A new, analysis-based, change of measure for tandem queues

In this paper, we introduce a simple analytical approximation for the overflow probability of a two-node tandem queue. From this, we derive a change of measure, which turns out to have good performance in almost the entire parameter space. The form of our new change of measure sheds an interesting new light on earlier changes of measure for the same problem, because here the transition zone from one measure to another - that they all have - arises naturally.\u

Alternative proof and interpretations for a recent state-dependent importance sampling scheme

Recently, a state-dependent change of measure for simulating overflows in the two-node tandem queue was proposed by Dupuis et al. (Ann. Appl. Probab. 17(4):1306–1346, 2007), together with a proof of its asymptotic optimality. In the present paper, we present an alternative, shorter and simpler proof. As a side result, we obtain interpretations for several of the quantities involved in the change of measure in terms of likelihood ratios

Large deviations for the total queue size in non-Markovian tandem queues

We consider a $d$-node tandem queue with arrival process and light-tailed service processes at all queues i.i.d. and independent of each other. We consider three variations of the probability that the number of customers in the system reaches some high level $N$, namely during a busy cycle, in steady state, and upon arrival of a new customer. We show that their decay rates for large $N$ have the same value and give an expression for this value

A New Approach to Assess the Gastrocnemius Muscle Volume in Rodents Using Ultrasound; Comparison with the Gastrocnemius Muscle Index

Introduction: The purpose of this study was to determine the reliability and validity of a new non-invasive ultrasound technique to measure gastrocnemius muscle atrophy after nerve denervation in an animal model. Methods: In sixteen rodents an eight mm sciatic nerve gap was created. In the following 8 weeks, each week, two rodents were euthanized and the gastrocnemius muscle was examined using two different ultrasound systems and two investigators. The standardized ultrasound measurement protocol consisted of identifying pre-defined anatomical landmarks: 1) the fibula, 2) the fibular nerve, and 3) the junction between the most distal point of the semitendinosus muscle and gastrocnemius muscle. Consequently, we measured the muscle thickness as the length of the line between the fibula and the junction between the two muscles, perpendicular to the fibular nerve. After the ultrasound recording, the muscle mass was determined. Results: A steep decline of muscle weight of 24% was observed after one week. In the following weeks, the weight further decreased and then remained stable from 6 weeks onwards, resulting in a maximal muscle weight decrease of 82%. The correlation coefficient was >0.96 between muscle diameter and weight using both ultrasound systems. The inter-rater reliability was excellent for both devices on the operated side (ICC of 0.99 for both ultrasound systems) and good for the non-operated site (ICC's: 0.84 & 0.89). The difference between the muscle mass ratio and the muscle thickness ratio was not more than 5% with two outliers of approximately 13%. Discussion: We have developed an innovative, highly reliable technique for quantifying muscle atrophy after nerve injury. This technique allows serial measurements in the same animal over time. This is a significant advantage compared to the conventional technique for quantifying muscle atrophy, which requires sacrificing the animal

Hypothesis testing for rare-event simulation: limitations and possibilities

One of the main applications of probabilistic model checking is to decide whether the probability of a property of interest is above or below a threshold. Using statistical model checking (SMC), this is done using a combination of stochastic simulation and statistical hypothesis testing. When the probability of interest is very small, one may need to resort to rare-event simulation techniques, in particular importance sampling (IS). However, IS simulation does not yield 0/1-outcomes, as assumed by the hypothesis tests commonly used in SMC, but likelihood ratios that are typically close to zero, but which may also take large values.\ud In this paper we consider two possible ways of combining IS and SMC. One involves a classical IS-scheme from the rare-event simulation literature that yields likelihood ratios with bounded support when applied to a certain (nontrivial) class of models. The other involves a particular hypothesis testing scheme that does not require a-priori knowledge about the samples, only that their variance is estimated well

A prediction model for recurrence after translabyrinthine surgery for vestibular schwannoma: toward personalized postoperative surveillance

Purpose The aim of this study is to compute and validate a statistical predictive model for the risk of recurrence, defined as regrowth of tumor necessitating salvage treatment, after translabyrinthine removal of vestibular schwannomas to individualize postoperative surveillance. Methods The multivariable predictive model for risk of recurrence was based on retrospectively collected patient data between 1995 and 2017 at a tertiary referral center. To assess for internal validity of the prediction model tenfold cross-validation was performed. A 'low' calculated risk of recurrence in this study was set at < 1%, based on clinical criteria and expert opinion. Results A total of 596 patients with 33 recurrences (5.5%) were included for analysis. The final prediction model consisted of the predictors 'age at time of surgery', 'preoperative tumor growth' and 'first postoperative MRI outcome'. The area under the receiver operating curve of the prediction model was 89%, with a C-index of 0.686 (95% CI 0.614-0.796) after cross-validation. The predicted probability for risk of recurrence was low (< 1%) in 373 patients (63%). The earliest recurrence in these low-risk patients was detected at 46 months after surgery. Conclusion This study presents a well-performing prediction model for the risk of recurrence after translabyrinthine surgery for vestibular schwannoma. The prediction model can be used to tailor the postoperative surveillance to the estimated risk of recurrence of individual patients. It seems that especially in patients with an estimated low risk of recurrence, the interval between the first and second postoperative MRI can be safely prolonged.Otorhinolaryngolog

Prognostic factors for the outcome of translabyrinthine surgery for vestibular schwannomas

Objective: To identify predictors of tumor recurrence and postoperative facial nerve function after translabyrinthine surgery for unilateral vestibular schwannomas. Study Design: Retrospective study. Setting: Tertiary referral center. Patients: Between 1996 and 2017 a total of 596 patients with unilateral vestibular schwannoma underwent translabyrinthine surgery. Pre- and postoperative clinical status, radiological, and surgical findings were evaluated. Intervention(s): Translabyrinthine surgery. Main Outcome Measure(s): Potential predictors for tumor recurrence and facial nerve outcome were analyzed using Cox regression and ordinal logistic regression, respectively. Results: The extent of tumor removal was total in 32%, near-total in 58%, and subtotal in 10%. In 5.5% (33/596) of patients the tumor recurred. Subtotal tumor resection (p = 0.004, hazard ratios [HR] = 10.66), a young age (p = 0.008, HR = 0.96), and tumor progression preoperatively (p = 0.042, HR = 2.32) significantly increased the risk of recurrence, whereas tumor size or histologic composition did not. A good postoperative facial nerve function (House-Brackmann grade 1-2) was achieved in 85%. The risk of postoperative facial nerve paresis or paralysis increased with tumor size (p < 0.001, OR = 1.52), but was not associated with the extent of tumor removal, histologic composition, or patient demographics. Conclusions: Translabyrinthine surgery is an effective treatment for vestibular schwannoma, with a good local control rate and facial nerve outcome. The extent of tumor removal is a clinically relevant predictor for tumor recurrence, as are young patient age and preoperative tumor progression. A large preoperative tumor size is associated with a higher risk of postoperative facial nerve paresis or paralysis.Development and application of statistical models for medical scientific researc