Asymptotic Properties of Aalen-Johansen Integrals for Competing Risks Data

Suzukawa, Akio

doi:10.14490/jjss.32.77

Cited by 7 publications

(13 citation statements)

References 23 publications

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“…Large clinical data sets, such as the Surrogate Endpoints for Aggressive Lymphoma (SEAL) collaboration, now are becoming available to address such questions. 55 In terms of methodology, even though the Aalen-Johansen estimator is the canonical nonparametric maximum likelihood estimator for multistate models with guaranteed asymptotical convergence, [17][18][19]21,29,56 caution must be exercised because the size of the available data gets smaller. This is unlikely to pose an issue for subpopulation analyses (eg, patients using R-CHOP) but might be a concern for individualized predictions because each covariate defining an individual patient also shrinks the size of the available data that the estimator uses.…”

Section: Discussionmentioning

confidence: 99%

A population‐based multistate model for diffuse large B‐cell lymphoma–specific mortality in older patients

Çaǧlayan

Goldstein

Ayer

et al. 2019

Cancer

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BACKGROUND: Despite effective therapies, outcomes for diffuse large B-cell lymphoma (DLCBL) remain heterogeneous in older individuals due to comorbid diseases and variations in disease biology. METHODS: Using the Surveillance, Epidemiology, and End Results (SEER)-Medicare database, the authors conducted a multistate survival analysis of 11,780 patients with DLBCL who were aged ≥65 years at the time of diagnosis (2002–2009). Cox proportional hazards models were used to specify the impact of prognostic factors on overall survival and cause-specific deaths, and the Aalen-Johansen estimator was used to project the course of DLBCL over time with or without standard therapy with rituximab, cyclophosphamide, doxorubicin, vincristine, and prednisone (R-CHOP). RESULTS: Advanced age (hazard ratio [HR] for ages 71–75 years: 1.25; HR for ages 76–80 years: 1.46; HR for ages 81–85 years: 1.88; and HR for age ≥86 years: 2.26), DLBCL stage (HR for Ann Arbor stage II: 1.28; HR for stage III: 1.54; and HR for stage IV: 1.95), Charlson Comorbidity Index (CCI) ≥1 (HR for CCI of 1, 1.15; and HR for CCI >1, 1.37), and not being married (HR, 1.12) were associated with an increased risk of DLBCL-specific death. Being female (HR, 0.91) and of higher socioeconomic status (HR, 0.91) were associated with a lower risk of DLBCL-related mortality after therapy. For patients treated with R-CHOP (3610 patients), the risk of death due to DLBCL was 14.0% and 18.6%, respectively, at 2 and 5 years of treatment and plateaued afterward, confirming a 5-year “cure” point while receiving R-CHOP among older patients. CONCLUSIONS: Conducting a survival analysis over a large data set, the current study evaluated competing risks for death within a multistate modeling framework, and identified age, sex, and CCI as risk factors for DLBCL-specific and other causes of death.

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Section: Discussionmentioning

confidence: 99%

A population‐based multistate model for diffuse large B‐cell lymphoma–specific mortality in older patients

Çaǧlayan

Goldstein

Ayer

et al. 2019

Cancer

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“…We adopt a strategy developed by Stute in Stute (1995) in order to prove his Theorem 1.1, a wellknown result which states that a Kaplan-Meier integral of the form ş φ dF n can be approximated by a sum of independent terms. This idea is used in Suzukawa (2002) in the context of competing risks. We thus intend to approximate p γ n,k by the integral r γ n,k " ş φ n dF pkq n of some deterministic function φ n , with respect to the Aalen-Johansen estimator, and approximate this integral by the mean q γ n,k of independent variables U i,n (defined a few lines below).…”

Section: Proofsmentioning

confidence: 99%

“…Proceeding as in Stute (1995) or Suzukawa (2002), and using the fact that for any given function f we have ş f dH p1,kq n " 1 n ř n i"1 f pZ i qI ξi"k , we can write 1 n…”

Section: Proof Of Propositionmentioning

confidence: 99%

Extreme value statistics for censored data with heavy tails under competing risks

Worms

2018

Metrika

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This paper addresses the problem of estimating, in the presence of random censoring as well as competing risks, the extreme value index of the (sub)-distribution function associated to one particular cause, in the heavy-tail case. Asymptotic normality of the proposed estimator (which has the form of an Aalen-Johansen integral, and is the first estimator proposed in this context) is established. A small simulation study exhibits its performances for finite samples. Estimation of extreme quantiles of the cumulative incidence function is also addressed.

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“…Such extrapolation beyond a chosen point 6 H is necessary when time to the first event has non-negligible probability that X > H . Suzukawa [16] extended Stute's proof of strong consistency to CIFs of competing risks, and [3] extended Suzakawa's work to SMP network states. In SMPs, the number of individuals entering the state is a random variable.…”

Section: Kaplan-meier Integrals and Truncationmentioning

confidence: 99%

Semiparametric methods for multistate survival models in randomised trials

Hudson

Simes

et al. 2013

Statistics in Medicine

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Transform methods have proved effective for networks describing a progression of events. In semi-Markov networks, we calculated the transform of time to a terminating event from corresponding transforms of intermediate steps. Saddlepoint inversion then provided survival and hazard functions, which integrated, and fully utilised, the network data. However, the presence of censored data introduces significant difficulties for these methods. Many participants in controlled trials commonly remain event-free at study completion, a consequence of the limited period of follow-up specified in the trial design. Transforms are not estimable using nonparametric methods in states with survival truncated by end-of-study censoring. We propose the use of parametric models specifying residual survival to next event. As a simple approach to extrapolation with competing alternative states, we imposed a proportional incidence (constant relative hazard) assumption beyond the range of study data. No proportional hazards assumptions are necessary for inferences concerning time to endpoint; indeed, estimation of survival and hazard functions can proceed in a single study arm. We demonstrate feasibility and efficiency of transform inversion in a large randomised controlled trial of cholesterol-lowering therapy, the Long-Term Intervention with Pravastatin in Ischaemic Disease study. Transform inversion integrates information available in components of multistate models: estimates of transition probabilities and empirical survival distributions. As a by-product, it provides some ability to forecast survival and hazard functions forward, beyond the time horizon of available follow-up. Functionals of survival and hazard functions provide inference, which proves sharper than that of log-rank and related methods for survival comparisons ignoring intermediate events.

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Asymptotic Properties of Aalen-Johansen Integrals for Competing Risks Data

Cited by 7 publications

References 23 publications

A population‐based multistate model for diffuse large B‐cell lymphoma–specific mortality in older patients

A population‐based multistate model for diffuse large B‐cell lymphoma–specific mortality in older patients

Extreme value statistics for censored data with heavy tails under competing risks

Semiparametric methods for multistate survival models in randomised trials

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