Hazard Function

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Elia Biganzoli - One of the best experts on this subject based on the ideXlab platform.

A. Mehrez - One of the best experts on this subject based on the ideXlab platform.

  • A Hazard Function approximation used in reliability theory
    IEEE Transactions on Reliability, 2001
    Co-Authors: B. Keren, A. Mehrez
    Abstract:

    The cumulative Hazard Function H(n) should accumulate to infinity over the distribution support, because the survivor Function is Sf(n)=exp(-H(n)). The widely used approximation for the cumulative Hazard Function, H(n)/spl ap//spl Sigma//sub k=1//sup n/h(k), for a small value of the Hazard Function, h(k), can be useful and reasonably accurate for computing the survivor Function. For the continuous case, assuming that pdf exists, the H(n) diverges as it should. For the discrete case, two examples show the use of the Hazard Function approximation. In example A for the uniform probability mass Function, the approximation diverges. In example B for the geometric probability mass Function, the approximation converges to the finite value, 1.606695, when it should be diverging. The result is surprising in light of the difference between the continuous case, pdf, and the discrete case, pmf. Thus in practice, the approximation must be used with caution.

S.v. Amari - One of the best experts on this subject based on the ideXlab platform.

  • Comment on: a Hazard Function approximation used in reliability theory
    IEEE Transactions on Reliability, 2005
    Co-Authors: S.v. Amari
    Abstract:

    In a recent paper, Keren & Mehrez have shown that in the case of a geometric probability mass Function, the approximation to the cumulative Hazard Function converges to a finite value (1.606695), when the actual value of the cumulative Hazard Function should be diverging. In this commentary, we show that gives incorrect results, and that the corresponding results for the approximation are actually diverging.

Patrizia Boracchi - One of the best experts on this subject based on the ideXlab platform.

  • modeling the covariates effects on the Hazard Function by piecewise exponential artificial neural networks an application to a controlled clinical trial on renal carcinoma
    BMC Bioinformatics, 2018
    Co-Authors: Marco Fornili, Federico Ambrogi, Patrizia Boracchi, Elia Biganzoli
    Abstract:

    In exploring the time course of a disease to support or generate biological hypotheses, the shape of the Hazard Function provides relevant information. For long follow-ups the shape of Hazard Function may be complex, with the presence of multiple peaks. In this paper we present the use of a neural network extension of the piecewise exponential model to study the shape of the Hazard Function in time in dependence of covariates. The technique is applied to a dataset of 247 renal cell carcinoma patients from a randomized clinical trial. An interaction effect of treatment with number of metastatic lymph nodes but not with pathologic T-stage is highlighted. Piecewise Exponential Artificial Neural Networks demonstrate a clinically useful and flexible tool in assessing interaction or time-dependent effects of the prognostic factors on the Hazard Function.

  • piecewise exponential artificial neural networks peann for modeling Hazard Function with right censored data
    Computational Intelligence Methods for Bioinformatics and Biostatistics, 2013
    Co-Authors: Marco Fornili, Federico Ambrogi, Patrizia Boracchi, Elia Biganzoli
    Abstract:

    The Hazard Function plays an important role in the study of disease dynamics in survival analysis. Longer follow-up for various kinds of cancer, particularly breast cancer, has made it possible the observation of complex shapes of the Hazard Function of occurrence of metastasis and death. The identification of the correct Hazard shape is important both for formulation and support of biological hypotheses on the mechanism underlying the disease.

  • flexible parametric modelling of the Hazard Function in breast cancer studies
    Journal of Applied Statistics, 2012
    Co-Authors: Ilaria Ardoino, Chris Bajdik, Paulo J. Lisboa, Elia M. Biganzoli, Patrizia Boracchi, Federico Ambrogi
    Abstract:

    In cancer research, study of the Hazard Function provides useful insights into disease dynamics, as it describes the way in which the (conditional) probability of death changes with time. The widely utilized Cox proportional Hazard model uses a stepwise nonparametric estimator for the baseline Hazard Function, and therefore has a limited utility. The use of parametric models and/or other approaches that enables direct estimation of the Hazard Function is often invoked. A recent work by Cox et al . [6] has stimulated the use of the flexible parametric model based on the Generalized Gamma (GG) distribution, supported by the development of optimization software. The GG distribution allows estimation of different Hazard shapes in a single framework. We use the GG model to investigate the shape of the Hazard Function in early breast cancer patients. The flexible approach based on a piecewise exponential model and the nonparametric additive Hazards model are also considered.

  • Flexible parametric modelling of the Hazard Function in breast cancer studies
    The 2010 International Joint Conference on Neural Networks (IJCNN), 2010
    Co-Authors: Ilaria Ardoino, Federico Ambrogi, Chris Bajdik, Paulo J. Lisboa, Elia M. Biganzoli, Patrizia Boracchi
    Abstract:

    In cancer research, study of the Hazard Function provides useful information on the disease dynamic, in addition to the identification of prognostic factors. The widely utilized Cox proportional Hazard model uses a stepwise nonparametric estimator for the baseline Hazard Function. Therefore the use of parametric models and/or other approaches to estimate the Hazard Function is often invoked. A recent work by C. Cox and colleagues has stimulated the use of a complex and flexible parametric model based on the General Gamma distribution, supported by the development of optimization software. Use of the General Gamma to study the shape of the Hazard Function is investigated. As a benchmark, the flexible approach based on piecewise exponential model and a nonparametric kernel estimate are considered. An example based on breast cancer survival is used to illustrate the main findings.

  • IJCNN - Flexible parametric modelling of the Hazard Function in breast cancer studies
    The 2010 International Joint Conference on Neural Networks (IJCNN), 2010
    Co-Authors: Ilaria Ardoino, Federico Ambrogi, Chris Bajdik, Paulo J. Lisboa, Elia Biganzoli, Patrizia Boracchi
    Abstract:

    In cancer research, study of the Hazard Function provides useful information on the disease dynamic, in addition to the identification of prognostic factors.

Marco Fornili - One of the best experts on this subject based on the ideXlab platform.