Cornelia Wichelhaus

Antimicrobial susceptibility and molecular epidemiology of Neisseria gonorrhoeae in Germany.

Antimicrobial drug resistance in Neisseria gonorrhoeae has become an increasing public health problem. Hence, surveillance of resistance development is of crucial importance to implement adequate treatment guidelines. Data on the spread of antibiotic resistance among gonococcal isolates in Germany, however, is scarce. In a resistance surveillance study conducted by the Paul Ehrlich Society for Chemotherapy between October 2010 and December 2011, 23 laboratories all over Germany were requested to send N. gonorrhoeae isolates to the study laboratory in Frankfurt am Main. Species verification was performed biochemically using ApiNH and with Matrix-Assisted Laser Desorption Ionization-Time of Flight Mass Spectrometry (MALDI-TOF MS). Antimicrobial susceptibility testing was performed using the Etest method. For molecular epidemiological analysis, N. gonorrhoeae strains were genotyped by means of N. gonorrhoeae multi-antigen sequence typing. A total of 213 consecutive gonococcal isolates were analyzed in this nationwide study. Applying EUCAST breakpoints, high resistance rates were found for ciprofloxacin (74%) and tetracycline (41%). Penicillin non-susceptibility was detected in 80% of isolates. The rate of azithromycin resistance was 6%, while all strains were susceptible to spectinomycin, cefixime, and ceftriaxone. Molecular typing of gonococcal isolates revealed a great heterogeneity of 99 different sequence types (ST), but ST1407 predominated (n=39). This is the first comprehensive German multi-centre surveillance study on antibiotic susceptibility and molecular epidemiology of N. gonorrhoeae with implications for antibiotic choice for treatment of gonorrhoea. The World Health Organization supports the concept that an efficacious treatment of gonorrhoea results in at least 95% of infections being cured. Accordingly, as spectinomycin is not available on the German market, only the third generation cephalosporins cefixime and ceftriaxone are regarded as valuable drugs for empirical treatment of gonorrhoea in Germany.

Product Form Models for Queueing Networks with an Inventory

We investigate a new class of stochastic networks that exhibit a product form steady state distribution. The stochastic networks developed here are integrated models for networks of service stations and inventories. We integrate a server with attached inventory under (r, Q)- or (r, S)-policy into Jackson or Gordon-Newell networks. Replenishment lead times are non-zero and random and depend on the load of the system. While the inventory is depleted the server with attached inventory does not accept new customers (lost sales regime), but we assume that the lost sales are not lost to the system. We pursue three different approaches to handle routing with respect to this node during the time the inventory is empty. We derive stationary distributions of joint queue lengths and inventory processes in explicit product form. The stationary distributions are then used to calculate performance measures of the respective systems. We discuss the advantages and disadvantages of product form modeling in the context of service-inventory systems. Finally, we sketch two network models where several nodes may have an attached inventory.

Nonparametric conditional variance and error density estimation in regression models with dependent errors and predictors

Abstract: This paper considers nonparametric regression models with long memory errors and predictors. Unlike in weak dependence situations, we show that the estimation of the conditional mean has influence on the estimation of both, the conditional variance and the error density. In particular, the estimation of the conditional mean has a negative effect on the asymptotic behaviour of the conditional variance estimator. On the other hand, surprisingly, estimation of the conditional mean may reduce convergence rates of the residual-based Parzen-Rosenblatt density estimator, as compared to the errors-based one. Our asymptotic results reveal small/large bandwidth dichotomous behaviour. In particular, we present a method which guarantees that a chosen bandwidth implies standard weakly dependent-type asymptotics. Our results are confirmed by an extensive simulation study. Furthermore, our theoretical lemmas may be used in different problems related to nonparametric regression with long memory, like crossvalidation properties, bootstrap, goodness-of-fit or quadratic forms.

Nonparametric estimation of the service time distribution in the discrete-time GI/G/∞ queue with partial information

Estimation of the service time distribution in the discrete-time GI/G/∞-queue based solely on information on the arrival and departure processes is considered. The focus is put on the estimation approach via the so called “sequence of differences”. Existing results for this approach are substantially extended by proving a functional central limit theorem for the resultant estimator. Here, the underlying function space is taken to be the space of sequences converging to zero. The moving block bootstrap technique is considered for the estimation of the resultant covariance kernel and is shown to be applicable under mild additional conditions.

Queueing Systems of INAR(1) Processes with Compound Poisson Arrivals

Integer valued autoregressive processes of order 1 (or INAR(1) processes) that may be interpreted as discrete time G/Geom/∞ queue length processes are considered. The arrivals are assumed to be compound Poisson distributed. It is shown that then the stationary distribution of the queue length process as well as the distribution of the departures from the system are again members of the class of compound Poisson distributions. This reveals remarkable invariance properties of the model. The derived explicit expressions allow for the calculation of important performance measures. It is further shown that time-reversibility of the queue length process as well as an analogue of Burke’s theorem hold only if the arrival process is Poisson.

Conditional variance estimation in regression models with long memory

In this article we study asymptotic properties of a non‐parametric kernel estimator of the conditional variance in a random design model with parametric mean and heteroscedastic errors, for a class of long‐memory errors and predictors. We establish small and large bandwidths asymptotics, which show a different behaviour compared with that of kernel estimators of the conditional mean. We distinguish between an oracle case (i.e. where the errors are directly observed) and a non‐oracle case (where the errors are replaced with residuals) and show non‐equivalence between the oracle and non‐oracle case. We also discuss a practical problem of bandwidth choice. Theoretical results are justified by simulation studies. We apply our theory to DJA and FTSE indices.

Nonparametric inference for stochastic feedforward networks based on cross-spectral analysis of point processes

Abstract: In this paper we study a nonparametric estimation problem for stochastic feedforward systems with nodes of type G/G/∞. We assume that we have observations of the external arrival and external departure processes of customers of the system, but no information about the movements of the indistinguishable customers in the network. Our aim is the construction of estimators for the characteristic functions and the densities of the service time distributions at the nodes as well as for the routing probabilities. Since the system is only partly observed we have to clarify first if the parameters are identifiable from the given data. The crucial point in our approach is the observation that in our stochastic networks under study the influence of the arrival processes on the departure processes can be described in a linear and time-invariant model. This makes it possible to apply cross-spectral techniques for multivariate point processes. The construction of the estimators is then based on smoothed periodograms. We prove asymptotic normality for the estimators. We present the statistical analysis for a tandem system of two nodes in full details and show afterwards how the results can be generalized to feedforward systems of three or more nodes and to systems with positive feedback probabilities at the nodes.

Dependence in Lag for Markov chains on partially ordered state spaces with applications to degradable networks

We study the property of dependence in lag for Markov chains on countable partially ordered state spaces and give conditions which ensure that a process is monotone in lag. In case of linearly ordered state spaces, proofs are based on the Lorentz inequality. However, we show that on partially ordered spaces Lorentz inequality is only true under additional assumptions. By using supermodular-type stochastic orders we derive comparison inequalities that compare the internal dependence structure of processes with that of their speeding-down versions. Applications of the results are presented for degradable exponential networks in which the nodes are subject to random breakdowns and repairs. We obtain comparison results for the breakdown processes as well as for the queue length processes that are not even Markovian on their own.

Estimation of the traffic intensity in a piecewise-stationary Mt/Gt/1 queue with probing

We use a probing strategy to estimate the time dependent traffic intensity in an Mt/Gt/1 queue, where the arrival rate and the general service-time distribution change from one time interval to another, and derive statistical properties of the proposed estimator. We present a method to detect a switch from a stationary interval to another using a sequence of probes to improve the estimation. At the end, we compare our results with two estimators proposed in the literature for the M/G/1 queue.