Kernel density estimation with doubly truncated data

In some applications with astronomical and survival data, doubly truncated data are sometimes encountered. In this work we introduce kernel-type density estimation for a random variable which is sampled under random double truncation. Two different estimators are considered. As usual, the estimators are defined as a convolution between a kernel function and an estimator of the cumulative distribution function, which may be the NPMLE [2] or a semiparametric estimator [9]. Asymptotic properties of the introduced estimators are explored. Their finite sample behaviour is investigated through simulations. Real data illustration is included.Fundação para a Ciência e a Tecnologia (FCT)Spanish Ministerio de Ciencia e Innovació

DTDA: An R Package to Analyze Randomly Truncated Data

In this paper, the R package DTDA for analyzing truncated data is described. This package contains tools for performing three different but related algorithms to compute the nonparametric maximum likelihood estimator of the survival function in the presence of random truncation. More precisely, the package implements the algorithms proposed by Efron and Petrosian (1999) and Shen (2008), for analyzing randomly one-sided and two-sided (i.e., doubly) truncated data. These algorithms and some recent extensions are briefly reviewed. Two real data sets are used to show how DTDA package works in practice.

Estimation of Transition Probabilities for the Illness-Death Model: Package TP.idm

In this paper the R package TP.idm to compute an empirical transition probability matrix for the illness-death model is introduced. This package implements a novel nonparametric estimator which is particularly well suited for non-Markov processes observed under right censoring. Variance estimates and confidence limits are also implemented in the package

DTDA: An R Package to Analyze Randomly Truncated Data

In this paper, the R package DTDA for analyzing truncated data is described. This package contains tools for performing three different but related algorithms to compute the nonparametric maximum likelihood estimator of the survival function in the presence of random truncation. More precisely, the package implements the algorithms proposed by Efron and Petrosian (1999) and Shen (2008), for analyzing randomly one-sided and two-sided (i.e., doubly) truncated data. These algorithms and some recent extensions are briefly reviewed. Two real data sets are used to show how DTDA package works in practice

Nonparametric location-scale models for censored successive survival times

Let (T1,T2) be gap times corresponding to two consecutive events,which are observed subject to (univariate) random right-censoring.The censoring variable corresponding to the second gap time T2 will in general depend on this gap time. Suppose the vector (T1,T2) satisfies the non parametric location-scale regression model T2=m(T1)+σ(T1)ɛ, where the functions m and σ are ‘smooth’, and ɛ is independent of T1. The aim of this paper is two fold. First, we propose a nonparametric estimator of the distribution of the error variable under this model. This problem differs from others considered in the recent related literature in that the censoring acts not only on the response but also on the covariate, having no obvious solution. On the basis of the idea of transfer of tail information (Van Keilegom and Akritas,1999), we then use the proposed estimator of the error distribution to introduce non parametric estimators for important targets such as: (a) the conditional distribution of T2 given T1; (b) the bivariate distribution of the gap times; and (c) the so-called transition probabilities. The asymptotic properties of these estimators are obtained. We also illustrate through simulations, that the new estimators based on the location-scale model may be have much better than existing ones.Ingrid Van Keilegom's research was financially supported by IAP research network P6/03 of the Belgian Government (Belgian Science Policy), and by the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC Grant agreement No. 203650. Jacob de Una-Alvarez acknowledges financial support from the project MTM2008-03129 of the Spanish Ministerio de Ciencia e Innovacion and also from the project PGIDIT07PXIB300191PR of the Xunta de Galicia. Luis F. Meira-Machado acknowledges financial support by Grant PTDC/MAT/104879/2008 (FEDER support included) of the Portuguese Ministry of Science, Technology and Higher Education and also from the project MTM2008-01603 of the Spanish Ministerio de Educacion y Ciencia

Alternatives to the Cox model in multi-state models

The introduction of time-dependent covariates in the survival process can make the patients survival change from one time point to the next as the values of the covariate change. A popular choice for the analysis of this data is the timedependent Cox regression model. In the present work we present multi-state models as an alternative for the analysis of such data

Nonparametric estimation of conditional transition probabilities in a non-Markov illness-death model

One important goal in multi-state modeling is the estimation of transition probabilities. In longitudinal medical studies these quantities are particularly of interest since they allow for long-term predictions of the process. In recent years signi ficant contributions have been made regarding this topic. However, most of the approaches assume independent censoring and do not account for the influence of covariates. The goal of the paper is to introduce feasible estimation methods for the transition probabilities in an illness-death model conditionally on current or past covariate measures. All approaches are evaluated through a simulation study, leading to a comparison of two di erent estimators. The proposed methods are illustrated using real a colon cancer data set.This research was nanced by FEDER Funds through Programa Operacional Factores de Competitividade COMPETE and by Portuguese Funds through FCT - Funda ção para a Cência e a Tecnologia, within Projects Est-C/MAT/UI0013/2011 and PTDC/MAT/104879/2008. We also acknowledge nancial support from the project Grants MTM2008-03129 and MTM2011-23204 (FEDER support included) of the Spanish Ministerio de Ciencia e Innovaci on and 10PXIB300068PR of the Xunta de Galicia. Partial support from a grant from the US National Security Agency (H98230-11-1-0168) is greatly appreciated