Presmoothed Kaplan–Meier and Nelson–Aalen estimators

Cao, Ricardo; López-de-Ullibarri, Ignacio; Janssen, Paul; Veraverbeke, Noël

doi:10.1080/10485250410001713981

Cited by 33 publications

(45 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…When the asymptotically optimal bandwidth is used, the presmoothed estimators have smaller asymptotic variance and, therefore, a better performance in terms of mean squared error (MSE). This improvement is of second order in the estimation of S and Λ (Cao et al 2005), but may be of first order for the density function (Cao and Jácome 2004). The simulation studies confirm this gain in efficiency under moderate sample sizes.…”

Section: Introductionsupporting

confidence: 64%

“…An asymptotic representation and asymptotic distributional properties of Λ P b 1 can be found in Cao et al (2005). Some evidence of the beneficial effect of presmoothing is also provided in that reference.…”

Section: Hazard Function and Cumulative Hazard Functionmentioning

confidence: 99%

“…However, ϕ P b can be decomposed as a sum of independent and identically distributed (i.i.d.) variables plus a negligible term of lower order (see Cao et al 2005;Cao and López-de-Ullibarri 2007;Jácome and Cao 2007). Replacing ϕ P b in Equation 6 with this i.i.d.…”

Section: Plug-in Bandwidth Selectormentioning

confidence: 99%

“…Theorems 7 and 8 of Cao et al (2005) give expressions for the optimal pilot bandwidths g 1 and g 2 , in the sense of minimizing the asymptotic MSE of Q g 1 and A g 2 . These bandwidths depend on some unknown functions: p, H and their first four derivatives.…”

Section: Plug-in Bandwidthmentioning

confidence: 99%

“…The presmoothed approach is based on the NW estimator of p, and has been extensively studied in the literature in the estimation of S and Λ (Cao, López-de-Ullibarri, Janssen, and Veraverbeke 2005), the density f (Cao and Jácome 2004;Jácome and Cao 2007;Jácome, Gijbels, and Cao 2008), the hazard rate λ (Cao and López-de-Ullibarri 2007), and also the quantile function ) (for an illustration of the use of nonparametric regression estimators other than the NW smoother, see . Nonparametric kernel regression, as the NW estimator, does not requires preliminary specification of a parametric family.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

survPresmooth: AnRPackage for Presmoothed Estimation in Survival Analysis

López-de-Ullibarri¹,

Jácome²

2013

J. Stat. Soft.

Self Cite

View full text Add to dashboard Cite

The survPresmooth package for R implements nonparametric presmoothed estimators of the main functions studied in survival analysis (survival, density, hazard and cumulative hazard functions). Presmoothed versions of the classical nonparametric estimators have been shown to increase efficiency if the presmoothing bandwidth is suitably chosen. The survPresmooth package provides plug-in and bootstrap bandwidth selectors, also allowing the possibility of using fixed bandwidths.

show abstract

Section: Introductionsupporting

confidence: 64%

Section: Hazard Function and Cumulative Hazard Functionmentioning

confidence: 99%

Section: Plug-in Bandwidth Selectormentioning

confidence: 99%

Section: Plug-in Bandwidthmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

survPresmooth: AnRPackage for Presmoothed Estimation in Survival Analysis

López-de-Ullibarri¹,

Jácome²

2013

J. Stat. Soft.

Self Cite

View full text Add to dashboard Cite

show abstract

A semiparametric estimator of the bivariate distribution function for censored gap times

Uña‐Álvarez

Amorim

2011

Biom. J.

View full text Add to dashboard Cite

Let (T(1), T(2)) be gap times corresponding to two consecutive events, which are observed subject to random right-censoring. In this paper, a semiparametric estimator of the bivariate distribution function of (T(1), T(2)) and, more generally, of a functional E [φ(T(1),T(2))] is proposed. We assume that the probability of censoring for T(2) given the (possibly censored) gap times belongs to a parametric family of binary regression curves. We investigate the conditions under which the introduced estimator is consistent. We explore the finite sample behavior of the estimator and of its bootstrap standard error through simulations. The main conclusion of this paper is that the semiparametric estimator may be much more efficient than purely nonparametric methods. Real data illustration is included.

show abstract

Logrank‐type tests with presmoothing

Jácome

López-de-Ullibarri

2014

Biometrical J

View full text Add to dashboard Cite

The logrank test is the most popular choice for testing the equality of two survival distributions with time-to-event data. It is based on the comparison of the Nelson-Aalen estimates of the corresponding cumulative hazard functions. The improvements of the logrank test in the literature have been accomplished using weighted logrank tests, with the weight chosen appropriately to maximize power. Notwithstanding, power also depends on the efficiency of the estimation of the cumulative hazard function. The presmoothed estimator has been shown to be more efficient than the Nelson-Aalen estimator under some general assumptions. We introduce a new logrank-type test that, instead of the Nelson-Aalen estimator, is based on its presmoothed counterpart. An extensive simulation study has been conducted to compare the performance of this new test with the classical one. This study shows that the new test has the proper size under the null hypothesis, while improving the power over a wide range of alternatives. The new test is illustrated with several real data examples.

show abstract

Presmoothed Kaplan–Meier and Nelson–Aalen estimators

Cited by 33 publications

References 10 publications

survPresmooth: AnRPackage for Presmoothed Estimation in Survival Analysis

survPresmooth: AnRPackage for Presmoothed Estimation in Survival Analysis

A semiparametric estimator of the bivariate distribution function for censored gap times

Logrank‐type tests with presmoothing

Contact Info

Product

Resources

About