RESUMO
The Non-Informative Nuisance Parameter Principle concerns the problem of how inferences about a parameter of interest should be made in the presence of nuisance parameters. The principle is examined in the context of the hypothesis testing problem. We prove that the mixed test obeys the principle for discrete sample spaces. We also show how adherence of the mixed test to the principle can make performance of the test much easier. These findings are illustrated with new solutions to well-known problems of testing hypotheses for count data.
RESUMO
To derive a latent trait (for instance ability) in a computer adaptive testing (CAT) framework, the obtained results from a model must have a direct relationship to the examinees' response to a set of items presented. The set of items is previously calibrated to decide which item to present to the examinee in the next evaluation question. Some useful models are more naturally based on conditional probability in order to involve previously obtained hits/misses. In this paper, we integrate an experimental part, obtaining the information related to the examinee's academic performance, with a theoretical contribution of maximum entropy. Some academic performance index functions are built to support the experimental part and then explain under what conditions one can use constrained prior distributions. Additionally, we highlight that heuristic prior distributions might not properly work in all likely cases, and when to use personalized prior distributions instead. Finally, the inclusion of the performance index functions, arising from current experimental studies and historical records, are integrated into a theoretical part based on entropy maximization and its relationship with a CAT process.
RESUMO
We propose a new survival model for lifetime data in the presence of surviving fraction and obtain some of its properties. Its genesis is based on extensions of the promotion time cure model, where an extra parameter controls the heterogeneity or dependence of an unobserved number of lifetimes. We construct a regression model to evaluate the effects of covariates in the cured fraction. We discuss inference aspects for the proposed model in a classical approach, where some maximum likelihood tools are explored. Further, an expectation maximization algorithm is developed to calculate the maximum likelihood estimates of the model parameters. We also perform an empirical study of the likelihood ratio test in order to compare the promotion time cure and the proposed models. We illustrate the usefulness of the new model by means of a colorectal cancer data set.
Assuntos
Neoplasias Colorretais/mortalidade , Análise de Sobrevida , Algoritmos , Neoplasias Colorretais/terapia , Humanos , Funções Verossimilhança , Modelos Estatísticos , Estados Unidos/epidemiologiaRESUMO
The postmastectomy survival rates are often based on previous outcomes of large numbers of women who had a disease, but they do not accurately predict what will happen in any particular patient's case. Pathologic explanatory variables such as disease multifocality, tumor size, tumor grade, lymphovascular invasion, and enhanced lymph node staining are prognostically significant to predict these survival rates. We propose a new cure rate survival regression model for predicting breast carcinoma survival in women who underwent mastectomy. We assume that the unknown number of competing causes that can influence the survival time is given by a power series distribution and that the time of the tumor cells left active after the mastectomy for metastasizing follows the beta Weibull distribution. The new compounding regression model includes as special cases several well-known cure rate models discussed in the literature. The model parameters are estimated by maximum likelihood. Further, for different parameter settings, sample sizes, and censoring percentages, some simulations are performed. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess local influences. The potentiality of the new regression model to predict accurately breast carcinoma mortality is illustrated by means of real data.