A fast cross-entropy method for estimating buffer overflows in queuing networks

In this paper, we propose a fast adaptive importance sampling method for the efficient simulation of buffer overflow probabilities in queueing networks. The method comprises three stages. First, we estimate the minimum cross-entropy tilting parameter for a small buffer level; next, we use this as a starting value for the estimation of the optimal tilting parameter for the actual (large) buffer level. Finally, the tilting parameter just found is used to estimate the overflow probability of interest. We study various properties of the method in more detail for the M/M/1 queue and conjecture that similar properties also hold for quite general queueing networks. Numerical results support this conjecture and demonstrate the high efficiency of the proposed algorithm.

The collision branching process

We consider a branching model, which we call the collision branching process (CBP), that accounts for the effect of collisions, or interactions, between particles or individuals. We establish that there is a unique CBP, and derive necessary and sufficient conditions for it to be nonexplosive. We review results on extinction probabilities, and obtain explicit expressions for the probability of explosion and the expected hitting times. The upwardly skip-free case is studied in some detail.

Asymmetry and duration dependence in Australian GDP and unemployment

The per iodic structure of business cycles suggests that significant asymmetries are present over different phases of the cycle. This paper uses markov regime-switching models with fixed and duration dependent transition probabilities to directly model expansions, contractions and durations in Australian GDP growth and unemployment growth. Evidence is found of significant asymmetry in growth rates across expansions and contractions for both series. GDP contractions exhibit duration dependence implying that as output recessions age the likelihood of switching into an expansion phase increases. Unemployment growth does not exhibit duration dependence in either phase. Evidence is also presented that non-linearities in unemployment growth are well explained by the asymmetries in the GDP growth cycle. The analysis suggests that recessions are periods of rapid and intense job destruction, that Australian unemployment tends to ratchet up in recessionary periods and, in contrast to US and UK studies, that shocks to Australian unemployment growth are more persistent in recessions than expansions. [E37 C5 C41].

Quasistationarity of continuous-time Markov chains with positive drift

We shall study continuous-time Markov chains on the nonnegative integers which are both irreducible and transient, and which exhibit discernible stationarity before drift to infinity sets in. We will show how this 'quasi' stationary behaviour can be modelled using a limiting conditional distribution: specifically, the limiting state probabilities conditional on not having left 0 for the last time. By way of a dual chain, obtained by killing the original process on last exit from 0, we invoke the theory of quasistationarity for absorbing Markov chains. We prove that the conditioned state probabilities of the original chain are equal to the state probabilities of its dual conditioned on non-absorption, thus allowing us to establish the simultaneous existence and then equivalence, of their limiting conditional distributions. Although a limiting conditional distribution for the dual chain is always a quasistationary distribution in the usual sense, a similar statement is not possible for the original chain.

Further results on the relationship between mu-invariant measures and quasi-stationary distributions for absorbing continuous-time Markov chains

This note considers continuous-time Markov chains whose state space consists of an irreducible class, C, and an absorbing state which is accessible from C. The purpose is to provide results on mu-invariant and mu-subinvariant measures where absorption occurs with probability less than one. In particular, the well-known premise that the mu-invariant measure, m, for the transition rates be finite is replaced by the more natural premise that m be finite with respect to the absorption probabilities. The relationship between mu-invariant measures and quasi-stationary distributions is discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.

Limiting conditional distributions for birth-death processes

In a recent paper [16], one of us identified all of the quasi-stationary distributions for a non-explosive, evanescent birth-death process for which absorption is certain, and established conditions for the existence of the corresponding limiting conditional distributions. Our purpose is to extend these results in a number of directions. We shall consider separately two cases depending on whether or not the process is evanescent. In the former case we shall relax the condition that absorption is certain. Furthermore, we shall allow for the possibility that the minimal process might be explosive, so that the transition rates alone will not necessarily determine the birth-death process uniquely. Although we shall be concerned mainly with the minimal process, our most general results hold for any birth-death process whose transition probabilities satisfy both the backward and the forward Kolmogorov differential equations.

Optimal quantum trajectories for discrete measurements

Using the method of quantum trajectories we show that a known pure state can be optimally monitored through time when subject to a sequence of discrete measurements. By modifying the way that we extract information from the measurement apparatus we can minimize the average algorithmic information of the measurement record, without changing the unconditional evolution of the measured system. We define an optimal measurement scheme as one which has the lowest average algorithmic information allowed. We also show how it is possible to extract information about system operator averages from the measurement records and their probabilities. The optimal measurement scheme, in the limit of weak coupling, determines the statistics of the variance of the measured variable directly. We discuss the relevance of such measurements for recent experiments in quantum optics.

Consistency of FDG-PET Accuracy and Cost-Effectiveness in Initial Staging of Patients With Hodgkin Lymphoma Across Jurisdictions

Introduction: Two hundred ten patients with newly diagnosed Hodgkin`s lymphoma (HL) were consecutively enrolled in this prospective trial to evaluate the cost-effectiveness of fluorine-18 ((18)F)-fluoro-2-deoxy-D-glucose-positron emission tomography (FDG-PET) scan in initial staging of patients with HL. Methods: All 210 patients were staged with conventional clinical staging (CCS) methods, including computed tomography (CT), bone marrow biopsy (BMB), and laboratory tests. Patients were also submitted to metabolic staging (MS) with whole-body FDG-PET scan before the beginning of treatment. A standard of reference for staging was determined with all staging procedures, histologic examination, and follow-up examinations. The accuracy of the CCS was compared with the MS. Local unit costs of procedures and tests were evaluated. Incremental cost-effectiveness ratio (ICER) was calculated for both strategies. Results: In the 210 patients with HL, the sensitivity for initial staging of FDG-PET was higher than that of CT and BMB in initial staging (97.9% vs. 87.3%; P < .001 and 94.2% vs. 71.4%, P < 0.003, respectively). The incorporation of FDG-PET in the staging procedure upstaged disease in 50 (24%) patients and downstaged disease in 17 (8%) patients. Changes in treatment would be seen in 32 (15%) patients. Cumulative cost for staging procedures was $3751/patient for CCS compared to $5081 for CCS + PET and $4588 for PET/CT. The ICER of PET/CT strategy was $16,215 per patient with modified treatment. PET/CT costs at the beginning and end of treatment would increase total costs of HL staging and first-line treatment by only 2%. Conclusion: FDG-PET is more accurate than CT and BMB in HL staging. Given observed probabilities, FDG-PET is highly cost-effective in the public health care program in Brazil.

Cost Effectiveness of Positron Emission Tomography in Patients With Hodgkin`s Lymphoma in Unconfirmed Complete Remission or Partial Remission After First-Line Therapy

Purpose To assess the cost effectiveness of fluorine-18-fluorodeoxyglucose positron emission tomography (FDG-PET) in patients with Hodgkin`s lymphoma (HL) with unconfirmed complete remission (CRu) or partial remission (PR) after first-line treatment. Patients and Methods One hundred thirty patients with HL were prospectively studied. After treatment, all patients with CRu/PR were evaluated with FDG-PET. In addition, PET-negative patients were evaluated with standard follow-up, and PET-positive patients were evaluated with biopsies of the positive lesions. Local unit costs of procedures and tests were evaluated. Cost effectiveness was determined by evaluating projected annual economic impact of strategies without and with FDG-PET on HL management. Results After treatment, CRu/PR was observed in 50 (40.0%) of the 127 patients; the sensitivity, specificity, and positive and negative predictive values of FDG-PET were 100%, 92.0%, 92.3%, and 100%, respectively (accuracy of 95.9%). Local restaging costs without PET were $350,050 compared with $283,262 with PET, a 19% decrease. The incremental cost-effectiveness ratio is -$3,268 to detect one true case. PET costs represented 1% of total costs of HL treatment. Simulated costs in the 974 patients registered in the 2008 Brazilian public health care database showed that the strategy including restaging PET would have a total program cost of $56,498,314, which is $516,942 less than without restaging PET, resulting in a 1% cost saving. Conclusion FDG-PET demonstrated 95.9% accuracy in restaging for patients with HL with CRu/PR after first-line therapy. Given the observed probabilities, FDG-PET is highly cost effective and would reduce costs for the public health care program in Brazil.

Salvage Radical Prostatectomy for Radiation-recurrent Prostate Cancer: A Multi-institutional Collaboration

Background: Oncologic outcomes in men with radiation-recurrent prostate cancer (PCa) treated with salvage radical prostatectomy (SRP) are poorly defined. Objective: To identify predictors of biochemical recurrence (BCR), metastasis, and death following SRP to help select patients who may benefit from SRP. Design, setting, and participants: This is a retrospective, international, multi-institutional cohort analysis. There was amedian follow-up of 4.4 yr following SRP performed on 404 men with radiation-recurrent PCa from 1985 to 2009 in tertiary centers. Intervention: Open SRP. Measurements: BCR after SRP was defined as a serum prostate-specific antigen (PSA) >= 0.1 or >= 0.2 ng/ml (depending on the institution). Secondary end points included progression to metastasis and cancerspecific death. Results and limitations: Median age at SRP was 65 yr of age, and median pre-SRP PSA was 4.5 ng/ml. Following SRP, 195 patients experienced BCR, 64 developed metastases, and 40 died from PCa. At 10 yr after SRP, BCR-free survival, metastasis-free survival, and cancer-specific survival (CSS) probabilities were 37% (95% confidence interval [CI], 31-43), 77% (95% CI, 71-82), and 83% (95% CI, 76-88), respectively. On preoperative multivariable analysis, pre-SRP PSA and Gleason score at postradiation prostate biopsy predicted BCR (p = 0.022; global p < 0.001) and metastasis (p = 0.022; global p < 0.001). On postoperative multivariable analysis, pre-SRP PSA and pathologic Gleason score at SRP predicted BCR (p = 0.014; global p < 0.001) and metastasis (p < 0.001; global p < 0.001). Lymph node involvement (LNI) also predicted metastasis (p = 0.017). The main limitations of this study are its retrospective design and the follow-up period. Conclusions: In a select group of patients who underwent SRP for radiation-recurrent PCa, freedom from clinical metastasis was observed in > 75% of patients 10 yr after surgery. Patients with lower pre-SRP PSA levels and lower postradiation prostate biopsy Gleason score have the highest probability of cure from SRP. (C) 2011 European Association of Urology. Published by Elsevier B. V. All rights reserved.

Cost-Effectiveness of Palliation of Unresectable Esophageal Cancer

Introduction Different modalities of palliation for obstructive symptoms in patients with unresectable esophageal cancer (EC) exist. However, these therapeutic alternatives have significant differences in costs and effectiveness. Methods A Markov model was designed to compare the cost-effectiveness (CE) of self-expandable stent (SES), brachytherapy and laser in the palliation of unresectable EC. Patients were assigned to one of the strategies, and the improvement in swallowing function was compared given the treatment efficacy, probability of survival, and risks of complications associated to each strategy. Probabilities and parameters for distribution were based on a 9-month time frame. Results Under the base-case scenario, laser has the lowest CE ratio, followed by brachytherapy at an incremental cost-effectiveness ratio (ICER) of $4,400.00, and SES is a dominated strategy. In the probabilistic analysis, laser is the strategy with the highest probability of cost-effectiveness for willingness to pay (WTP) values lower than $3,201 and brachytherapy for all WTP yielding a positive net health benefit (NHB) (threshold $4,440). The highest probability of cost-effectiveness for brachytherapy is 96%, and consequently, selection of suboptimal strategies can lead to opportunity losses for the US health system, ranging from US$ 4.32 to US$ 38.09 million dollars over the next 5-20 years. Conclusion Conditional to the WTP and current US Medicare costs, palliation of unresectable esophageal cancers with brachytherapy provides the largest amount of NHB and is the strategy with the highest probability of CE. However, some level of uncertainly remains, and wrong decisions will be made until further knowledge is acquired.

Cost-effectiveness analysis of routine rotavirus vaccination in Brazil

Objective. The objective of this study was to conduct a cost-effectiveness analysis of a universal rotavirus vaccination program among children : 5 years of age in Brazil. Methods. Considering a hypothetical annual cohort of approximately 3 300 000 newborns followed over 5 years, a decision-tree model was constructed to examine the possible clinical and economic effects of rotavirus infection with and without routine vaccination of children. Probabilities and unit costs were derived from published research and national administrative data. The impact of different estimates for key parameters was studied using sensitivity analysis. The analysis was conducted from both healthcare system and societal perspectives. Results. The vaccination program was estimated to prevent approximately 1735 351 (54%) of the 3 210 361 cases of rotavirus gastroenteritis and 703 (75%) of 933 rotavirus-associated deaths during the 5-year period. At a vaccine price of 18.6 Brazilian reais (R$) per dose, this program would cost R$121 673 966 and would save R$38 536 514 in direct costs to the public healthcare system and R$71 778 377 in direct and indirect costs to society. The program was estimated to cost R$1 028 and R$1 713 per life-years saved (LYS)from the societal and healthcare system perspectives, respectively. Conclusions. Universal rotavirus vaccination was a cost-effective strategy for both perspectives. However, these findings are highly sensitive to diarrhea incidence rate, proportion of severe cases, vaccine coverage, and vaccine price.

A general hazard model for lifetime data in the presence of cure rate

Historically, the cure rate model has been used for modeling time-to-event data within which a significant proportion of patients are assumed to be cured of illnesses, including breast cancer, non-Hodgkin lymphoma, leukemia, prostate cancer, melanoma, and head and neck cancer. Perhaps the most popular type of cure rate model is the mixture model introduced by Berkson and Gage [1]. In this model, it is assumed that a certain proportion of the patients are cured, in the sense that they do not present the event of interest during a long period of time and can found to be immune to the cause of failure under study. In this paper, we propose a general hazard model which accommodates comprehensive families of cure rate models as particular cases, including the model proposed by Berkson and Gage. The maximum-likelihood-estimation procedure is discussed. A simulation study analyzes the coverage probabilities of the asymptotic confidence intervals for the parameters. A real data set on children exposed to HIV by vertical transmission illustrates the methodology.

A Comparison of Bayesian and Sampling Theory Inferences in a Probit Model

HE PROBIT MODEL IS A POPULAR DEVICE for explaining binary choice decisions in econometrics. It has been used to describe choices such as labor force participation, travel mode, home ownership, and type of education. These and many more examples can be found in papers by Amemiya (1981) and Maddala (1983). Given the contribution of economics towards explaining such choices, and given the nature of data that are collected, prior information on the relationship between a choice probability and several explanatory variables frequently exists. Bayesian inference is a convenient vehicle for including such prior information. Given the increasing popularity of Bayesian inference it is useful to ask whether inferences from a probit model are sensitive to a choice between Bayesian and sampling theory techniques. Of interest is the sensitivity of inference on coefficients, probabilities, and elasticities. We consider these issues in a model designed to explain choice between fixed and variable interest rate mortgages. Two Bayesian priors are employed: a uniform prior on the coefficients, designed to be noninformative for the coefficients, and an inequality restricted prior on the signs of the coefficients. We often know, a priori, whether increasing the value of a particular explanatory variable will have a positive or negative effect on a choice probability. This knowledge can be captured by using a prior probability density function (pdf) that is truncated to be positive or negative. Thus, three sets of results are compared:those from maximum likelihood (ML) estimation, those from Bayesian estimation with an unrestricted uniform prior on the coefficients, and those from Bayesian estimation with a uniform prior truncated to accommodate inequality restrictions on the coefficients.

The use and abuse of population viability analysis

A recent study by Brook ef al. empirically tested the performance of population viability analysis (PVA) using data from 21 populations across a wide range of species. The study concluded that PVAs are good at predicting the future dynamics of populations. We suggest that this conclusion is a result of a bias in the studies that Brook et al, included in their analyses, We present arguments that PVAs can only be accurate at predicting extinction probabilities if data are extensive and reliable, and if the distribution of vital rates between individuals and years can be assumed stationary in the future, or if any changes can be accurately predicted. In particular, we note th at although catastrophes are likely to have precipitated many extinctions, estimates of the probability of catastrophes are unreliable.