Estimation of the shape and scale parameters of Pareto distribution using ranked set sampling

In the current paper, the estimation of the shape and location parameters α and c, respectively, of the Pareto distribution will be considered in cases when c is known and when both are unknown. Simple random sampling (SRS) and ranked set sampling (RSS) will be used, and several traditional and ad hoc estimators will be considered. In addition, the estimators of α, when c is known using an RSS version based on the order statistic that maximizes the Fisher information for a fixed set size, will be considered. These estimators will be compared in terms of their biases and mean square errors. The estimators based on RSS can be real competitors against those based on SRS.     

A generalized linear mixed model for longitudinal binary data with a marginal logit link function

Longitudinal studies of a binary outcome are common in the health, social, and behavioral sciences. In general, a feature of random effects logistic regression models for longitudinal binary data is that the marginal functional form, when integrated over the distribution of the random effects, is no longer of logistic form. Recently, Wang and Louis (2003) proposed a random intercept model in the clustered binary data setting where the marginal model has a logistic form. An acknowledged limitation of their model is that it allows only a single random effect that varies from cluster to cluster. In this paper, we propose a modification of their model to handle longitudinal data, allowing separate, but correlated, random intercepts at each measurement occasion. The proposed model allows for a flexible correlation structure among the random intercepts, where the correlations can be interpreted in terms of Kendall's τ. For example, the marginal correlations among the repeated binary outcomes can decline with increasing time separation, while the model retains the property of having matching conditional and marginal logit link functions. Finally, the proposed method is used to analyze data from a longitudinal study designed to monitor cardiac abnormalities in children born to HIV-infected women.     

Application of Bayesian analyses to doubly randomized delayed start,matched control designs to demonstrate disease modification

Disease modification is a primary therapeutic aim when developing treatments for most chronic progressive diseases. The best treatments do not simply affect disease symptoms but fundamentally improve disease course by slowing, halting, or reversing disease progression. One of many challenges for establishing disease modification relates to the identification of adequate analytic tools to show differences in a disease course following intervention. Traditional approaches rely on the comparisons of slopes or noninferiority margins. However, it has proven difficult to conclusively demonstrate disease modification using such approaches. To address these challenges, we propose a novel adaptation of the delayed start study design that incorporates posterior probabilities identified by hierarchical Bayesian inference approaches to establish evidence for disease modification. Our models compare the size of treatment differences at the end of the delayed start period with those at the end of the early start period. Simulations that compare several models are provided. These include general linear models, repeated measures models, spline models, and model averaging. Our work supports the superiority of model averaging for accurately characterizing complex data that arise in real world applications. This novel approach has been applied to the design of an ongoing, doubly randomized, matched control study that aims to show disease modification in young persons with schizophrenia (the Disease Recovery Evaluation and Modification (DREaM) study). The application of this Bayesian methodology to the DREaM study highlights the value of this approach and demonstrates many practical challenges that must be addressed when implementing this methodology in a real world trial.     

Incomplete covariates in the Cox model with applications to biological marker data

A common occurrence in clinical trials with a survival end point is missing covariate data. With ignorably missing covariate data, Lipsitz and Ibrahim proposed a set of estimating equations to estimate the parameters of Cox's proportional hazards model. They proposed to obtain parameter estimates via a Monte Carlo EM algorithm. We extend those results to non-ignorably missing covariate data. We present a clinical trials example with three partially observed laboratory markers which are used as covariates to predict survival.