On the accuracy in high‐dimensional linear models and its application to genomic selection

Genomic selection is today a hot topic in genetics. It consists in predicting breeding values of selection candidates, using the large number of genetic markers now available owing to the recent progress in molecular biology. One of the most popular methods chosen by geneticists is ridge regression. We focus on some predictive aspects of ridge regression and present theoretical results regarding the accuracy criteria, that is, the correlation between predicted value and true value. We show the influence of singular values, the regularization parameter, and the projection of the signal on the space spanned by the rows of the design matrix. Asymptotic results in a high‐dimensional framework are given; in particular, we prove that the convergence to optimal accuracy highly depends on a weighted projection of the signal on each subspace. We discuss on how to improve the prediction. Last, illustrations on simulated and real data are proposed.     

Non‐parametric interval estimation for the partial area under the ROC curve

Accurate diagnosis of disease is a critical part of health care. New diagnostic and screening tests must be evaluated based on their abilities to discriminate diseased conditions from non‐diseased conditions. For a continuous‐scale diagnostic test, a popular summary index of the receiver operating characteristic (ROC) curve is the area under the curve (AUC). However, when our focus is on a certain region of false positive rates, we often use the partial AUC instead. In this paper we have derived the asymptotic normal distribution for the non‐parametric estimator of the partial AUC with an explicit variance formula. The empirical likelihood (EL) ratio for the partial AUC is defined and it is shown that its limiting distribution is a scaled chi‐square distribution. Hybrid bootstrap and EL confidence intervals for the partial AUC are proposed by using the newly developed EL theory. We also conduct extensive simulation studies to compare the relative performance of the proposed intervals and existing intervals for the partial AUC. A real example is used to illustrate the application of the recommended intervals. The Canadian Journal of Statistics 39: 17–33; 2011 © 2011 Statistical Society of Canada     

Label‐ and Level‐Invariant Graphical Log‐Linear Models

We introduce two types of graphical log‐linear models: label‐ and level‐invariant models for triangle‐free graphs. These models generalise symmetry concepts in graphical log‐linear models and provide a tool with which to model symmetry in the discrete case. A label‐invariant model is category‐invariant and is preserved after permuting some of the vertices according to transformations that maintain the graph, whereas a level‐invariant model equates expected frequencies according to a given set of permutations. These new models can both be seen as instances of a new type of graphical log‐linear model termed the restricted graphical log‐linear model, or RGLL, in which equality restrictions on subsets of main effects and first‐order interactions are imposed. Their likelihood equations and graphical representation can be obtained from those derived for the RGLL models.     

Nonparametric adaptive likelihood weights

The weighted likelihood can be used to make inference about one population when data from similar populations are available. The author shows heuristically that the weighted likelihood can be seen as a special case of the entropy maximization principle. This leads him to propose the minimum averaged mean squared error (MAMSE) weights. He describes an algorithm for calculating these weights and shows its convergence using the Kuhn‐Tucker conditions. He explores the performance and properties of the weighted likelihood based on MAMSE weights through simulations.     

Risk patterns in drug safety study using relative times by accelerated failure time models when proportional hazards assumption is questionable: an illustrative case study of cancer risk of patients on glucose‐lowering therapies

Observational drug safety studies may be susceptible to confounding or protopathic bias. This bias may cause a spurious relationship between drug exposure and adverse side effect when none exists and may lead to unwarranted safety alerts. The spurious relationship may manifest itself through substantially different risk levels between exposure groups at the start of follow‐up when exposure is deemed too short to have any plausible biological effect of the drug. The restrictive proportional hazards assumption with its arbitrary choice of baseline hazard function renders the commonly used Cox proportional hazards model of limited use for revealing such potential bias. We demonstrate a fully parametric approach using accelerated failure time models with an illustrative safety study of glucose‐lowering therapies and show that its results are comparable against other methods that allow time‐varying exposure effects. Our approach includes a wide variety of models that are based on the flexible generalized gamma distribution and allows direct comparisons of estimated hazard functions following different exposure‐specific distributions of survival times. This approach lends itself to two alternative metrics, namely relative times and difference in times to event, allowing physicians more ways to communicate patient's prognosis without invoking the concept of risks, which some may find hard to grasp. In our illustrative case study, substantial differences in cancer risks at drug initiation followed by a gradual reduction towards null were found. This evidence is compatible with the presence of protopathic bias, in which undiagnosed symptoms of cancer lead to switches in diabetes medication. Copyright © 2015 John Wiley & Sons, Ltd.     

An Approximate Bayesian Algorithm for Combining Forecasts*

In this paper we propose a consensus forecasting method based on a convex combination of individual forecast densities. The exact Bayesian updating of the convex combination weights is very complex and practically prohibitive. We propose a simple sequential updating alternative method based on function approximation. Several examples illustrate the method.     

The Rationality of Under‐employing the Best‐performing Soccer Players

Abstract. This paper analyses the influence of sport performance (productivity) and other variables measuring the economic contribution of soccer players, upon the coach's decision of selecting a particular player. Using as dependent variable the proportion of time that individuals play in the Spanish professional soccer league, the paper concludes that players' economic market value does significantly affect the coach's choice, revealing the existence of other aims different from maximizing sport performance. We also examine the type of discrimination associated with lower chances of playing, which leads to smaller earnings and poorer career opportunities. The empirical evidence does not support discrimination due to nationality.     

INFORMATION GATHERING IN ORGANIZATIONS: EQUILIBRIUM,WELFARE, AND OPTIMAL NETWORK STRUCTURE

We model an organization as a game in which all agents share a common decision problem and some level of coordination is necessary between individual actions. Agents have individual private information concerning the task they have to perform, and they share this private information through pairwise channels of communication. We analyze how this communication pattern, modeled by means of a network structure, affects individual behavior and aggregate welfare. In the unique equilibrium of this Bayesian game, each agent's optimal action depends on a properly defined knowledge index that measures how the aggregation of information helps him to infer higher‐order beliefs about other's information after communication. Adding communication channels is not always beneficial for the organization because it can lead to mis‐coordination. We single out the geometry of interagent communication links that the manager could implement in order to improve the organization's performance.