The wild bootstrap for multivariate Nelson–Aalen estimators

Bluhmki, Tobias; Dobler, Dennis; Beyersmann, Jan; Pauly, Markus

doi:10.1007/s10985-018-9423-x

Cited by 14 publications

(16 citation statements)

References 71 publications

(109 reference statements)

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“…In a way similar to Bluhmki et al (2016), one can show that p x W 1 ptqq tPr0,Ks is a martingale with respect to the filtration pF t q tPr0,Ks given by F t " σpξ i N 1i puq, N 1i pvq, Y i pvq : u P r0, ts, v P r0, Ks, i " 1, . .…”

Section: Aalen Estimatormentioning

confidence: 93%

“…The wild bootstrap is typically applied in the following way (see e.g. Lin 1997, Martinussen and Scheike 2006, Beyersmann et al 2013or Bluhmki et al 2016 for resampling more general counting process-based Nelson-Aalen estimators): First, the (independent) martingale increments dM 1i puq in the martingale representation of ? np p A 1´A1 q are replaced by independently weighted counting process increments, i.e., by ξ i dN 1i puq.…”

Section: Aalen Estimatormentioning

confidence: 99%

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A discontinuity adjustment for subdistribution function confidence bands applied to right-censored competing risks data

Dobler¹

2017

Electron. J. Statist.

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The wild bootstrap is the resampling method of choice in survival analytic applications. Theoretic justifications rely on the assumption of existing intensity functions which is equivalent to an exclusion of ties among the event times. However, such ties are omnipresent in practical studies. It turns out that the wild bootstrap should only be applied in a modified manner that corrects for altered limit variances and emerging dependencies. This again ensures the asymptotic exactness of inferential procedures. An analogous necessity is the use of the Greenwood-type variance estimator for Nelson-Aalen estimators which is particularly preferred in tied data regimes. All theoretic arguments are transferred to bootstrapping Aalen-Johansen estimators for cumulative incidence functions in competing risks. An extensive simulation study as well as an application to real competing risks data of male intensive care unit patients suffering from pneumonia illustrate the practicability of the proposed technique.where the last equality follows from the orthogonality of all involved single martingales. Inserting the above representation for the optional variation process yieldsIn a last step, we replace the unknown increments of the cumulative hazard function ∆A 1 puq with Nelson-Aalen increments ∆ p A 1 puq " Y puq´1∆N 1 puq and obtain the Greenwood-type variance estimator

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Section: Aalen Estimatormentioning

confidence: 93%

Section: Aalen Estimatormentioning

confidence: 99%

A discontinuity adjustment for subdistribution function confidence bands applied to right-censored competing risks data

Dobler¹

2017

Electron. J. Statist.

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“…A topic for future research is the application of image processing software, which has recently been applied in the context of survival analysis. 67,68 Our empirical procedure enables simulation studies plausibly mimicking complex real-world time-to-event data (see elsewhere for recent applications 74,75 ). This may also be relevant for sample size calculations, when historical data (without access to individual patient data) would be incorporated.…”

Section: Discussionmentioning

confidence: 99%

Bootstrapping complex time‐to‐event data without individual patient data, with a view toward time‐dependent exposures

Bluhmki¹,

Putter

Allignol

et al. 2019

Statistics in Medicine

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We consider nonparametric and semiparametric resampling of multistate event histories by simulating multistate trajectories from an empirical multivariate hazard measure. One advantage of our approach is that it does not necessarily require individual patient data, but may be based on published information. This is also attractive for both study planning and simulating realistic real‐world event history data in general. The concept extends to left‐truncation and right‐censoring mechanisms, nondegenerate initial distributions, and nonproportional as well as non‐Markov settings. A special focus is on its connection to simulating survival data with time‐dependent covariates. For the case of qualitative time‐dependent exposures, we demonstrate that our proposal gives a more natural interpretation of how such data evolve over the course of time than many of the competing approaches. The multistate perspective avoids any latent failure time structure and sampling spaces impossible in real life, whereas its parsimony follows the principle of Occam's razor. We also suggest empirical simulation as a novel bootstrap procedure to assess estimation uncertainty in the absence of individual patient data. This is not possible for established procedures such as Efron's bootstrap. A simulation study investigating the effect of liver functionality on survival in patients with liver cirrhosis serves as a proof of concept. Example code is provided.

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“…Resampling procedures usually provide a good estimation of the distribution of the process‐valued estimators of, for example, nonparametric cumulative hazard functions, even for small samples (Bluhmki et al ., 2019). We apply the wild bootstrap to construct Hall‐Wellner or equal precision confidence bands for the baseline function in the present context.…”

Section: Multiplier Resampling For Nested‐case Control Designsmentioning

confidence: 99%

Dynamic inference in general nested case‐control designs

Feifel¹,

Dobler

2020

Biometrics

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Nested case‐control designs are attractive in studies with a time‐to‐event endpoint if the outcome is rare or if interest lies in evaluating expensive covariates. The appeal is that these designs restrict to small subsets of all patients at risk just prior to the observed event times. Only these small subsets need to be evaluated. Typically, the controls are selected at random and methods for time‐simultaneous inference have been proposed in the literature. However, the martingale structure behind nested case‐control designs allows for more powerful and flexible non‐standard sampling designs. We exploit that structure to find simultaneous confidence bands based on wild bootstrap resampling procedures within this general class of designs. We show in a simulation study that the intended coverage probability is obtained for confidence bands for cumulative baseline hazard functions. We apply our methods to observational data about hospital‐acquired infections.

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The wild bootstrap for multivariate Nelson–Aalen estimators

Cited by 14 publications

References 71 publications

A discontinuity adjustment for subdistribution function confidence bands applied to right-censored competing risks data

A discontinuity adjustment for subdistribution function confidence bands applied to right-censored competing risks data

Bootstrapping complex time‐to‐event data without individual patient data, with a view toward time‐dependent exposures

Dynamic inference in general nested case‐control designs

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