15 x 10('-3). The combined K(,c) for Reactions 4-7 or Reaction 3 is 2.4 M.^ The overall K(,c) for the GS reaction determined by combination of values for Reactions 1-3 is 1.56 x 10('-3). ^

The Three Body Problem and the Runge-Lenz Equivalent Constant of the Motion

The Runge-Lenz equivalent for the Hydrogen Molecular Cation (and the Earth, Moon and Sun) problem is obtained

Continued Fraction Solutions to Hermite's, Legendre's and Laguerre's Differential Equation

The continued fraction method for solving differential equations is illustrated using three famous differential equations used in quantum chemistry.

Benoit-Constant Coquelin, Brustbild

Signatur des Originals: S 36/F08408