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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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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...
A General Model for the Hazard Rate with Covariables and Methods tor Sample Size Determination for Cohort Studies
, 1977
"... This research is concerned with developing improved methods for analyzing survival data and determining appropriate sample sizes for cohort studies. The model proposed for the hazard function incorporating covariables is a polynomial with different functions of the covariables as coefficients of the ..."
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Cited by 10 (0 self)
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This research is concerned with developing improved methods for analyzing survival data and determining appropriate sample sizes for cohort studies. The model proposed for the hazard function incorporating covariables is a polynomial with different functions of the covariables as coefficients of the various powers of time. This model does not require the assumption that the hazards for different individuals be in constant ratio over time, and it allows for testing whether this assumption is reasonable. The model is parametric, which allows for easy specification of the survival curve and interpretation of results. At the same time, it is general enough so that the form of the hazard is not unduly restricted. Methods for fitting the model to data, testing hypotheses about
Information bounds for Cox regression models with missing data
 Annals of Statistics
, 2004
"... We derive information bounds for the regression parameters in Cox models when data are missing at random. These calculations are of interest for understanding the behavior of efficient estimation in casecohort designs, a type of twophase design often used in cohort studies. The derivations make us ..."
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Cited by 6 (2 self)
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We derive information bounds for the regression parameters in Cox models when data are missing at random. These calculations are of interest for understanding the behavior of efficient estimation in casecohort designs, a type of twophase design often used in cohort studies. The derivations make use of key lemmas appearing in Robins,
FUNCTIONAL ANOVA MODELING FOR PROPORTIONAL HAZARDS REGRESSION
"... The logarithm of the relative risk function in a proportional hazards model involving one or more possibly timedependent covariates is treated as a specified sum of a constant term, main effects, and selected interaction terms. Maximum partial likelihood estimation is used, where the maximization i ..."
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The logarithm of the relative risk function in a proportional hazards model involving one or more possibly timedependent covariates is treated as a specified sum of a constant term, main effects, and selected interaction terms. Maximum partial likelihood estimation is used, where the maximization is taken over a suitably chosen finitedimensional estimation space, whose dimension increases with the sample size and which is constructed from linear spaces of functions of one covariate and their tensor products. The L 2 rate of convergence for the estimate and its ANOVA components is obtained. An adaptive numerical implementation is discussed, whose performance is compared to (full likelihood) hazard regression both with and without the restriction to proportional hazards.
Information Bounds for Regression Models with Missing Data
, 2000
"... In this paper we revisit the information bound calculations in Robins, Rotnitzky, and Zhao (1994) and Robins, Hsieh, and Newey (1995) for regression models with missing covariates. We present an approach to their calculations based on score operators which verifies the bounds established in sections ..."
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Cited by 3 (2 self)
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In this paper we revisit the information bound calculations in Robins, Rotnitzky, and Zhao (1994) and Robins, Hsieh, and Newey (1995) for regression models with missing covariates. We present an approach to their calculations based on score operators which verifies the bounds established in sections 25 of RRZ and in section 3 of RHN (up to typos in the case of RHN). In the case of the Cox regression model for survival data treated in RRZ section 8, we obtain different results than those of RRZ. The integral equation we present for the least favorable direction simplifies to the known information bound for the Cox model with complete data. We give examples of our information calculations for casecohort designs and errors in variables regression models for survival data.
Goodnessof…t Testing for Duration Models with Censored Grouped Data
, 2009
"... We propose a new goodness of …t test for duration models with censored grouped heterogeneous data. The impact of parameter estimation uncertainty is properly addressed, ensuring that the proposed test has an asymptotically valid Type I error. The asymptotic distribution of the test statistic is a fu ..."
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We propose a new goodness of …t test for duration models with censored grouped heterogeneous data. The impact of parameter estimation uncertainty is properly addressed, ensuring that the proposed test has an asymptotically valid Type I error. The asymptotic distribution of the test statistic is a functional form of a chisquare process, whose covariance kernel depends on nuisance parameters and is not distribution free. Accordingly, a simple parametric bootstrap method is used to obtain the critical values of the proposed test. Our simulation study shows that our new test has accurate size and reasonable power in …nite samples.
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
Statistical Methods for Censored Survival Data
"... Methods of statistical analysis of censored survival times are brieflyreviewed and illustrated by application to clinical trials data. These include estimation of the survival curve, nonparametric tests to compare several survival curves, tests for trend, and regression analysis. Extensions of the ..."
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Methods of statistical analysis of censored survival times are brieflyreviewed and illustrated by application to clinical trials data. These include estimation of the survival curve, nonparametric tests to compare several survival curves, tests for trend, and regression analysis. Extensions of the methodology are made for application to epidemiologic casecontrol studies. These are used to estimate relative risks for leukemia asociated with radiation exposures. A final section provides some annotated references to the recent literature.
Use of Machine Learning in Bioinformatics to Identify Prognostic and Predictive Molecular Signatures in Human Breast Cancer
, 2004
"... ..."
Grouped Failure Times TIED FAILURE TIMES  TWO CONTRIBUTIONS TO THE ENCYCLOPEDIA OF BIOSTATISTICS
, 1997
"... ionships between smoking and lung cancer or heart disease and the life span study of over 100,000 Japanese atom bomb survivors in Hiroshima and Nagasaki #Beebe #4##. Another important reason for grouping data is that it is often di#cult or even impossible to obtain exact life time, because ethical, ..."
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ionships between smoking and lung cancer or heart disease and the life span study of over 100,000 Japanese atom bomb survivors in Hiroshima and Nagasaki #Beebe #4##. Another important reason for grouping data is that it is often di#cult or even impossible to obtain exact life time, because ethical, physical or economic restrictions in research design allow the subjects in the followup study to be monitored only periodically. Thus, this type of study only provides the grouped information, i.e., the exact failure time is unknown and the only available information is whether the event of interest occurred between two inspection times. The following study illustrate situations where periodic inspection is used: The National Labor Survey of Youth #NLSY# study of time to weaning of breastfed newborns in which 927 #rstborn children of mothers who chose to breast feed their children were interviewed yearly. Similar to continuous data in survival analysis, grouped survival data can involve c