Nonparametric estimation of the cumulative incidences of competing risks under double truncation

Uña‐Álvarez, Jacobo de

doi:10.1002/bimj.201800323

Cited by 10 publications

(2 citation statements)

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“…To be specific, the performance of the Pearson correlation coefficient, the weighted least squares estimator for the linear regression model, and the cumulative incidence functions for competing risks are investigated. See Mandel et al [14] for simulations of Cox regression with a doubly truncated response, and de Uña-Álvarez [5] for more on competing risks under double truncation.…”

Section: Simulation Studymentioning

confidence: 99%

Efron–Petrosian integrals for doubly truncated data with covariates: An asymptotic analysis

Uña‐Álvarez¹,

Keilegom²

2021

Bernoulli

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In survival analysis, epidemiology and related fields there exists an increasing interest in statistical methods for doubly truncated data. Double truncation appears with interval sampling and other sampling schemes, and refers to situations in which the target variable is subject to two (left and right) random observation limits. Doubly truncated data require specific corrections for the observational bias, and this affects a variety of settings including the estimation of marginal and multivariate distributions, regression problems, and multi-state models. In this work multivariate Efron-Petrosian integrals for doubly truncated data are introduced. These integrals naturally arise when the goal is the estimation of the mean of a general transformation which involves the doubly truncated variable and covariates. An asymptotic representation of the Efron-Petrosian integrals as a sum of i.i.d. terms is derived and, from this, consistency and distributional convergence are established. As a by-product, uniform i.i.d. representations for the marginal nonparametric maximum likelihood estimator and its corresponding weighting process are provided. Applications to correlation analysis, regression, and competing risks models are presented. A simulation study is reported too.

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Section: Simulation Studymentioning

confidence: 99%

Efron–Petrosian integrals for doubly truncated data with covariates: An asymptotic analysis

Uña‐Álvarez¹,

Keilegom²

2021

Bernoulli

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“…The interest in the random double truncation model has rapidly increased in the last years. Recent methods to handle doubly truncated outcomes include, among other topics, smoothing methods, 19,20 proportional hazards regression, 14,21 rank regression for linear models, 22 competing risks, 23 two-sample problems, 24 the estimation of a bivariate distribution, 2,25,26 or maximum likelihood theory for parametric models. 27,28 Formally testing for an ignorable sampling bias is important in all these settings with double truncation because, when there is no sampling bias, ordinary methods apply and the estimation variance can be reduced.…”

Section: Introductionmentioning

confidence: 99%

Testing for an ignorable sampling bias under random double truncation

Uña‐Álvarez

2023

Statistics in Medicine

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In clinical and epidemiological research doubly truncated data often appear. This is the case, for instance, when the data registry is formed by interval sampling. Double truncation generally induces a sampling bias on the target variable, so proper corrections of ordinary estimation and inference procedures must be used. Unfortunately, the nonparametric maximum likelihood estimator of a doubly truncated distribution has several drawbacks, like potential nonexistence and nonuniqueness issues, or large estimation variance. Interestingly, no correction for double truncation is needed when the sampling bias is ignorable, which may occur with interval sampling and other sampling designs. In such a case the ordinary empirical distribution function is a consistent and fully efficient estimator that generally brings remarkable variance improvements compared to the nonparametric maximum likelihood estimator. Thus, identification of such situations is critical for the simple and efficient estimation of the target distribution. In this article, we introduce for the first time formal testing procedures for the null hypothesis of ignorable sampling bias with doubly truncated data. The asymptotic properties of the proposed test statistic are investigated. A bootstrap algorithm to approximate the null distribution of the test in practice is introduced. The finite sample performance of the method is studied in simulated scenarios. Finally, applications to data on onset for childhood cancer and Parkinson's disease are given. Variance improvements in estimation are discussed and illustrated.

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2022

Wiley Series in Probability and Statistics

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Nonparametric estimation of the cumulative incidences of competing risks under double truncation

Cited by 10 publications

References 20 publications

Efron–Petrosian integrals for doubly truncated data with covariates: An asymptotic analysis

Efron–Petrosian integrals for doubly truncated data with covariates: An asymptotic analysis

Testing for an ignorable sampling bias under random double truncation

Packages and Functions in R

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