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Robust treatment planning for intensity modulated radiotherapy of prostate cancer based on coverage probabilities

RADIOTHERAPY AND ONCOLOGY 2006年第1期78卷 27-35页

作者： Baum, C Alber, M Birkner, M Nüsslin, F Univ Tubingen Klin Radioonkol Sekt Biomed Phys D-72076 Tubingen Germany

Background and purpose: To evaluate an optimization approach where coverage probabilities are incorporated into the optimization of intensity modulated radiotherapy (IMRT) to overcome the problem of margin definition in the case of overlapping planning target volume and organs at risk. Patients and methods: IMRT plans were generated for three optimization approaches: based on a planning CT plus margin (A), on prostate and rectum contours from five pre-treatment CT plus margin (B), and on coverage probabilities (C). For approach (C), the probability of organ occupation was computed for each voxel from five pretreatment CTs and the population distribution of systematic setup error and it was used as local weight in the costfunctions. Monte Carlo simulations of treatment courses were used to compute the probability distribution of prostate and rectal wall equivalent uniform dose (EUD). Results: Treatment simulations showed best and most robust results for prostate and rectal wall EUD within the population for (C). For (A) the rectal wall EUD was on average about 1.5 Gy greater than in (C), while the prostate EUD was lower than those from (C) for most of the patients for (B) (especially for those with great organ motion). Conclusions: The incorporation of coverage probabilities, as local weights allows for dose escalation as well as improved rectal sparing and results in a safer and more robust IMRT treatment. (c) 2005 Elsevier Ireland Ltd. All rights reserved.

关键词： IMRT coverage probabilities organ motion setup errors treatment planning prostate cancer

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ASSESSING coverage-probabilities FOR APPROXIMATE MINIMAX ESTIMATORS WITH RESPECT TO INTERVAL RESTRICTIONS

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 1994年第1-2期50卷 59-74页

作者： SCHIPP, B TRENKLER, G STAHLECKER, P UNIV DORTMUND DEPT STATW-4600 DORTMUND 50GERMANY UNIV HAMBURG DEPT ECOND-20146 HAMBURGGERMANY

If a priori information given by interval or ellipsoidal constraints on the unknown coefficients is used by (approximate) Minimax estimators, it is not ensured, that the estimates lie within the restricted set. In the present paper, the probability of such events is investigated on the basis of multivariate two-sided normal probability integrals.

关键词： MINIMAX ESTIMATION A-PRIORI INFORMATION coverage probabilities

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Exact likelihood inference for two exponential populations under joint Type-II censoring

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2008年第5期52卷 2725-2738页

作者： Balakrishnan, N. Rasouli, Abbas McMaster Univ Dept Math & Stat Hamilton ON L8S 4K1 Canada Zanjan Univ Dept Math Zanjan 45195 Iran

Comparative lifetime experiments are of paramount importance when the object of a study is to ascertain the relative merits of two competing products in regard to the duration of their service life. In this paper, we discuss exact inference for two exponential populations when Type-II censoring is implemented on the two samples in a combined manner. We obtain the conditional maximum likelihood estimators (MLEs) of the two exponential mean parameters. We then derive the moment generating functions and the exact distributions of these MLEs along with exact confidence intervals and simultaneous confidence regions. Moreover, simultaneous approximate confidence regions based on the asymptotic normality of the MLEs and simultaneous credible confidence regions from a Bayesian viewpoint are also discussed. A comparison of the exact, approximate, bootstrap and Bayesian intervals is also made in terms of coverage probabilities. Finally, an example is presented in order to illustrate all the methods of inference discussed here. (C) 2007 Elsevier B.V. All rights reserved.

关键词： exponential distribution joint Type-II censoring likelihood inference confidence bounds simultaneous confidence intervals Bayes inference life-testing bootstrap intervals coverage probabilities

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Approximate tolerance limits for Zipf-Mandelbrot distributions

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2013年第7期392卷 1702-1711页

作者： Young, D. S. US Bur Census Washington DC 20233 USA

Zipf-Mandelbrot distributions are commonly used to model natural phenomena where the frequency of an event's occurrence is inversely proportional to its rank based on that frequency of occurrence. This discrete distribution typically exhibits a large number of rare events;however, it may be of interest to obtain reasonable limits that bound the majority of the number of different events. We propose the use of statistical tolerance limits as a way to quantify such a bound. The tolerance limits are constructed using Wald confidence limits for the Zipf-Mandelbrot parameters and are shown through a simulation study to have coverage probabilities near the nominal levels. We also calculate Zipf-Mandelbrot tolerance limits for two real datasets and discuss the associated computer code developed for the R. programming language. Published by Elsevier B.V.

关键词： coverage probabilities Fractal structure King effect Tolerance package Zeta distribution

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Studying the SINR Process of the Typical User in Poisson Networks Using Its Factorial Moment Measures

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IEEE TRANSACTIONS ON INFORMATION THEORY 2015年第12期61卷 6774-6794页

作者： Blaszczyszyn, Bartlomiej Keeler, Holger Paul Inria ENS F-75214 Paris France Weierstrass Inst D-10117 Berlin Germany

Based on a stationary Poisson point process, a wireless network model with random propagation effects (shadowing and/or fading) is considered in order to examine the process formed by the signal-to-interference-plus-noise ratio (SINR) values experienced by a typical user with respect to all the base stations in the down-link channel. This SINR process is completely characterized by deriving its factorial moment measures, which involve numerically tractable, explicit integral expressions. This novel framework naturally leads to expressions for the k-coverage probability, including the case of random SINR threshold values considered in multi-tier network models. While the k-coverage probabilities correspond to the marginal distributions of the order statistics of the SINR process, a more general relation is presented, connecting the factorial moment measures of the SINR process to the joint densities of these order statistics. This gives a way for calculating the exact values of the coverage probabilities arising in a general scenario of signal combination and interference cancellation between base stations. The presented framework consisting of the mathematical representations of SINR characteristics with respect to the factorial moment measures holds for the whole domain of SINR, and is amenable to considerable model extension.

关键词： Heterogeneous networks multi-tier networks Poisson process Poisson-Dirichlet process SINR coverage probabilities interference cancellation antenna cooperation shadowing fading propagation invariance factorial moment expansions stochastic geometry

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On Designing Time-Censored Step-Stress Life Test for Lomax Distribution

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JOURNAL OF TESTING AND EVALUATION 2016年第1期44卷 230-236页

作者： Ismail, Ali A. King Saud Univ Coll Sci Dept Stat & Operat Res POB 2455 Riyadh 11451 Saudi Arabia Cairo Univ Fac Econ & Polit Sci Dept Stat Giza 12613 Egypt

This article presents optimum time step-stress partially accelerated life tests (SSPALTs) where a pre-specified censoring time is considered. The time to failure is assumed to have Lomax distribution. Maximum likelihood estimates (MLEs) of SSPALT model parameters are obtained. Moreover, a confidence intervals estimation for the parameters with associated coverage probabilities is obtained. In addition, optimum test plans for SSPALT are also developed. Such test plans minimize the generalized asymptotic variance (GAV) of the MLEs of the model parameters. To demonstrate the theoretical results, Monte Carlo simulations are introduced and a real life example is provided.

关键词： reliability Lomax distribution step-stress partially accelerated life tests maximum likelihood estimation confidence intervals coverage probabilities optimum test plans Type-I censoring Monte Carlo simulation

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Pointwise exact bootstrap distributions of ROC curves

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MACHINE LEARNING 2010年第1-2期78卷 103-136页

作者： Dugas, Charles Gadoury, David Univ Montreal Dept Math & Stat Montreal PQ H3T 1J4 Canada

We derive pointwise exact bootstrap distributions of ROC curves and the difference between ROC curves for threshold and vertical averaging. From these distributions, pointwise confidence intervals are derived and their performance is measured in terms of coverage accuracy. Improvements over techniques currently in use are obtained, in particular in the extremes of ROC curves where we show that typical drastic falls in coverage accuracy can be avoided.

关键词： Receiver operating characteristics Bootstrap coverage probabilities Model selection

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Optimum Failure-Censored Step-Stress Life Test Plans for the Lomax Distribution

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STRENGTH OF MATERIALS 2016年第3期48卷 437-443页

作者： Ismail, Ali A. King Saud Univ Dept Stat & Operat Res Coll Sci POB 2455 Riyadh 11451 Saudi Arabia Cairo Univ Fac Econ & Polit Sci Dept Stat Giza 12613 Egypt

This article studies partially accelerated life testing (PALT) under step-stress supposing that the time to failure has Lomax distribution with failure-censoring. Maximum likelihood estimators of PALT model parameters with the associated mean square error are obtained. Also, confidence intervals estimations of the parameters with the associated coverage probabilities are calculated. In addition, optimal test designs are considered. To validate the theoretical results simulation studies are performed.

关键词： stress Lomax distribution partial acceleration interval estimation coverage probabilities optimal design type-II censoring Newton-Raphson equations non-linearity Monte Carlo simulation

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Estimation for the three-parameter gamma distribution based on progressively censored data

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STATISTICAL METHODOLOGY 2012年第3期9卷 305-319页

作者： Basak, Indrani Balakrishnan, N. Penn State Altoona Altoona PA USA McMaster Univ Hamilton Hamilton ON Canada

Some work has been done in the past on the estimation for the three-parameter gamma distribution based on complete and censored samples. In this paper, we develop estimation methods based on progressively Type-II censored samples from a three-parameter gamma distribution. In particular, we develop some iterative methods for the determination of the maximum likelihood estimates (MLEs) of all three parameters. It is shown that the proposed iterative scheme converges to the MLEs. In this context, we propose another method of estimation which is based on missing information principle and moment estimators. Simple alternatives to the above two methods are also suggested. The proposed estimation methods are then illustrated with a numerical example. We also consider the interval estimation based on large-sample theory and examine the actual coverage probabilities of these confidence intervals in case of small samples using a Monte Carlo simulation study. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Progressive censoring Missing value principle Maximum likelihood estimators Iterative procedure Moment estimators coverage probabilities Monte Carlo simulation

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A synthesis of exact inferential results for exponential step-stress models and associated optimal accelerated life-tests

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METRIKA 2009年第2-3期69卷 351-396页

作者： Balakrishnan, N. McMaster Univ Dept Math & Stat Hamilton ON L8S 4K1 Canada

A reliability experimenter is often interested in studying the effects of extreme or varying stress factors such as load, pressure, temperature and voltage on the lifetimes of experimental units. Accelerated life-tests allow the experimenter to vary the levels of these stress factors in order to obtain information on the parameters of the lifetime distributions more rapidly than under normal operating conditions. Step-stress tests are a particular class of accelerated life-tests which allow the experimenter to change the stress levels at pre-fixed times during the life-testing experiment. One of the prominent models assumed in step-stress tests is the cumulative exposure model which connects the lifetime distribution of units at one stress level to the lifetime distributions at preceding stress levels. Under such a cumulative exposure model and the assumption that the lifetimes at different stress levels are exponentially distributed, we review in this article various developments on exact inferential methods for the model parameters based on different forms of censored data. We also describe the approximate confidence intervals based on the asymptotic properties of maximum likelihood estimators as well as the bootstrap confidence intervals, and provide some comparisons between these methods. Finally, we present some examples to illustrate all the inferential methods discussed here.

关键词： Step-stress models Type-I censoring Type-II censoring Progressive censoring Hybrid censoring Exponential distribution Accelerated life-test Cumulative exposure model Maximum likelihood estimation Conditional moment generating function Conditional inference Stochastic monotonicity Fisher information Bootstrap method coverage probabilities Optimal step-stress change Gamma distribution Truncated binomial distribution Truncated trinomial distribution Truncated multinomial distribution Truncated exponential distribution Mixture distribution Order statistics Bias Mean square error Competing risks

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