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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...
Bayesian information criterion for censored survival models
 Biometrics
"... We investigate the Bayesian Information Criterion (BIC) for variable selection in models for censored survival data. Kass and Wasserman (1995) showed that BIC provides a close approximation to the Bayes factor when a unitinformation prior on the parameter space is used. We propose a revision of the ..."
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Cited by 15 (2 self)
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We investigate the Bayesian Information Criterion (BIC) for variable selection in models for censored survival data. Kass and Wasserman (1995) showed that BIC provides a close approximation to the Bayes factor when a unitinformation prior on the parameter space is used. We propose a revision of the penalty term in BIC so that it is de ned in terms of the number of uncensored events instead of the number of observations. For the simplest censored data model, that of exponential distributions of survival times (i.e. a constant hazard rate), this revision results in a better approximation to the exact Bayes factor based on a conjugate unitinformation prior. In the Cox proportional hazards regression model, we propose de ning BIC in terms of the maximized partial likelihood. Using the number of deaths rather than the number of individuals in the BIC penalty term corresponds to a more realistic prior on the parameter space, and is shown to improve predictive performance for assessing stroke risk in the Cardiovascular Health Study.
Bayesian Analysis of Multivariate Survival Data Using Monte Carlo Methods
 Canadian Journal of Statistics
, 1995
"... This paper deals with the analysis of multivariate survival data from a Bayesian perspective using Markov Chain Monte Carlo methods. Metropolis along with Gibbs algorithm (Metropolis et al., 1953; Muller, 1991) is used to calculate some of the marginal posteriors. Multivariate survival model is prop ..."
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Cited by 10 (4 self)
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This paper deals with the analysis of multivariate survival data from a Bayesian perspective using Markov Chain Monte Carlo methods. Metropolis along with Gibbs algorithm (Metropolis et al., 1953; Muller, 1991) is used to calculate some of the marginal posteriors. Multivariate survival model is proposed since, survival times within the same `group' are correlated as a consequence of a frailty random block effect (Vaupel et al., 1979). The conditional proportional hazards model of Clayton and Cuzick (1985) is used with a martingale structured prior process (Arjas and Gasbarra, 1994) for the discretized baseline hazard. Besides the calculation of the marginal posteriors of the parameters of interest, this paper presents some Bayesian EDA diagnostic techniques to detect model adequacy. The methodology is exemplified with the kidney infection data where the times to infections within the same patients are expected to be correlated. Key Words: Autocorrelated prior process, credible regions,...
The hazards of mutual fund underperformance
 Journal of Empirical Finance
, 1999
"... This paper investigates the process determining mutual funds ’ conditional probability of closure, i.e., their hazard function. Using a nonparametric approach to estimate the effects of a fund’s age on its hazard rate, we find a distinctly nonlinear, inverse Ushaped pattern in the relationship. He ..."
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Cited by 10 (10 self)
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This paper investigates the process determining mutual funds ’ conditional probability of closure, i.e., their hazard function. Using a nonparametric approach to estimate the effects of a fund’s age on its hazard rate, we find a distinctly nonlinear, inverse Ushaped pattern in the relationship. Hence, young and very old funds are least likely to be closed down. A fund’s relative performance and Ž less significantly. the level of return in the sector in which the fund operates are also identified as important factors in the closure decision. Results from semiparametric Cox regressions are compared with those from the discrete choice probit model used by Brown and Goetzmann wBrown, S.J., Goetzmann, W., 1995. Performance persistence, Journal of Finance. Vol. 50, pp. 679–698 x. Finally, we provide a complete summary of the fund attrition process by estimating the survivor function, indicating the proportion of funds that survive up to a given age, and we identify the effect
Implementing Approximate Bayesian Inference for Survival Analysis using Integrated Nested Laplace Approximations
, 2010
"... In this report, we investigate the use of INLA, (Martino and Rue, 2008) to solve Bayesian inferential problems in Bayesisan Survival analsysis. In particular we consider the Exponential and Weibulldistributed lifetimes with and without censoring and frailty, and Coxmodels with piecewise constant an ..."
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Cited by 5 (3 self)
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In this report, we investigate the use of INLA, (Martino and Rue, 2008) to solve Bayesian inferential problems in Bayesisan Survival analsysis. In particular we consider the Exponential and Weibulldistributed lifetimes with and without censoring and frailty, and Coxmodels with piecewise constant and piecewise linear baseline hazard. We demonstrate that all these models can (in most cases) be expressed as a latent Gaussian model (LGM) so that integrated nested Laplace approximations proposed by Rue et al. (2009) can be applied. We show comparison with the results obtained with INLA and those obtained with extensive runs with Markov chain Monte Carlo methods. The results obtained are again ”practically exact” and support the general experience of Rue et al. (2009).
A Model for the Analysis of Survival with an Intervening Event
, 1978
"... Methods introduced by Lagakos for incorporating infonnation from a timedependent covariable (an intervening event) into the analysis of failure times are generalized. The research was motivated by two followup studiesone involving industrial workers where disI ability retirement is the interve ..."
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Cited by 1 (0 self)
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Methods introduced by Lagakos for incorporating infonnation from a timedependent covariable (an intervening event) into the analysis of failure times are generalized. The research was motivated by two followup studiesone involving industrial workers where disI ability retirement is the intervening event and the other, patients with coronary artery disease where the first nonfatal myocardial infarctiOn after diagnosis for the disease is the intervening event. The generalized model
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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Cited by 1 (0 self)
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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.
SURVIVAL ANALYSIS \H'l1I
, 1982
"... by K. L.Q. READ · r • R.R. HARRIS"', A.A. NOURA t and DENNIS GILLINGS';'i' SUMMARY A general approach to the analysis of survival data is developed, based on the fitting of loglinear and similar models to multidimensional contingency tables formed from such data by suitable categorisation of the ti ..."
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by K. L.Q. READ · r • R.R. HARRIS"', A.A. NOURA t and DENNIS GILLINGS';'i' SUMMARY A general approach to the analysis of survival data is developed, based on the fitting of loglinear and similar models to multidimensional contingency tables formed from such data by suitable categorisation of the time domain and the covariates (including treatment). Consideration is given to nonproportional hazards, timedependent or sequentially realised covariates, alternative transformations of the survivor function and subsets of the parameters which may be involved nonlinearly. The work is presented in terms of weighted least squares estimation, though this is not necessary to the underlying formulation and other methods, of fitting may be adopted. Some keywonds: Survival analysis, categorical data, loglinear models, conplementary loglog transforn~tion, timerelated covariates, weiehted least squares. p 'I
Approved by:
, 1981
"... (Under the direction of C. M. SUCHINDRAN) ·e This research is concerned with developing a methodology for performing a life table analysis for data obtained in a complex sample survey. Four methods for estimating the variance of a function estimated using complex survey data are reviewed. These four ..."
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(Under the direction of C. M. SUCHINDRAN) ·e This research is concerned with developing a methodology for performing a life table analysis for data obtained in a complex sample survey. Four methods for estimating the variance of a function estimated using complex survey data are reviewed. These four methods are then applied to estimates of the conditional probabilities of an event and the associated survivorship probabilities, and suggestions are made as to the Ibest l variance estimation method to use. A test statistic analogous to the MantelHaenszel test is developed for comparing survivorship probabilities between two or more domains of interest for complex survey data. Use of the test statistic is illustrated for two data sets. Values of the test statistic based on the complex survey design are compared to values obtained using the MantelHaenszel test statistic assuming a simple random sample. Life table regression models are reviewed and a model is developed which can be used with complex survey data. This brings to discussion the issue of likelihood based inference and estimation in complex surveys. Arguments based upon superpopulation models are given which support the use of likelihood methods for complex survey data. Variance estimates for the maximum likelihood estimators obtained from complex survey data are developed, and examples illustrating the given approach are given. i i ACKNOWLEDGMENTS It has been a great privilege to have been a student in the