Choosing between Cox proportional hazards and logistic models for interval-censored data via bootstrap

This work develops a new methodology in order to discriminate models for interval-censored data based on bootstrap residual simulation by observing the deviance difference from one model in relation to another, according to Hinde (1992). Generally, this sort of data can generate a large number of tied observations and, in this case, survival time can be regarded as discrete. Therefore, the Cox proportional hazards model for grouped data (Prentice & Gloeckler, 1978) and the logistic model (Lawless, 1982) can befitted by means of generalized linear models. Whitehead (1989) considered censoring to be an indicative variable with a binomial distribution and fitted the Cox proportional hazards model using complementary log-log as a link function. In addition, a logistic model can be fitted using logit as a link function. The proposed methodology arises as an alternative to the score tests developed by Colosimo et al. (2000), where such models can be obtained for discrete binary data as particular cases from the Aranda-Ordaz distribution asymmetric family. These tests are thus developed with a basis on link functions to generate such a fit. The example that motivates this study was the dataset from an experiment carried out on a flax cultivar planted on four substrata susceptible to the pathogen Fusarium oxysoprum. The response variable, which is the time until blighting, was observed in intervals during 52 days. The results were compared with the model fit and the AIC values.

Integrable aspects of the scaling q-state Potts models I: bound states and bootstrap closure

We discuss the q-state Potts models for q less than or equal to 4, in the scaling regimes close to their critical or tricritical points. Starting from the kink S-matrix elements proposed by Chim and Zamolodchikov, the bootstrap is closed for the scaling regions of all critical points, and for the tricritical points when 4 > q greater than or equal to 2. We also note a curious appearance of the extended last line of Freudenthal's magic square in connection with the Potts models. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Estimation of population profiles of two strains of the fly Megaselia scalaris (Diptera: Phoridae) by bootstrap simulation

A partir de perfis populacionais experimentais de linhagens do díptero forídeo Megaselia scalaris, foi determinado o número mínimo de perfis amostrais que devem ser repetidos, via processo de simulação bootstrap, para se ter uma estimativa confiável do perfil médio populacional e apresentar estimativas do erro-padrão como medida da precisão das simulações realizadas. Os dados originais são provenientes de populações experimentais fundadas com as linhagens SR e R4, com três réplicas cada, e que foram mantidas por 33 semanas pela técnica da transferência seriada em câmara de temperatura constante (25 ± 1,0ºC). A variável usada foi tamanho populacional e o modelo adotado para cada perfíl foi o de um processo estocástico estacionário. Por meio das simulações, os perfis de três populações experimentais foram amplificados, determinando-se, dessa forma, o tamanho mínimo de amostra. Fixado o tamanho de amostra, simulações bootstrap foram realizadas para construção de intervalos de confiança e comparação dos perfis médios populacionais das duas linhagens. Os resultados mostram que com o tamanho de amostra igual a 50 inicia-se o processo de estabilização dos valores médios.

Orthogonal projections and bootstrap resampling procedures in the study of infraspecific variation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Bootstrap confidence regions for canonical variates: Application to studies of evolutionary differentiation

Theory recently developed to construct confidence regions based on the parametric bootstrap is applied to add inferential information to graphical displays of sample centroids in canonical variate analysis. Problems of morphometric differentiation among subspecies and species are addressed using numerical resampling procedures.

Métodos de bootstrap e aplicações em problemas biológicos

Pós-graduação em Matemática Universitária - IGCE

Precision of distances and ordering of microsatellite markers in consensus linkage maps of chromosomes 1, 3 and 4 from two reciprocal chicken populations using bootstrap sampling

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Bootstrap confidence intervals for industrial recurrent event data

Industrial recurrent event data where an event of interest can be observed more than once in a single sample unit are presented in several areas, such as engineering, manufacturing and industrial reliability. Such type of data provide information about the number of events, time to their occurrence and also their costs. Nelson (1995) presents a methodology to obtain asymptotic confidence intervals for the cost and the number of cumulative recurrent events. Although this is a standard procedure, it can not perform well in some situations, in particular when the sample size available is small. In this context, computer-intensive methods such as bootstrap can be used to construct confidence intervals. In this paper, we propose a technique based on the bootstrap method to have interval estimates for the cost and the number of cumulative events. One of the advantages of the proposed methodology is the possibility for its application in several areas and its easy computational implementation. In addition, it can be a better alternative than asymptotic-based methods to calculate confidence intervals, according to some Monte Carlo simulations. An example from the engineering area illustrates the methodology.

L'utilizzo del metodo Bootstrap nella statistica inferenziale

In questo lavoro viene introdotto il metodo Bootstrap, sviluppato a partire dal 1979 da Bradley Efron. Il Bootstrap è una tecnica statistica di ricampionamento basata su calcoli informatici, e quindi definita anche computer-intensive. In particolare vengono analizzati i vantaggi e gli svantaggi di tale metodo tramite esempi con set di dati reali implementati tramite il software statistico R. Tali analisi vertono su due tra i principali utilizzi del Bootstrap, la stima puntuale e la costruzione di intervalli di confidenza, basati entrambi sulla possibilità di approssimare la distribuzione campionaria di un qualsiasi stimatore, a prescindere dalla complessità di calcolo.

A Bootstrap Test for the Probability of Ruin in the Compound Poisson Risk Process

In this article we propose a bootstrap test for the probability of ruin in the compound Poisson risk process. We adopt the P-value approach, which leads to a more complete assessment of the underlying risk than the probability of ruin alone. We provide second-order accurate P-values for this testing problem and consider both parametric and nonparametric estimators of the individual claim amount distribution. Simulation studies show that the suggested bootstrap P-values are very accurate and outperform their analogues based on the asymptotic normal approximation.

POOR PERFORMANCE OF BOOTSTRAP CONFIDENCE INTERVALS FOR THE LOCATION OF A QUANTITATIVE TRAIT LOUCS

The aim of many genetic studies is to locate the genomic regions (called quantitative trait loci, QTLs) that contribute to variation in a quantitative trait (such as body weight). Confidence intervals for the locations of QTLs are particularly important for the design of further experiments to identify the gene or genes responsible for the effect. Likelihood support intervals are the most widely used method to obtain confidence intervals for QTL location, but the non-parametric bootstrap has also been recommended. Through extensive computer simulation, we show that bootstrap confidence intervals are poorly behaved and so should not be used in this context. The profile likelihood (or LOD curve) for QTL location has a tendency to peak at genetic markers, and so the distribution of the maximum likelihood estimate (MLE) of QTL location has the unusual feature of point masses at genetic markers; this contributes to the poor behavior of the bootstrap. Likelihood support intervals and approximate Bayes credible intervals, on the other hand, are shown to behave appropriately.