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Smoothing Hazard Functions and TimeVarying Effects in Discrete Duration and Competing Risks Models
 Journal of the American Statistical Association
, 1996
"... this paper we propose state space or dynamic models as a flexible technique, which makes simultaneous modelling and smooth estimation of hazard functions and covariate effects possible. The development is related to a dynamic version of the piecewise exponential model and extensions to point process ..."
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Cited by 8 (4 self)
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this paper we propose state space or dynamic models as a flexible technique, which makes simultaneous modelling and smooth estimation of hazard functions and covariate effects possible. The development is related to a dynamic version of the piecewise exponential model and extensions to point processes studied by Gamerman (1991, 1992) and, more closely, to dynamic grouped survival models with only one terminating event (Fahrmeir 1994), where a generalized Kalman filter and smoother (GKFS) is proposed for estimating hazard functions and timevarying effects. Here we extend this approach to models with multiple terminating events (Section 2) and develop a numerically efficient Fisher scoring smoothing algorithm (Section 3). It is obtained by extending iterative Kalmantype techniques for multicategorical time series (Fahrmeir and Tutz, 1994 Ch.8; Fahrmeir and Wagenpfeil, 1995) to the present situation. The smoothing algorithms can be derived as posterior mode estimators or, from a nonparametric point of view, as penalized likelihood estimators. For only one terminating event (m=1), they generally improve (GKFS) with regard to numerical accuracy and approximation quality. Datadriven choice of smoothing or hyperparameters can be achieved by an EMtype algorithm or by crossvalidation. 5
The graft versus leukemia effect after bone marrow transplantation: a case study using structural nested failure time models. Biometrics
, 1999
"... SUMMARY. Over the last decade, J. M. Robins has developed a set of tools for assessing, from observational data, the causal effects of a timedependent treatment or exposure in the presence of timedependent covariates that may be simultaneously confounders and intermediate variables. This report c ..."
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Cited by 6 (0 self)
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SUMMARY. Over the last decade, J. M. Robins has developed a set of tools for assessing, from observational data, the causal effects of a timedependent treatment or exposure in the presence of timedependent covariates that may be simultaneously confounders and intermediate variables. This report concerns a case study of the application of one these techniques, Gestimation using structural nested failure time models, to the problem of assessing the effect of graft versus host disease on leukemia relapse after bone marrow transplantation.
Nonparametric inference for cumulative incidence functions in competing risks studies
 Statistics in Medicine 16
, 1997
"... In the competing risks problem, a useful quantity is the cumulative incidence function, which is the probability of occurrence by time t for a particular type of failure in the presence of other risks. The estimator of this function as given by Kalbfleisch and Prentice is consistent, and, properly n ..."
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Cited by 5 (0 self)
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In the competing risks problem, a useful quantity is the cumulative incidence function, which is the probability of occurrence by time t for a particular type of failure in the presence of other risks. The estimator of this function as given by Kalbfleisch and Prentice is consistent, and, properly normalized, converges weakly to a zeromean Gaussian process with a covariance function for which a consistent estimator is provided. A resampling technique is developed to approximate the distribution of this process, which enables one to construct confidence bands for the cumulative incidence curve over the entire time span of interest and to perform Kolmogorov—Smirnov type tests for comparing two such curves. An AIDS
Dynamic DiscreteTime Duration Models
 Diskussionspapier Nr. 14 des SFB 386, LMU Munchen
, 1997
"... Discretetime grouped duration data, with one or multiple types of terminating events, are often observed in social sciences or economics. In this paper we suggest and discuss dynamic models for flexible Bayesian nonparametric analysis of such data. These models allow simultaneous incorporation and ..."
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Cited by 2 (0 self)
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Discretetime grouped duration data, with one or multiple types of terminating events, are often observed in social sciences or economics. In this paper we suggest and discuss dynamic models for flexible Bayesian nonparametric analysis of such data. These models allow simultaneous incorporation and estimation of baseline hazards and timevarying covariate effects, without imposing particular parametric forms. Methods for exploring the possibility of timevarying effects, as for example the impact of nationality or unemployment insurance benefits on the probability of reemployment, have recently gained increasing interest. Our modeling and estimation approach is fully Bayesian and makes use of Markov Chain Monte Carlo (MCMC) simulation techniques. A detailed analysis of unemployment duration data, with fulltime job, parttime job and other causes as terminating events, illustrates our methods and shows how they can be used to obtain refined results and interpretations. Key words...
The 2sample problem for failure rates depending on a continuous mark: an application to vaccine efficacy
, 2007
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Parametric Model Discrimination for Heavily Censored Survival Data
, 2008
"... Simultaneous discrimination among various parametric lifetime models is an important step in the parametric analysis of survival data. We consider a plot of the skewness versus the coefficient of variation for the purpose of discriminating among parametric survival models. We extend the method of C ..."
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Simultaneous discrimination among various parametric lifetime models is an important step in the parametric analysis of survival data. We consider a plot of the skewness versus the coefficient of variation for the purpose of discriminating among parametric survival models. We extend the method of Cox & Oakes from complete to censored data by developing an algorithm based on a competing risks model and kernel function estimation. A byproduct of this algorithm is a nonparametric survival function estimate.
PROPORTIONAL HAZARDS MODELS WITH CONTINUOUS MARKS
, 2006
"... For timetoevent data with finitely many competing risks, the proportional hazards model has been a popular tool for relating the causespecific outcomes to covariates [Prentice et al. Biometrics 34 (1978) 541–554]. This article studies an extension of this approach to allow a continuum of competin ..."
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For timetoevent data with finitely many competing risks, the proportional hazards model has been a popular tool for relating the causespecific outcomes to covariates [Prentice et al. Biometrics 34 (1978) 541–554]. This article studies an extension of this approach to allow a continuum of competing risks, in which the cause of failure is replaced by a continuous mark only observed at the failure time. We develop inference for the proportional hazards model in which the regression parameters depend nonparametrically on the mark and the baseline hazard depends nonparametrically on both time and mark. This work is motivated by the need to assess HIV vaccine efficacy, while taking into account the genetic divergence of infecting HIV viruses in trial participants from the HIV strain that is contained in the vaccine, and adjusting for covariate effects. Markspecific vaccine efficacy is expressed in terms of one of the regression functions in the markspecific proportional hazards model. The new approach is
Omnibus Tests for Comparison of Competing Risks with Adjustment for Covariate Effects
"... This paper develops omnibus tests for comparing causespecific hazard rates and cumulative incidence functions at specified covariate levels. Confidence bands for the difference and the ratio of two conditional cumulative incidence functions are also constructed. The omnibus test is formulated in te ..."
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This paper develops omnibus tests for comparing causespecific hazard rates and cumulative incidence functions at specified covariate levels. Confidence bands for the difference and the ratio of two conditional cumulative incidence functions are also constructed. The omnibus test is formulated in terms of a test process given by a weighted difference of estimates of cumulative causespecific hazard rates under Cox proportional hazards models. A simulation procedure is devised for sampling from the null distribution of the test process, leading to graphical and numerical techniques for detecting significant differences in the risks. The approach is applied to a cohort study of typespecific HIV infection rates. Key words: Causespecific hazard rates; Cox proportional hazards model; Cumulative incidence function; Dependent competing risks; Human immunodeficiency virus. 1 1. Introduction In longitudinal studies, where individuals are subject to failure f
Comparing SubSurvival Functions in a Competing Risks Model
"... In the competing risks literature, one usually compares whether two risks are equal or whether one is "more serious." In this paper, we propose tests for the equality of two competing risks against an ordered alternative specified by their subsurvival functions. These tests are naturally developed ..."
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In the competing risks literature, one usually compares whether two risks are equal or whether one is "more serious." In this paper, we propose tests for the equality of two competing risks against an ordered alternative specified by their subsurvival functions. These tests are naturally developed as extensions of those based on hazard rates and cumulative incidence functions. We note that the interpretation of the new test results is more direct compared to the situation when the hypotheses are framed in terms of their cumulative incidence functions. The proposed tests are of the KolmogrovSmirnov type, based on maximum differences between subsurvival functions. Our simulation studies indicate that they are excellent competitors of the existing tests, that are based mainly on differences between cumulative incidence functions. A numerical example will demonstrate the advantages of the proposed tests. 1 Introduction The competing risks problem involves subjects or experimental unit...
Institute of Statistics ~o Series No. 1868TANALYTIC EXPRESSIONS FOR MAXIMUM LIKELIHOOD ESTIMATORS IN A NONPARAMETRIC MODEL OF ruMOR INCIDENCE AND DEATH
, 1989
"... PAIGE L. WilLIAMS. Analytic Expressions for Maximum Likelihood Estimators in a Nonparametric Model ofTumor Incidence and Death (under the direction ofDr. Christopher 1. Portier) ABSTRACf: The primary objective ofa longtenn animal carcinogenicity experiment is the comparison of tumor incidence rates ..."
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PAIGE L. WilLIAMS. Analytic Expressions for Maximum Likelihood Estimators in a Nonparametric Model ofTumor Incidence and Death (under the direction ofDr. Christopher 1. Portier) ABSTRACf: The primary objective ofa longtenn animal carcinogenicity experiment is the comparison of tumor incidence rates among treatment groups. Complications arise in the statistical analysis of tumor incidence data when the tumor type ofinterest is not observable. Since reliance on assumptions regarding tumor and treatment lethality is likely to introduce bias, this research focuses attention on the estimation of tumor incidence rates from longterm animal studies which incorporate interim sacrifices. A nonparametric stochastic model is described with transition rates between states corresponding to the tumor incidence rate, overall death rate, and death rate for tumorfree animals. Exact analytic solutions for the maximum likelihood estimators (MLE's) ofthe discrete hazard rates are presented, and constrained MLE's are derived for a study design with up to three intervals under the imposition of boundary constraints. For a study design with more than three intervals, alternative estimators ofthe discrete death rates and tumor incidence rate are