A nonidentifiability aspect of the problem of competing risks.

Tsiatis, Anastasios A.

doi:10.1073/pnas.72.1.20

Cited by 747 publications

(436 citation statements)

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“…As recently pointed out by Tsiatis (1) and Peterson (2), serious errors can be made in estimating the (potential) survival functions in the competing risks problem if the risks are assumed to be independent when in fact they are not. Furthermore, there is no way of knowing from the data in the competing risks problem whether or not an error is being made, since the data contain no information on whether or not the risks are independent.…”

Section: Introductionmentioning

confidence: 99%

Bounds for a joint distribution function with fixed sub-distribution functions: Application to competing risks

Peterson

1976

Proc. Natl. Acad. Sci. U.S.A.

217

120

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This paper gives sharp bounds for the joint survival function G(ti, t2,. . . ,t.) -X1 > tb, X2 > t2,. . . ,Xr > tr), and for the marginal survival functions Sjt) = X > t), j = 1,2,.. . ,r, when the sub-survival functions S;(t)= AX >,=mn=1,2.rXk) are fixed. Theorem 1 gives the bounds for r = 2, and Theorem 2 gives the bounds for general r. Theorem 3 applies the result to the competing risks problem, and presents empirical bounds based on the observations. Finally, an example illustrates the bounds.

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Section: Introductionmentioning

confidence: 99%

Bounds for a joint distribution function with fixed sub-distribution functions: Application to competing risks

Peterson

1976

Proc. Natl. Acad. Sci. U.S.A.

217

120

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“…The cohort-level covariateconditioned risk event-time marginals are therefore given by p(t r |z) = i,zi=z h i r (t)e − t 0 ds h i r (s) / i,zi=z 1, and can be used to develop expressions for the marginal survival functions and hazard rates 1 .…”

Section: Separating Direct From Indirect Associations and Quantifyingmentioning

confidence: 99%

“…alternative parametrisations [28,29], application to the cumulative incidence of non-primary risks [30], and the inclusion of frailty factors [31]. Other authors have focused on identifying which mathematical constraints need to be imposed on multi-risk survival analysis models in order to circumvent the identifiability problem of [1], and infer the joint event-time distribution unambiguously from survival data e.g. [32,33,34].…”

Section: Introductionmentioning

confidence: 99%

A latent class model for competing risks

et al. 2017

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Survival data analysis becomes complex when the proportional hazards assumption is violated at population level, or when crude hazard rates are no longer estimators of marginal ones. We develop a Bayesian survival analysis method to deal with these situations, based on assuming that the complexities are induced by latent cohort or disease heterogeneity that is not captured by covariates, and that proportional hazards hold at the level of individuals. This leads to a description from which risk-specific marginal hazard rates and survival functions are fully accessible, 'decontaminated' of the effects of informative censoring, and which includes Cox, random effects and latent class models as special cases. Simulated data confirm that our approach can map a cohort's substructure, and remove heterogeneity-induced informative censoring effects. Application to data from the ULSAM cohort leads to plausible alternative explanations for previous counter-intuitive inferences on prostate cancer. The importance of managing cardiovascular disease as a comorbidity in women diagnosed with breast cancer is suggested on application to data from the AMORIS study.

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“…As shown by Tsiatis (1975), independence of failure times and censoring times is not testable in the usual data structures. Without that assumption, marginal distributions are not identifiable.…”

Section: Specific Modelsmentioning

confidence: 99%

Diagnostics Cannot Have Much Power Against General Alternatives

Freedman¹,

Collier²,

Sekhon³

et al. 2009

Statistical Models and Causal Inference

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Model diagnostics are shown to have little power unless alternative hypotheses can be narrowly defined. For example, independence of observations cannot be tested against general forms of dependence. Thus, the basic assumptions in regression models cannot be inferred from the data. Equally, the proportionality assumption in proportional-hazards models is not testable. Specification error is a primary source of uncertainty in forecasting, and this uncertainty will be difficult to resolve without external calibration. Model-based causal inference is even more problematic.

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A nonidentifiability aspect of the problem of competing risks.

Cited by 747 publications

References 1 publication

Bounds for a joint distribution function with fixed sub-distribution functions: Application to competing risks

Bounds for a joint distribution function with fixed sub-distribution functions: Application to competing risks

A latent class model for competing risks

Diagnostics Cannot Have Much Power Against General Alternatives

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