Lutz Mattner

Stochastic ordering of classical discrete distributions

For several pairs (P, Q) of classical distributions on ℕ0, we show that their stochastic ordering P ≤st Q can be characterized by their extreme tail ordering equivalent to P({k *})/Q({k *}) ≥ 1 ≥ lim k→k * P({k})/Q({k}), with k * and k * denoting the minimum and the supremum of the support of P + Q, and with the limit to be read as P({k *})/Q({k *}) for finite k *. This includes in particular all pairs where P and Q are both binomial (b n 1,p 1 ≤st b n 2,p 2 if and only if n 1 ≤ n 2 and (1 - p 1) n 1 ≥ (1 - p 2) n 2 , or p 1 = 0), both negative binomial (b − r 1,p 1 ≤st b − r 2,p 2 if and only if p 1 ≥ p 2 and p 1 r 1 ≥ p 2 r 2 ), or both hypergeometric with the same sample size parameter. The binomial case is contained in a known result about Bernoulli convolutions, the other two cases appear to be new. The emphasis of this paper is on providing a variety of different methods of proofs: (i) half monotone likelihood ratios, (ii) explicit coupling, (iii) Markov chain comparison, (iv) analytic calculation, and (v) comparison of Lévy measures. We give four proofs in the binomial case (methods (i)-(iv)) and three in the negative binomial case (methods (i), (iv), and (v)). The statement for hypergeometric distributions is proved via method (i).

Evaluation of the Impact of the Source (Patient Versus Staff) on Nosocomial Norovirus Outbreak Severity

OBJECTIVE To study the dependence of infection risk and outbreak size on the type of index case (i.e., patient or staff). METHODS Nosocomial outbreaks were reviewed and categorized into those started by patients and those started by staff. Infection risks and outbreak sizes were evaluated taking into account the index case category. RESULTS Of the 30 nosocomial outbreaks of norovirus with person-to-person transmission, 20 (67%) involved patients as the index cases. Patient-indexed outbreaks affected significantly more patients than did staff-indexed outbreaks (difference in means, 16.25; 95% confidence interval [CI95], 5.1 to 27.0). For the numbers of affected staff, no dependence on the index case category was detectable (difference in means, -1.05; CI95, -9.0 to 6.9). For patients exposed during patient-indexed outbreaks, the risk of acquiring a norovirus infection was approximately 4.8 times as high as the corresponding risk for patients exposed during staff-indexed outbreaks (odds ratio [OR], 4.79; CI95, 1.82 to 8.28). The infection risk for exposed staff during patient-indexed outbreaks was approximately 1.5 times as high as the corresponding risk during staff-indexed outbreaks (OR, 1.51; CI95, 0.92 to 2.49). CONCLUSIONS Patient-indexed norovirus outbreaks generally affect more patients than do staff-indexed outbreaks. Staff appear to be similarly affected by both outbreak index category groups. This study demonstrates the importance of obtaining complete outbreak data, including the index case classification as staff or patient, during norovirus outbreak investigations. Such information may be useful for further targeting prevention measures

Social network analysis and valid Markov chain Monte Carlo tests of null models

Analyses of animal social networks derived from group-based associations often rely on randomisation methods developed in ecology (Manly, Ecology 76:1109–1115, 1995) and made available to the animal behaviour community through implementation of a pair-wise swapping algorithm by Bejder et al. (Anim Behav 56:719–725, 1998). We report a correctable flaw in this method and point the reader to a wider literature on the subject of null models in the ecology literature. We illustrate the importance of correcting the method using a toy network and use it to make a preliminary analysis of a network of associations among eagle rays.

Surveillance invasiver Fadenpilzmykosen in lungentransplantierten Patienten: Effekt antimykotischer Prophylaxe mit Itraconazol und Voriconazol

Von Jan 2002 bis Dez 2003 wurden alle Lungentransplantierten der Medizinischen Hochschule Hannover prospektiv während des postoperativen Krankenhausaufenthalts hinsichtlich der Entwicklung von invasiven Fadenpilzmykosen beobachtet. Patienten wurden als positiv eingestuft, wenn die EORTC‐Kriterien ‘probable or proven’ erfüllt waren. Retrospektiv wurde ermittelt, welche antimykotische Prophylaxe die Patienten erhielten. Von 157 lungentransplantierten Patienten entwickelten 8 eine invasive Mykose (Inzidenz 5.1% nach 17 ± 10 Tagen postoperativ). Sie führten zu einer 14‐fach erhöhten Mortalität (OR 13.8, CI95% 2.5–82, P = 0.001). Präoperative Kolonisierung der Atemwege mit Aspergillus stellte einen signifikanten Risikofaktor dar (P < 0.001, OR 21.9, CI95% 4.9–97). 101 Patienten erhielten vom ersten postoperativen Tag an Itraconazol als antimykotische Prophylaxe. 6 von ihnen entwickelten eine invasive Aspergillose (4.7%). 38 Patienten erhielten eine erst nach >14 Tagen einsetzende antimykotische Prophylaxe mit Itraconazol. Von diesen entwickelten 2 Patienten (3%) eine invasive Aspergillose. Bei 18 Patienten, von denen 10 präoperativ mit Aspergillus besiedelt waren, wurde seit Ende 2002 eine Prophylaxe mit Voriconazol in den ersten 30 postoperativen Tagen durchgeführt. Darunter kam es zu einer Zygomykose. Invasive Fadenpilzmykosen treten bei Lungentransplantierten trotz einer antimykotischen Prophylaxe mit einer hohen Inzidenz von 5% in der frühen postoperativen Phase auf und führen zu einer hohen Mortalität. Ein Management, bei definierten Hochrisikopatienten eine Voriconazol‐Prophylaxe durchzuführen, scheint einer Itraconazolprophylaxe überlegen zu sein. Zur definitiven Klärung sind jedoch noch kontrollierte Studien an größeren Patientenkollektiven erforderlich.

STRICT DEFINITENESS OF INTEGRALS VIA COMPLETE MONOTONICITY OF DERIVATIVES

Let k be a nonnegative integer and let φ : (0,∞) → R be a C∞ function with (−)k · φ(k) completely monotone and not constant. If σ 6= 0 is a signed measure on any euclidean space Rd, with vanishing moments up to order k−1, then the integral ∫Rd ∫Rd φ(‖x−y‖2) dσ(x)dσ(y) is strictly positive whenever it exists. For general d no larger class of continuous functions φ seems to admit the same conclusion. Examples and applications are indicated. A section on ”bilinear integrability” might be of independent interest.

Completeness of location families, translated moments, and uniqueness of charges

SummaryA sufficient condition for statistical completeness of location families generated by a probability density in euclidean space is given. As an application, completeness of families generated by a symmetric stable law is proved. Our criterion, complementing a classical result of Wiener and recent work of Isenbeck and Rüschendorf, is in terms of regularity of the generating density and zerofreeness of its characteristic function. Its proof rests on a local version of the convolution theorem for Fourier transforms of tempered distributions. A more general version of the criterion is applicable to apparently different problems, as is illustrated by giving a simultaneous proof of a theorem on translated moments by P. Hall and a uniqueness result of M. Riesz in potential theory.

ON THE NORMAL APPROXIMATION TO SYMMETRIC BINOMIAL DISTRIBUTIONS

The optimal constant over the square root of n error bound in the central limit theorem for distribution functions of sums of independent symmetric Bernoulli random variables is

An identity for expectations of functions of order statistics

1/\sqrt{2\pi n}

Lower Bounds for Tails of Sums of Independent Symmetric Random Variables

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Associations between the drill (Mandrillus leucophaeus) and sympatric monkeys in Korup National Park, Cameroon.

SummaryWe consider an identity for expectations of general functions of order statistics valid in a parametric class of probability distributions. Corresponding characterization results are indicated.