ABSTRACT
In this article, we discuss an extension of the classical negative binomial cure rate model with piecewise exponential distribution of the time to event for concurrent causes, which enables the modeling of monotonic and non-monotonic hazard functions (ie, the shape of the hazard function is not assumed as in traditional parametric models). This approach produces a flexible cure rate model, depending on the choice of time partition. We discuss local influence on this negative binomial power piecewise exponential model. We report on Monte Carlo simulation studies and application of the model to real melanoma and leukemia datasets.
Subject(s)
Melanoma , Models, Statistical , Computer Simulation , Humans , Melanoma/diagnosis , Melanoma/therapy , Monte Carlo Method , Survival AnalysisABSTRACT
Dilobopterus costalimai Young is one of the most important pests in Brazilian citrus crop because it transmits Xylella fastidiosa, a bacterium that causes Citrus Variegated Chlorosis (CVC). We studied the spatial distribution of the insect, in order to develop a sampling plan to determine the proper moment to control the pest. D. costalimai was collected fortnightly, between 11/1999 until 4/2000, in a thirteen-year-old citrus orchard, where no insecticide was sprayed against this insect. Thirteen samples were performed in a grid of 100 yellow sticky traps (10 x 25 cm) in Taquaritinga County, Sao Paulo State. The variance of the sampling was higher than the mean in all samplings, with index ratio variance/mean (I) between 1.07 and 2.90, Morisita index between 1.07 and 1.57, k exponent of negative binomial distribution between 1.56 and 14.79. The chi-square goodness-of-fit test to Poisson distribution were not significant in seven samplings, however adjust to negative binomial were not significant in all samplings. The index b of Taylor´s Power Law was 1.3054, thus showing an aggregated distribution for this species in the field.
Dilobopterus costalimai Young é considerada uma das mais importantes pragas na citricultura brasileira por ser vetora de Xylella fastidiosa, bactéria causadora da doença Clorose Variegada dos Citros (CVC). Neste trabalho estudou-se a distribuição espacial do inseto com o objetivo de desenvolver um plano de amostragem para determinar o momento de controlar a praga. Foram feitas amostragens quinzenais de D. costalimai em um pomar de laranja-doce de treze anos de idade sem aplicação de inseticidas para controle desse inseto, entre 11/1999 e 4/2000. Treze amostragens foram realizadas em 100 pontos, utilizando-se armadilhas amarelas adesivas (10 x 25 cm), em Taquaritinga, estado de São Paulo. A variância amostral foi superior à média em todas as amostragens, com índice razão variância/média (I) entre 1,07 e 2,90, índice de Morisita entre 1,07 e 1,57, expoente k da distribuição binomial negativa variando de 1,56 a 14,79. Os testes de qui-quadrado de ajuste à distribuição de Poisson não foram significativos em sete amostragens, enquanto os testes de ajuste à distribuição binomial negativa não foram significativos em todas as amostragens. O coeficiente b da lei de potência de Taylor foi igual a 1,3054 mostrando que a praga se distribui de forma agregada no campo.
