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Interval estimation for a binomial proportion
 Statist. Sci
, 2001
"... Abstract. We revisit the problem of interval estimation of a binomial proportion. The erratic behavior of the coverage probability of the standardWaldconfidence interval has previously been remarkedon in the literature (Blyth andStill, Agresti andCoull, Santner andothers). We begin by showing that t ..."
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Cited by 80 (2 self)
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Abstract. We revisit the problem of interval estimation of a binomial proportion. The erratic behavior of the coverage probability of the standardWaldconfidence interval has previously been remarkedon in the literature (Blyth andStill, Agresti andCoull, Santner andothers). We begin by showing that the chaotic coverage properties of the Waldinterval are far more persistent than is appreciated. Furthermore, common textbook prescriptions regarding its safety are misleading and defective in several respects andcannot be trusted. This leads us to consideration of alternative intervals. A number of natural alternatives are presented, each with its motivation and context. Each interval is examinedfor its coverage probability andits length. Basedon this analysis, we recommendthe Wilson interval or the equaltailedJeffreys prior interval for small n andthe interval suggestedin Agresti andCoull for larger n. We also provide an additional frequentist justification for use of the Jeffreys interval. Key words and phrases: Bayes, binomial distribution, confidence intervals, coverage probability, Edgeworth expansion, expected length, Jeffreys prior, normal approximation, posterior.
Applied Multilevel Analysis
 Techniques and Applications, Mahwah: Lawrence Erlbaum
, 1995
"... CONTENTS 1 Introduction .............................................................................................. 1 1.1 Why do we need special multilevel analysis techniques? .................. 6 1.2 Multilevel theories .................................................................... ..."
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Cited by 41 (0 self)
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CONTENTS 1 Introduction .............................................................................................. 1 1.1 Why do we need special multilevel analysis techniques? .................. 6 1.2 Multilevel theories ............................................................................... 7 1.3 Models described in this book ............................................................. 8 2 Multilevel Regression Models ............................................................. 11 2.1 The basic twolevel regression model ............................................... 11 2.2 Computing parameter estimates and analysis strategy .................. 16 2.3 An example of a simple twolevel regression model ......................... 24 2.4 Standardizing regression coefficients ............................................... 26 2.5 Interpreting interactions ................................................................... 27 3 Working with HLM, VARCL and MLn
Accounting for Model Uncertainty in Survival Analysis Improves Predictive Performance
 In Bayesian Statistics 5
, 1995
"... Survival analysis is concerned with finding models to predict the survival of patients or to assess the efficacy of a clinical treatment. A key part of the modelbuilding process is the selection of the predictor variables. It is standard to use a stepwise procedure guided by a series of significanc ..."
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Cited by 39 (12 self)
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Survival analysis is concerned with finding models to predict the survival of patients or to assess the efficacy of a clinical treatment. A key part of the modelbuilding process is the selection of the predictor variables. It is standard to use a stepwise procedure guided by a series of significance tests to select a single model, and then to make inference conditionally on the selected model. However, this ignores model uncertainty, which can be substantial. We review the standard Bayesian model averaging solution to this problem and extend it to survival analysis, introducing partial Bayes factors to do so for the Cox proportional hazards model. In two examples, taking account of model uncertainty enhances predictive performance, to an extent that could be clinically useful. 1 Introduction From 1974 to 1984 the Mayo Clinic conducted a doubleblinded randomized clinical trial involving 312 patients to compare the drug DPCA with a placebo in the treatment of primary biliary cirrhosis...
Bayesian Semiparametric Inference for the Accelerated Failure Time Model
, 1997
"... Bayesian semiparametric inference is considered for a loglinear model. This model consists of a parametric component for the regression coefficients and a nonparametric component for the unknown error distribution. Bayesian analysis is studied for the case of a parametric prior on the regressio ..."
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Cited by 14 (0 self)
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Bayesian semiparametric inference is considered for a loglinear model. This model consists of a parametric component for the regression coefficients and a nonparametric component for the unknown error distribution. Bayesian analysis is studied for the case of a parametric prior on the regression coefficients and a mixtureofDirichletprocesses prior on the unknown error distribution. A Markov chain Monte Carlo (MCMC) method is developed to compute the features of the posterior distribution. A model selection method for obtaining a more parsimonious set of predictors is studied. The method adds indicator variables to the regression equation. The set of indicator variables represents all the possible subsets to be considered. A MCMC method is developed to search stochastically for the best subset. These procedures are applied to two examples, one with censored data. Key words and phrases: Censored data; Log linear model; Markov chain Monte Carlo algorithm; Metropolis algori...
Heterogeneities in Macroparasite Infections: Patterns and Processes
, 2002
"... ome rather complex. Some of the variation in parasite loads we observe is predictable. For example, in mammals and some other taxa, males tend to be more heavily infected than females, perhaps due to differences in immune function (Potdin 1996a, Schalk and Forbes 1997, McCurdy et al. 1998). Parasit ..."
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Cited by 9 (1 self)
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ome rather complex. Some of the variation in parasite loads we observe is predictable. For example, in mammals and some other taxa, males tend to be more heavily infected than females, perhaps due to differences in immune function (Potdin 1996a, Schalk and Forbes 1997, McCurdy et al. 1998). Parasite loads tend to increase with age and may plateau in older animals, though if acquired immunity is important (or there is parasiteinduced host mortality) then they may tdtimately decline again, so reducing the degree of parasite aggregation. Genetic differences in susceptibility to infection may also be important, though their extent and direction are much more difficult to predict. Other factors that may contribute to the observed heterogeneities in worm burdens are the condition of the host (which may be a function of parasite load), host behaviour, parasite genetics and seasonality. Comparative studies of aggregation suggest that the infection process and the habitat of the host may make
An evaluation of the effectiveness of overt and covert speed enforcement achieved through mobile radar operations
, 2001
"... The effect of mobile radar enforcement and supporting publicity on road trauma during July 1995June 1997 was examined in terms of the number of casualty crashes that occurred on undivided roads in 100 km/h speed zones in rural Victoria. The crashbased analysis compared crash frequencies for the pe ..."
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Cited by 2 (2 self)
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The effect of mobile radar enforcement and supporting publicity on road trauma during July 1995June 1997 was examined in terms of the number of casualty crashes that occurred on undivided roads in 100 km/h speed zones in rural Victoria. The crashbased analysis compared crash frequencies for the period in which up to 73 mobile radar devices were operational (July 1995June 1997) with corresponding twoyear period before their introduction (July 1992June 1994) when there was no mobile radar enforcement. The crash effects were examined according to the type of Police vehicle used during each session of mobile radar operation. The type of vehicle used was either a marked patrol car – signifying the overt operation, or an unmarked patrol car signifying the covert operation. Interactions of the enforcement with varying levels of mobile radar publicity awareness were also considered. The analysis found evidence of casualty crash reductions in rural regions of Victoria, when the speed enforcement operations were either i) covert (unmarked patrol cars) or ii) a mix of overt and covert (marked and unmarked patrol cars). The strongest effects on casualty crashes occurred when a mix of overt and covert mobile radar enforcement was accompanied by high awareness levels of mobile radar publicity during July 1996June 1997. Under these circumstances, a marginally statistically significant
Breast screening, prognostic factors and survival: Results from the Swedish two county study
 British Journal of Cancer
, 1991
"... Summary The results of the Swedish twocounty study are analysed with respect to tumour size, nodal status and malignancy grade, and the relationship of these prognostic factors to screening and to survival. It is shown that these factors can account for much of the differences in survival between i ..."
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Summary The results of the Swedish twocounty study are analysed with respect to tumour size, nodal status and malignancy grade, and the relationship of these prognostic factors to screening and to survival. It is shown that these factors can account for much of the differences in survival between incidence screen detected, interval and control group cancers but to a lesser extent for cancers detected at the prevalence screen where length bias is greatest. Furthermore, examination of the relationships among the prognostic factors and mode of detection indicates that malignancy grade, as a measure of inherent malignant capacity, evolves as a tumour grows. The proportion of cancers with poor malignancy grade is several fold lower for cancers of diameter less than 15 cm than for cancers greater than 30 cm, independent of the length bias of screening. The implications of these findings for screening frequency are briefly discussed. It has been shown that mortality from breast cancer can be reduced by mass screening using mammography (Shapiro et al., 1982; Tabar et al., 1985), a reduction resulting from earlier diagnosis. The natural history of breast cancer, however, is clearly heterogeneous, with substantial variation
Research on the Upstream Passage of Juvenile Salmon through Culverts: Retrofit Baffles” Final Report
, 2006
"... of sponsored research activities. Neither Client nor Battelle nor any person acting on behalf of either: MAKES ANY WARRANTY OR REPRESENTATION, EXPRESS OR IMPLIED, with respect to the accuracy, completeness, or usefulness of the information contained in this report, or that the use of any information ..."
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of sponsored research activities. Neither Client nor Battelle nor any person acting on behalf of either: MAKES ANY WARRANTY OR REPRESENTATION, EXPRESS OR IMPLIED, with respect to the accuracy, completeness, or usefulness of the information contained in this report, or that the use of any information, apparatus, process, or composition disclosed in this report may not infringe privately owned rights; or Assumes any liabilities with respect to the use of, or for damages resulting from the use of, any information, apparatus, process, or composition disclosed in this report. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by Battelle. The views and opinions of authors expressed herein do not necessarily state or reflect those of Battelle This document was printed on recycled paper. (9/2003) PNWD3672
Introduction to Generalized Linear Modelling
, 2008
"... Preliminary statement. When I first wrote my lecture notes for the Part II ..."
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Preliminary statement. When I first wrote my lecture notes for the Part II
The InandOutofSample (IOS) Likelihood Ratio
"... A new test of model misspecification, based on the ratio of insample and outofsample likelihoods, is proposed. The test is broadly applicable, and in simple problems approximates well known, intuitive methods. Using jackknife influence curve approximations, it is shown that the test statistic c ..."
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A new test of model misspecification, based on the ratio of insample and outofsample likelihoods, is proposed. The test is broadly applicable, and in simple problems approximates well known, intuitive methods. Using jackknife influence curve approximations, it is shown that the test statistic can be viewed asymptotically as a multiplicative contrast between two estimates of the information matrix that are equal under correct model specification. This approximation is used to show that the statistic is asymptotically normally distributed, though it is suggested that pvalues be computed using the parametric bootstrap. The resulting methodology is demonstrated with a variety of examples and simulations involving both discrete and continuous data.