Analysis of Survival Data with Two Dependent Competing Risks

Bagai, Isha; Рао, Б. Л. С. Пракаса

doi:10.1002/bimj.4710340707

Cited by 4 publications

(6 citation statements)

References 22 publications

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“…We generate n = 250, X 1 , X 2 observations from two independent Weibull distributions. Figure 1 shows the results for Weibull distributions with parameters (3,1) and 4,2, respectively. Figure 2 shows the results for Weibull distributions with parameters (6,1) and (3,2), respectively.…”

Section: Examplementioning

confidence: 99%

“…We generate n = 250 X 1 , X 2 observations from two independent Gamma distributions - Figure 3 is for Gamma with parameters (6,1) and (3 (iv) The performance ofĤ is similar for both Normal and Laplace error densities. (v) Our estimators of the sub-density functions are smoother than the original subdensities.…”

Section: Examplementioning

confidence: 99%

“…Bagai and Prakasa Rao (1992) considered an additive model based on two dependent competing risks X and Y , where X = X 0 +X 1 , Y = X 0 +X 2 and X 0 , X 1 , X 2 are independent random variables. For example, an individual may be exposed to risk of death due to heart and kidney failure.…”

Section: Introductionmentioning

confidence: 99%

“…However, X, Y are not observable in the presence of competing risks. Bagai and Prakasa Rao (1992) assumed that X 0 , X 1 , X 2 are independent exponential random variables with parameters λ 0 , λ 1 and λ 2 , respectively. Consider the class with λ 0 fixed.…”

Section: Introductionmentioning

confidence: 99%

“…In the nonparametric case, let X 0 , X 1 , X 2 be independent random variables with distribution functions G, F 1 and F 2 , density functions g, f 1 and f 2 , survival functionsḠ,F 1 and F 2 and failure rate functions r G , r F 1 and r F 2 , respectively (note r G (x) = g(x)/Ḡ(x).) Then Bagai and Prakasa Rao (1992) showed that when T, δ are observable, then in the class of distributions with X 0 fixed, individual distributions F 1 and F 2 are not identifiable but the ratio of failure rates H defined by…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On a deconvolution problem under competing risks

2016

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Bagai and Prakasa Rao (1992) considered a competing risks model with two dependent risks. The two risks are initially independent but dependence arises because of the additive effect of an independent risk on the two initially independent risks. They showed that the ratio of failure rates are identifiable in the nonparametric set up. In this paper, we consider it as a measurement error/deconvolution problem and suggest a nonparametric kernel type estimator for the ratio of two failure rates. The local error properties of the proposed estimator are studied. Simulation studies show the efficacy of the proposed estimator.

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Section: Examplementioning

confidence: 99%

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On a deconvolution problem under competing risks

2016

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Removing Cancer when it is Correlated with other Causes of Death

Carrière

1995

Biometrical J

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This paper presents an identifiability theorem in the theory of dependent competing risks and it applies the result by examining the effect of removing cancer from the United States population when cancer is correlated with the other causes of death. The paper shows how dependence can be modeled with copula functions and it shows that calculating the survival probabilities after cancer is removed is equivalent to solving a system of nonlinear differential equations.

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Assessing the Impact of Preventive Maintenance Based on Censored Data

Bedford

2004

Quality & Reliability Eng

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Recent work in the field of competing risks enables us to start an assessment of the impact of preventive maintenance on the failure characteristics of a piece of equipment. Competing risk is the term given when more than one factor conspires to take a piece of equipment out of service. A simple example of this is given by preventive maintenance and failure. Each could occur to a piece of equipment but only one actually can. The preventive maintenance time may censor the unobserved latent failure time, thus ensuring that the statistical analysis of the failure times is made more difficult. Maintenance optimization models require knowledge of the underlying failure distribution. The Kaplan-Meier estimator (and other similar techniques) is commonly used to remove the effect of the censoring variable on the estimate of the distribution of the variable of interest. When the censoring variable is preventative maintenance, however, it is most unlikely that the assumptions of the Kaplan-Meier estimator (independence between the latent failure and preventive maintenance times) are valid. In this paper we give an overview of some of the different methods which have recently emerged in this area. These make different assumptions about the relation between PM and failure to allow the PM censoring to be 'removed'. Potentially, these methods would allow us to look at changing maintenance strategies. Although they are in the early stages of development they do already allow us to quantify the effect of some changes.

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Analysis of Survival Data with Two Dependent Competing Risks

Cited by 4 publications

References 22 publications

On a deconvolution problem under competing risks

On a deconvolution problem under competing risks

Removing Cancer when it is Correlated with other Causes of Death

Assessing the Impact of Preventive Maintenance Based on Censored Data

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