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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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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...
Application of Survival Analysis Methods to Long Term Care Insurance
 Insurance: Mathematics and Economics
, 2002
"... With the introduction of compulsory long term care (LTC) insurance in Germany in 1995, a large claims portfolio with a signi cant proportion of censored observations became available. In rst part of this paper we present an analysis of part of this portfolio using the Cox proportional hazard model ( ..."
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With the introduction of compulsory long term care (LTC) insurance in Germany in 1995, a large claims portfolio with a signi cant proportion of censored observations became available. In rst part of this paper we present an analysis of part of this portfolio using the Cox proportional hazard model (Cox (1972)) to estimate transition intensities. It is shown that this approach allows the inclusion of censored observations as well as the inclusion of time dependent risk factors such as time spent in LTC. This is in contrast to the more commonly used Poisson regression with graduation approach (see for example Renshaw and Haberman (1995), where censored observations and time dependent risk factors are ignored. In the second part we show how these estimated transition intensities can be used in a multiple state Markov process (see Haberman and Pitacco (1999)) to calculate premiums for LTC insurance plans. Keywords: Cox Proportional Hazard, Survival Analysis, long term care insurance, multiple state Markov model Both at Center of Mathematical Sciences, Munich University of Technology, D80290 Munich, Germany, email: cczado@ma.tum.de, rudolph@ma.tum.de, http://www.ma.tum.de/stat/ 1
Stability or regularity of the daily travel time in Lyon ? Application of a duration model
 International Journal of Transport Economics
, 2006
"... Abstract: Escaping unidimensional analysis limits and linear regression irrelevancy, the duration model incorporates impacts of covariates on the duration variable and permits to test the dependence of daily travel times on elapsed time. In the perspective of a discussion of Zahavi’s hypothesis, the ..."
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Abstract: Escaping unidimensional analysis limits and linear regression irrelevancy, the duration model incorporates impacts of covariates on the duration variable and permits to test the dependence of daily travel times on elapsed time. In the perspective of a discussion of Zahavi’s hypothesis, the duration model approach is applied to the daily travel times of Lyon (France). The relationships between daily travel times and socioeconomic attributes and activity duration only support the “weak version of TTB stability hypothesis”. Furthermore the nonmonotonic estimated hazard questions the minimisation of daily travel times.
Doing data analysis with proportional hazards models: Model building, interpretation and diagnosis. Paper presented at the Annual Meeting of the American Educational Research Association
, 1988
"... Guidelines for articulation of a framework for practical application of proportionalhazards models (PHMs) to professional survival analysis are provided. Focus is on data analysis fitting the PHMs with the semiparametric methods of partial likelihood; this strategy is available in the BMDP2L and S ..."
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Guidelines for articulation of a framework for practical application of proportionalhazards models (PHMs) to professional survival analysis are provided. Focus is on data analysis fitting the PHMs with the semiparametric methods of partial likelihood; this strategy is available in the BMDP2L and SAS PROC PHGLM computer programs. Areas in which advice and clarification are particularly apt include the definition of terms, the model and its assumptions, modelbuilding, and interpretation and reporting of estimated model parameters. The presentation is based on a databased example from a study of 10year teacher survival patterns for a cohort of teachers who entered the profession in 1972 in Michigan. Survival analysis seeks to predict the duration during which a subject remains in a situation, in this case, the teaching profession. Discrete and continuous time analysis are examined; and
FULL LIKELIHOOD INFERENCES IN THE COX MODEL: AN EMPIRICAL LIKELIHOOD APPROACH
, 2009
"... Abstract: For the regression parameter β0 in the Cox model, there have been several estimators constructed based on various types of approximated likelihood, but none of them has demonstrated smallsample advantage over Cox’s partial likelihood estimator. In this article, we derive the full likelih ..."
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Abstract: For the regression parameter β0 in the Cox model, there have been several estimators constructed based on various types of approximated likelihood, but none of them has demonstrated smallsample advantage over Cox’s partial likelihood estimator. In this article, we derive the full likelihood function for (β0, F0), where F0 is the baseline distribution in the Cox model. Using the empirical likelihood parameterization, we explicitly profile out nuisance parameter F0 to obtain the fullprofile likelihood function for β0 and the maximum likelihood estimator (MLE) for (β0, F0). The relation between the MLE and Cox’s partial likelihood estimator for β0 is made clear by showing that Taylor’s expansion gives Cox’s partial likelihood estimating function as the leading term of the fullprofile likelihood estimating function. We show that the log fulllikelihood ratio has an asymptotic chisquared distribution, while the simulation studies indicate that for small or moderate sample sizes, the MLE performs favorably over Cox’s partial likelihood estimator. In a real dataset example, our full likelihood ratio test and Cox’s partial likelihood ratio test lead to statistically different conclusions.
Summary
, 2007
"... Receiver operating characteristic (ROC) curves evaluate the discriminatory power of a continuous marker to predict a binary outcome. The most popular parametric model for an ROC curve is the binormal model, which assumes that the marker, after an unspecified monotone transformation, is normally dist ..."
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Receiver operating characteristic (ROC) curves evaluate the discriminatory power of a continuous marker to predict a binary outcome. The most popular parametric model for an ROC curve is the binormal model, which assumes that the marker, after an unspecified monotone transformation, is normally distributed conditional on the outcome. Here we present an alternative to the binormal model based on the Lehmann family, also known as the proportional hazards specification. The resulting ROC curve and its functionals (such as the area under the curve) have simple analytic forms. Closedform expressions for the functional estimates and their corresponding asymptotic variances are derived. This family accommodates the comparison of multiple markers, covariate adjustments and clustered data through a regression formulation. Evaluation of the underlying assumptions, model fitting and model selection can be performed using any off the shelf proportional hazards statistical software 1 package.
C © 2013 Biometrika Trust Printed in Great Britain
"... Highlights, trends and influences are identified associated with the pages of Biometrika subsequent to the editorship of Karl Pearson. Some key words: Biometrika; General statistical methodology; History of statistics. 1. ..."
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Highlights, trends and influences are identified associated with the pages of Biometrika subsequent to the editorship of Karl Pearson. Some key words: Biometrika; General statistical methodology; History of statistics. 1.
That of sophisters, economists and calculators has succeeded
"... me to change direction from mathematics to finance, and particularly Professor Tony Antoniou for having the confidence in me which enabled me to take this step. I am further indebted to Professor Antoniou, as my first supervisor, for his wisdom, invaluable guidance, encouragement and unfailing good ..."
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me to change direction from mathematics to finance, and particularly Professor Tony Antoniou for having the confidence in me which enabled me to take this step. I am further indebted to Professor Antoniou, as my first supervisor, for his wisdom, invaluable guidance, encouragement and unfailing good humour throughout the writing of this thesis. My thanks also to my second supervisor, Dr John Hunter, for his assistance in matters methodological and numerical and advice on many other issues. I wish to thank my parents for their unfailing support and encouragement throughout these years. Finally I should like to express my gratitude to many other colleagues and friends, too numerous to mention individually, who have offered support, _ encouragement and help throughout the writing of this thesis. Many thanks to you all.
Epidemiologic Perspectives & Innovations BioMed Central Methodology Methods for stratification of persontime and events – a prerequisite for Poisson regression and SIR estimation
, 2008
"... This is an Open Access article distributed under the terms of the Creative Commons Attribution License ..."
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This is an Open Access article distributed under the terms of the Creative Commons Attribution License