Nonparametric Bayesian Estimation of Survival Curves from Incomplete Observations

Susarla, V.; Ryzin, John Van

doi:10.2307/2286858

Cited by 78 publications

(67 citation statements)

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“…In this expression, n( ) is the number of lifetimes (complete or censored) which are greater than , {x j } is the set of distinct censored lifetimes, n(x − ) is the number of lifetimes (complete or censored) that are greater than or equal to x j , and (x j ) is the number of censored lifetimes that are equal to x j . Derived by Susarla and van Ryzin, 11 the posterior mean in (6) serves as a nonparametric MMSE estimator of S( ). Note that conventionally the Dirichlet process is parameterized by a bounded nonnegative measure (A) for A ⊂ [0, ∞).…”

Section: The Fusion-based Approachmentioning

confidence: 99%

“…It is helpful to observe that, as m → ∞ the Susarla-van Ryzin estimator (6) approaches S 0 ( ) and as m → 0, it reduces to the Kaplan-Meier estimator. 11 In general, the hyperparameter m plays the role of a weight on the prior that can be exploited to control the balance between the robustness of the prior mean against the fidelity of the Kaplan-Meier estimator to the observed data.…”

Section: The Fusion-based Approachmentioning

confidence: 99%

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Hierarchical nonparametric survival modeling for demand forecasting with fragmented categorical covariates

2019

Appl Stoch Models Bus & Ind

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This paper addresses the problem of data fragmentation when incorporating imbalanced categorical covariates in nonparametric survival models. The problem arises in an application of demand forecasting where certain categorical covariates are important explanatory factors for the diversity of survival patterns but are severely imbalanced in the sense that a large percentage of data segments defined by these covariates have very small sample sizes. Two general approaches, called the class‐based approach and the fusion‐based approach, are proposed to handle the problem. Both reply on judicious utilization of a data segment hierarchy defined by the covariates. The class‐based approach allows certain segments in the hierarchy to have their private survival functions and aggregates the others to share a common survival function. The fusion‐based approach allows all survival functions to borrow and share information from all segments based on their positions in the hierarchy. A nonparametric Bayesian estimator with Dirichlet process priors provides the data‐sharing mechanism in the fusion‐based approach. The hyperparameters in the priors are treated as fixed quantities and learned from data by taking advantage of the data segment hierarchy. The proposed methods are motivated and validated by a case study with real‐world data from an operation of software development service.

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Section: The Fusion-based Approachmentioning

confidence: 99%

Section: The Fusion-based Approachmentioning

confidence: 99%

Hierarchical nonparametric survival modeling for demand forecasting with fragmented categorical covariates

2019

Appl Stoch Models Bus & Ind

View full text Add to dashboard Cite

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“…If we use Dp(s, α * ) as prior for the distribution of S(t), then the posterior distribution given the sample Z n of randomly censored observations is a mixture of Dirichlet processes (Blum and Susarla, 1977) and thus the conjugacy property is not satisfied anymore when data are censored. The p-th order moment of the posterior distribution of S(t) is (Susarla and Van Ryzin, 1976)…”

Section: Robust Estimation Of Survival Probabilities From Right Censomentioning

confidence: 99%

“…Bayesian nonparametric procedures have appeared after Ferguson (1973), who introduced the Dirichlet process (DP). DP priors are behind the most popular Bayesian nonparametric models, and a number of authors have proposed nonparametric approaches based on them to estimate survival functions with censored data (Susarla and Van Ryzin, 1976;Blum and Susarla, 1977;Zhou, 2004). In particular, Susarla and Van Ryzin (1976) developed an estimator for survival functions that converges to the Kaplan-Meier estimator as the prior strength of the DP goes to zero.…”

Section: Introductionmentioning

confidence: 99%

“…DP priors are behind the most popular Bayesian nonparametric models, and a number of authors have proposed nonparametric approaches based on them to estimate survival functions with censored data (Susarla and Van Ryzin, 1976;Blum and Susarla, 1977;Zhou, 2004). In particular, Susarla and Van Ryzin (1976) developed an estimator for survival functions that converges to the Kaplan-Meier estimator as the prior strength of the DP goes to zero. An extension to the so-called "neutral to the right" priors was considered by Ferguson and Phadia (1979).…”

Section: Introductionmentioning

confidence: 99%

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Reliable survival analysis based on the Dirichlet process

et al. 2015

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We present a robust Dirichlet process for estimating survival functions from samples with right-censored data. It adopts a prior near-ignorance approach to avoid almost any assumption about the distribution of the population lifetimes, as well as the need of eliciting an infinite dimensional parameter (in case of lack of prior information), as it happens with the usual Dirichlet process prior. We show how such model can be used to derive robust inferences from right-censored lifetime data. Robustness is due to the identification of the decisions that are prior-dependent, and can be interpreted as an analysis of sensitivity with respect to the hypothetical inclusion of fictitious new samples in the data. In particular, we derive a nonparametric estimator of the survival probability and a hypothesis test about the probability that the lifetime of an individual from one population is shorter than the lifetime of an individual from another. We evaluate these ideas on simulated data and on the Australian AIDS survival dataset. The methods are publicly available through an easy-to-use R package.

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Bayesian accelerated failure time analysis with application to veterinary epidemiology

2000

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Standard methods for analysing survival data with covariates rely on asymptotic inferences. Bayesian methods can be performed using simple computations and are applicable for any sample size. We propose a practical method for making prior specifications and discuss a complete Bayesian analysis for parametric accelerated failure time regression models. We emphasize inferences for the survival curve rather than regression coefficients. A key feature of the Bayesian framework is that model comparisons for various choices of baseline distribution are easily handled by the calculation of Bayes factors. Such comparisons between non‐nested models are difficult in the frequentist setting. We illustrate diagnostic tools and examine the sensitivity of the Bayesian methods. Copyright © 2000 John Wiley & Sons, Ltd.

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Nonparametric Bayesian Estimation of Survival Curves from Incomplete Observations

Cited by 78 publications

References 0 publications

Hierarchical nonparametric survival modeling for demand forecasting with fragmented categorical covariates

Hierarchical nonparametric survival modeling for demand forecasting with fragmented categorical covariates

Reliable survival analysis based on the Dirichlet process

Bayesian accelerated failure time analysis with application to veterinary epidemiology

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