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The PLMIX package offers a comprehensive framework aimed at endowing the R statistical environment with some recent methodological advances in modelling and clustering partially ranked data. The us...

We propose the use of probability models for ranked data as a useful alternative to a quantitative data analysis to investigate the outcome of bioassay experiments, when the preliminary choice of an appropriate normalization method for the raw numerical responses is difficult or subject to criticism. We review standard distance-based and multistage ranking models and in this last context we propose an original generalization of the Plackett-Luce model to account for the order of the ranking elicitation process. The usefulness of the novel model is illustrated with its maximum likelihood estimation for a real data set. Specifically, we address the heterogeneous nature of experimental units via model-based clustering and detail the necessary steps for a successful likelihood maximization through a hybrid version of the Expectation-Maximization algorithm. The performance of the mixture model using the new distribution as mixture components is compared with those relative to alternative mixture models for random rankings. A discussion on the interpretation of the identified clusters and a comparison with more standard quantitative approaches are finally provided., (revised to properly include references)

The elicitation of an ordinal judgment on multiple alternatives is often required in many psychological and behavioral experiments to investigate preference/choice orientation of a specific population. The Plackett-Luce model is one of the most popular and frequently applied parametric distributions to analyze rankings of a finite set of items. The present work introduces a Bayesian finite mixture of Plackett-Luce models to account for unobserved sample heterogeneity of partially ranked data. We describe an efficient way to incorporate the latent group structure in the data augmentation approach and the derivation of existing maximum likelihood procedures as special instances of the proposed Bayesian method. Inference can be conducted with the combination of the Expectation-Maximization algorithm for maximum a posteriori estimation and the Gibbs sampling iterative procedure. We additionally investigate several Bayesian criteria for selecting the optimal mixture configuration and describe diagnostic tools for assessing the fitness of ranking distributions conditionally and unconditionally on the number of ranked items. The utility of the novel Bayesian parametric Plackett-Luce mixture for characterizing sample heterogeneity is illustrated with several applications to simulated and real preference ranked data. We compare our method with the frequentist approach and a Bayesian nonparametric mixture model both assuming the Plackett-Luce model as a mixture component. Our analysis on real datasets reveals the importance of an accurate diagnostic check for an appropriate in-depth understanding of the heterogenous nature of the partial ranking data.

Summary. Motivated by the absolute risk predictions required in medical decision making and patient counseling, we propose an approach for the combined analysis of case-control and prospective studies of disease risk factors. The approach is hierarchical to account for parameter heterogeneity among studies and among sampling units of the same study. It is based on modeling the retrospective distribution of the covariates given the disease outcome, a strategy that greatly simplifies both the combination of prospective and retrospective studies and the computation of Bayesian predictions in the hierarchical casecontrol context. Retrospective modeling differentiates our approach from most current strategies for inference on risk factors, which are based on the assumption of a specific prospective model. To ensure modeling flexibility, we propose using a mixture model for the retrospective distributions of the covariates. This leads to a general nonlinear regression family for the implied prospective likelihood. After introducing and motivating our proposal, we present simple results that highlight its relationship with existing approaches, develop Markov chain Monte Carlo methods for inference and prediction, and present an illustration using ovarian cancer data.

Peptide Microarray Immunoassay (PMI for brevity) is a novel technology that enables researchers to map a large number of proteomic measurements at a peptide level, providing information regarding the relationship between antibody response and clinical sensitivity. PMI studies aim at recognizing antigen-specific antibodies from serum samples and at detecting epitope regions of the protein antigen. PMI data present new challenges for statistical analysis mainly due to the structural dependence among peptides. A PMI is made of a complete library of consecutive peptides. They are synthesized by systematically shifting a window of a fixed number of amino acids through the finite sequence of amino acids of the antigen protein as ordered in the primary structure of the protein. This implies that consecutive peptides have a certain number of amino acids in common and hence are structurally dependent. We propose a new flexible Bayesian hierarchical model framework, which allows one to detect recognized peptides and bound epitope regions in a single framework, taking into account the structural dependence between peptides through a suitable latent Markov structure. The proposed model is illustrated using PMI data from a recent study about egg allergy. A simulation study shows that the proposed model is more powerful and robust in terms of epitope detection than simpler models overlooking some of the dependence structure. The Author 2011. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.2011 © The Author 2011. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Motivated by a real data set deriving from a study on the genetic determinants of the behavior of Mycobacterium tuberculosis (MTB) hosted in macrophage, we take advantage of the presence of control spots and illustrate modelling issues for background correction and the ensuing empirical findings resulting from a Bayesian hierarchical approach to the problem of detecting differentially expressed genes. We prove the usefulness of a fully integrated approach where background correction and normalization are embedded in a single model-based framework, creating a new tailored model to account for the peculiar features of DNA array data where null expressions are planned by design. We also advocate the use of an alternative normalization device resulting from a suitable reparameterization. The new model is validated by using both simulated and our MTB data. This work suggests that the presence of a substantial fraction of exact null expressions might be the effect of an imperfect background calibration and shows how this can be suitably re-calibrated with the information coming from control spots. The proposed idea can be extended to all experiments in which a subset of genes whose expression levels can be ascribed mainly to background noise is planned by design.