Abstract: The present article discusses and compares multiple testing procedures (MTPs) for controlling the family wise error rate. Machekano and Hubbard (2006) have proposed empirical Bayes approach that is a resampling based multiple testing procedure asymptotically controlling the familywise error rate. In this paper we provide some additional work on their procedure, and we develop resampling based step-down procedure asymptotically controlling the familywise error rate for testing the families of one-sided hypotheses. We apply these procedures for making successive comparisons between the treatment effects under a simple-order assumption. For example, the treatment means may be a sequences of increasing dose levels of a drug. Using simulations, we demonstrate that the proposed step-down procedure is less conservative than the Machekano and Hubbard’s procedure. The application of the procedure is illustrated with an example.
Abstract: Response variables that are scored as counts, for example, number of mastitis cases in dairy cattle, often arise in quantitative genetic analysis. When the number of zeros exceeds the amount expected such as under the Poisson density, the zero-inflated Poisson (ZIP) model is more appropriate. In using the ZIP model in animal breeding studies, it is necessary to accommodate genetic and environmental covariances. For that, this study proposes to model the mixture and Poisson parameters hierarchically, each as a function of two random effects, representing the genetic and environmental sources of variability, respectively. The genetic random effects are allowed to be correlated, leading to a correlation within and between clusters. The environmental effects are introduced by independent residual terms, accounting for overdispersion above that caused by extra-zeros. In addition, an inter correlation structure between random genetic effects affecting mixture and Poisson parameters is used to infer pleiotropy, an expression of the extent to which these parameters are influenced by common genes. The methods described here are illustrated with data on number of mastitis cases from Norwegian Red cows. Bayesian analysis yields posterior distributions useful for studying environmental and genetic variability, as well as genetic correlation.
Abstract: Count data often have excess zeros in many clinical studies. These zeros usually represent “disease-free state”. Although disease (event) free at the time, some of them might be at a high risk of having the putative outcome while others may be at low or no such risk. We postulate these zeros as a one of the two types, either as ‘low risk’ or as ‘high risk’ zeros for the disease process in question. Low risk zeros can arise due to the absence of risk factors for disease initiation/progression and/or due to very early stage of the disease. High risk zeros can arise due to the presence of significant risk factors for disease initiation/ progression or could be, in rare situations, due to misclassification, more specific diagnostic tests, or below the level of detection. We use zero inflated models which allows us to assume that zeros arise from one of the two separate latent processes-one giving low-risk zeros and the other high-risk zeros and subsequently propose a strategy to identify and classify them as such. To illustrate, we use data on the number of involved nodes in breast cancer patients. Of the 1152 patients studied, 38.8% were node- negative (zeros). The model predicted that about a third (11.4%) of negative nodes are “high risk” and the remaining (27.4%) are at “low risk” of nodal positivity. Posterior probability based classification was more appropriate compared to other methods. Our approach indicates that some node negative patients may be re-assessed for their diagnosis about nodal positivity and/or for future clinical management of their disease. The approach developed here is applicable to any scenario where the disease or outcome can be characterized by count-data.
An extension of truncated Poisson distribution having two parameters for a group of two types of population is derived and named as Bounded Poisson (BP) distribution. To estimate the parameters, method of moment has been employed. To check the suitability and applicability of the model it has been applied on real data set on human fertility derived from the third round of National Family Health Survey conducted in 2005-06 in Uttar Pradesh, India. Proposed model provides a good fitting to the data under consideration.
A new four-parameter lifetime distribution named as the power Lomax Poisson is introduced and studied. The subject distribution is obtained by combining the power Lomax and Poisson distributions. Structural properties of the power Lomax Poisson model are implemented. Estimation of the model parameters are performed using the maximum likelihood, least squares and weighted least squares techniques. An intensive simulation study is performed for evaluating the performance of different estimators based on their relative biases, standard errors and mean square errors. Eventually, the superiority of the new compounding distribution over some existing distribution is illustrated by means of two real data sets. The results showed the fact that, the suggested model can produce better fits than some well-known distributions.