Comparison of the marginal hazard model and the sub-distribution hazard model for competing risks under an assumed copula

Emura, Takeshi; Shih, Jia-Han; Ha, Il Do; Wilke, Ralf A.

doi:10.1177/0962280219892295

Cited by 34 publications

(29 citation statements)

References 47 publications

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“…By definition ( 16), b i = β for all i and σ 2 b = 0. For other models than (16) this is not true. This observation forms the basis for estimation.…”

Section: Semiparametric Modelmentioning

confidence: 94%

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A single risk approach to the semiparametric copula competing risks model

Lo¹,

Wilke²

2022

Preprint

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A typical situation in competing risks analysis is that the researcher is only interested in a subset of risks. This paper considers a depending competing risks model with the distribution of one risk being a parametric or semi-parametric model, while the model for the other risks being unknown. Identifiability is shown for popular classes of parametric models and the semiparametric proportional hazards model. The identifiability of the parametric models does not require a covariate, while the semiparametric model requires at least one. Estimation approaches are suggested which are shown to be √ n-consistent. Applicability and attractive finite sample performance are demonstrated with the help of simulations and data examples.

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“…By definition ( 16), b i = β for all i and σ 2 b = 0. For other models than (16) this is not true. This observation forms the basis for estimation.…”

Section: Semiparametric Modelmentioning

confidence: 94%

“…The case of k > 1 is considered later. By evaluating (16) for two arbitrarily different values of z, say z 1 = z 2 , we define…”

Section: Semiparametric Modelmentioning

confidence: 99%

A single risk approach to the semiparametric copula competing risks model

Lo¹,

Wilke²

2022

Preprint

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“…This implies that the null holds for both the Cox model and the Fine and Gray sub-distribution hazard model, or equivalently, the true β = γ = 0. Under the alternative, the true values for δ, β, and γ are not necessarily equal 35 ; this is because δ represents the latent hazard ratio conditional on the frailty (latent with respect to the unobserved distribution of T 1,kj conditional on the frailty but marginalized over T 2,kj ), whereas β and γ represent the population-averaged cause-specific and sub-distribution hazard ratio (population-averaged due to marginalizing over the cluster-specific frailty). To address this complexity, we defined the truth for β and γ as the probability limits under which the respective estimating equations have mean zero.…”

Section: Parameter Configurationsmentioning

confidence: 99%

A comparison of analytical strategies for cluster randomized trials with survival outcomes in the presence of competing risks

Wang

et al. 2022

Stat Methods Med Res

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While statistical methods for analyzing cluster randomized trials with continuous and binary outcomes have been extensively studied and compared, little comparative evidence has been provided for analyzing cluster randomized trials with survival outcomes in the presence of competing risks. Motivated by the Strategies to Reduce Injuries and Develop Confidence in Elders trial, we carried out a simulation study to compare the operating characteristics of several existing population-averaged survival models, including the marginal Cox, marginal Fine and Gray, and marginal multi-state models. For each model, we found that adjusting for the intraclass correlations through the sandwich variance estimator effectively maintained the type I error rate when the number of clusters is large. With no more than 30 clusters, however, the sandwich variance estimator can exhibit notable negative bias, and a permutation test provides better control of type I error inflation. Under the alternative, the power for each model is differentially affected by two types of intraclass correlations—the within-individual and between-individual correlations. Furthermore, the marginal Fine and Gray model occasionally leads to higher power than the marginal Cox model or the marginal multi-state model, especially when the competing event rate is high. Finally, we provide an illustrative analysis of Strategies to Reduce Injuries and Develop Confidence in Elders trial using each analytical strategy considered.

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“…Moreover, these measures of treatment effect are rather difficult to interpret. A third approach is the Cox‐type proportional marginal hazards model, which requires the assumption that the joint distribution of the competing risks is identifiable (e.g., Emura, Shih, Ha, & Wilke, 2020). Other available methods for the analysis of competing risks data include the pseudo‐observation method (Andersen, Klein, & Rosthøj, 2003) and direct binomial regression (Scheike, Zhang, & Gerds, 2008), to name a few.…”

Section: Introductionmentioning

confidence: 99%

A new measure of treatment effect in clinical trials involving competing risks based on generalized pairwise comparisons

Cantagallo

Backer²,

Kiciński

et al. 2020

Biometrical J

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In survival analysis with competing risks, the treatment effect is typically expressed using cause‐specific or subdistribution hazard ratios, both relying on proportional hazards assumptions. This paper proposes a nonparametric approach to analyze competing risks data based on generalized pairwise comparisons (GPC). GPC estimate the net benefit, defined as the probability that a patient from the treatment group has a better outcome than a patient from the control group minus the probability of the opposite situation, by comparing all pairs of patients taking one patient from each group. GPC allow using clinically relevant thresholds and simultaneously analyzing multiple prioritized endpoints. We show that under proportional subdistribution hazards, the net benefit for competing risks settings can be expressed as a decreasing function of the subdistribution hazard ratio, taking a value 0 when the latter equals 1. We propose four net benefit estimators dealing differently with censoring. Among them, the Péron estimator uses the Aalen–Johansen estimator of the cumulative incidence functions to classify the pairs for which the patient with the best outcome could not be determined due to censoring. We use simulations to study the bias of these estimators and the size and power of the tests based on the net benefit. The Péron estimator was approximately unbiased when the sample size was large and the censoring distribution's support sufficiently wide. With one endpoint, our approach showed a comparable power to a proportional subdistribution hazards model even under proportional subdistribution hazards. An application of the methodology in oncology is provided.

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Comparison of the marginal hazard model and the sub-distribution hazard model for competing risks under an assumed copula

Cited by 34 publications

References 47 publications

A single risk approach to the semiparametric copula competing risks model

A single risk approach to the semiparametric copula competing risks model

A comparison of analytical strategies for cluster randomized trials with survival outcomes in the presence of competing risks

A new measure of treatment effect in clinical trials involving competing risks based on generalized pairwise comparisons

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