Median treatment effect in randomized trials

For two response variables y _t and y _c corresponding to two treatments for two policies) T and C , we wish to learn about quantiles of y _t− y _c from the marginal quantiles of y _t and y _c; only one of y _t and y _c is observed for an individual. We find that, in general, this is difficult for quantiles other than the median unless strong assumptions are imposed on how y _t is related to y _c. For the median, we present conditions under which the sign of the median treatment effect is identified.     

Model and design correspondence in finite population sampling

A correspondence rule is suggested for the choice of a sampling design when prior knowledge concerning a finite population is available. Designs satisfying the correspondence rule are discussed in the case of random permutations models. A general optimality theorem is given for strategies under such models. Approximate correspondences satisfied by systematic sampling and πps sampling are also indicated.     

Effects of correlation in modeling clustered binary data

A simulation study is conducted to determine the effects of varying correlation structures on two estimation procedures used to model clustered binary data; a parametric model, the beta-binomial, and a non-parametric model, the exchangeable binary. The simulations detected bias in estimation of the mean response parameter and the correlation parameter when assuming a parametric model. In addition it was found that variance parameters can be severely underestimated if the correlation structure is considered strictly a nuisance parameter.     

Almost nonparametric inference for repeated measures in mixture models

We consider ways to estimate the mixing proportions in a finite mixture distribution or to estimate the number of components of the mixture distribution without making parametric assumptions about the component distributions. We require a vector of observations on each subject. This vector is mapped into a vector of 0s and 1s and summed. The resulting distribution of sums can be modelled as a mixture of binomials. We then work with the binomial mixture. The efficiency and robustness of this method are compared with the strategy of assuming multivariate normal mixtures when, typically, the true underlying mixture distribution is different. It is shown that in many cases the approach based on simple binomial mixtures is superior.     

Bivariate prior distributions via branching exchangeable sequences

This paper provides a novel approach to constructing bivariate prior distributions. The idea is based on the notion of partial exchangeability. In particular, in a simple extension of the exchangeable sequence, we create two dependent exchangeable sequences via a branching mechanism. This implies the existence of a bivariate prior distribution.     

Improved inference for a linear mixed-effects model when the subpopulation effects are clustered

We provide Bayesian methodology to relax the assumption that all subpopulation effects in a linear mixed-effects model have, after adjustment for covariates, a common mean. We expand the model specification by assuming that the m subpopulation effects are allowed to cluster into d groups where the value of d, 1?d?m, and the composition of the d groups are unknown, a priori. Specifically, for each partition of the m effects into d groups we only assume that the subpopulation effects in each group are exchangeable and are independent across the groups. We show that failure to take account of this clustering, as with the customary method, will lead to serious errors in inference about the variances and subpopulation effects, but the proposed, expanded, model leads to appropriate inferences. The efficacy of the proposed method is evaluated by contrasting it with both the customary method and use of a Dirichlet process prior. We use data from small area estimation to illustrate our method.     

Permutational Multiple Testing Adjustments With Multivariate Multiple Group Data

We consider the multiple comparison problem where multiple outcomes are each compared among several different collections of groups in a multiple group setting. In this case there are several different types of hypotheses, with each specifying equality of the distributions of a single outcome over a different collection of groups. Each type of hypothesis requires a different permutational approach. We show that under a certain multivariate condition it is possible to use closure over all hypotheses, although intersection hypotheses are tested using Boole's inequality in conjunction with permutation distributions in some cases. Shortcut tests are then found so that the resulting testing procedure is easily performed. The error rate and power of the new method is compared to existing competitors through simulation of correlated data. An example is analyzed, consisting of multiple adverse events in a clinical trial.     

Construction of non-exchangeable bivariate distribution functions

A method is given for constructing bivariate distributions functions by means of the copula functions, and, hence, it is used for obtaining distribution functions that can describe the behaviour of non–exchangeable random vectors.     

Likelihood estimation for exchangeable multinomial data

In this article, maximum likelihood estimates of an exchangeable multinomial distribution using a parametric form to model the parameters as functions of covariates are derived. The non linearity of the exchangeable multinomial distribution and the parametric model make direct application of Newton Rahpson and Fisher's scoring algorithms computationally infeasible. Instead parameter estimates are obtained as solutions to an iterative weighted least-squares algorithm. A completely monotonic parametric form is proposed for defining the marginal probabilities that results in a valid probability model.