Eva Cantoni

Robust Inference for Generalized Linear Models

By starting from a natural class of robust estimators for generalized linear models based on the notion of quasi-likelihood, we define robust deviances that can be used for stepwise model selection as in the classical framework. We derive the asymptotic distribution of tests based on robust deviances, and we investigate the stability of their asymptotic level under contamination. The binomial and Poisson models are treated in detail. Two applications to real data and a sensitivity analysis show that the inference obtained by means of the new techniques is more reliable than that obtained by classical estimation and testing procedures.

Resistant selection of the smoothing parameter for smoothing splines

Robust automatic selection techniques for the smoothing parameter of a smoothing spline are introduced. They are based on a robust predictive error criterion and can be viewed as robust versions of Cp and cross-validation. They lead to smoothing splines which are stable and reliable in terms of mean squared error over a large spectrum of model distributions.

Pain as an important predictor of psychosocial health in patients with rheumatoid arthritis

To examine the evolution of psychosocial aspects of health‐related quality of life in rheumatoid arthritis (RA) patients, and to identify their predictors.

Temperature related mortality and ambulance service interventions during the heat waves of 2003 in Ticino (Switzerland).

Summary.ObjectivesThis study investigates a potential increase in mortality and in the demand for ambulance emergency services among the elderly in particular, in Ticino in the summer of 2003.MethodsMortality rates and emergency ambulance interventions rates were compared with records from the previous years. We considered the whole population, aged 65 and over, as well as 75 and over.ResultsThe 2003 mortality in the population was not signifi cantly different from the previous years. The number of deaths among the elderly showed a small but significant deviation from the expected values during the first heat wave in June 2003, with no significant impact on the seasonal results. The number of ambulance service interventions was larger than during the previous years.ConclusionThese results are consistent with findings in other studies. The heat waves (especially in June), were correlated with a higher number of ambulance callouts. In addition to some geographic, climatic, and social factors that had a protective impact, the response of the emergency services is likely to have contributed to a certain reduction in mortality.Zusammenfassung.Temperaturabhängige Sterblichkeit und Notfalleinsätze während der Hitzewellen im Jahr 2003 im Kanton Tessin (Schweiz)ZielDie Studie untersucht, ob im Kanton Tessin während der Sommermonate 2003 ein Anstieg der Sterblichkeit und der Anzahl Notfalleinsätze, besonders unter der älteren Bevölkerung, zu verzeichnen war.MethodenDie Sterblichkeitsraten und Notfalleinsätze wurden mit den Angaben des Vorjahres verglichen. Dabei wurde die Gesamtbevölkerung in Betracht gezogen sowie die Altersgruppe der über 65-Jährigen und der über 75-Jährigen.ErgebnisseDie Sterblichkeit im Jahr 2003 variierte nicht signi fikant gegenüber den Vorjahren. Bei der Gesamtbevölkerung wurde eine bedeutend höhere Sterblichkeit während der ersten Hitzewelle vom Juni 2003 beobachtet, ohne bedeutende Auswirkungen auf die Monats- und Saisonergebnisse. Die Anzahl der Notfalleinsätze war höher als in den Vorjahren.SchlussfolgerungDie vorliegenden Ergebnisse stimmen mit anderen Studien überein. Während der Hitzewellen (besonders derjenigen vom Juni) wurde ein Anstieg der Notfalleinsätze verzeichnet. Neben geographischen, meteorologischen und sozialen Aspekten, die eine schützende Wirkung hatten, war vermutlich auch der Einsatz der Notfalldienste für den Rückgang der Sterbefälle mit verantwortlich.Résumé.Mortalité liée à la température et interventions des services d’ambulances durant les vagues de chaleur de 2003 dans le canton du Tessin (Suisse)ObjectifsEnquêter sur une possible augmentation de la mortalité et de l’utilisation des services d’ambulances, en particulier pour les personnes âgées, durant l’été 2003 dans le canton du Tessin.MéthodesLes taux de mortalité et le nombre d’intervention des services d’ambulances ont été comparés avec les chiffres des années précédentes. L’étude a porté sur la population totale, sur les 65 ans et plus, ainsi que sur les 75 ans et plus.RésultatsLa mortalité de la population n’est pas significativement supérieure à celle des années précédentes. Les décès des personnes âgées mettent en évidence une déviation légère mais significative par rapport aux valeurs attendues durant la première vague de chaleur (juin 2003), mais sans impact sur les résultats saisonniers. Le nombre d’interventions des services d’ambulances a été supérieur à celui des années précédentes.ConclusionCes résultats corroborent les conclusions d’autres travaux. Les vagues de chaleur (surtout celle de juin), sont en lien avec un nombre plus élevé d’interventions des services d’ambulances. Outre certains facteurs géographiques, météorologiques et sociaux qui ont sans doute eu un effet protecteur, la réponse des systèmes d’interventions d’urgence a probablement aussi contribué à une certaine réduction de la mortalité.

Variable selection in additive models by non-negative garrote

We adapt Breiman’s non-negative garrote method to perform variable selection in non-parametric additive models. The technique avoids methods of testing for which no general reliable distributional theory is available. In addition, it removes the need for a full search of all possible models, something which is computationally intensive, especially when the number of variables is moderate to high. The method has the advantages of being conceptually simple and computationally fast. It provides accurate predictions and is effective at identifying the variables generating the model. To illustrate our procedure, we analyse logbook data on blue sharks (Prionace glauca) from the US pelagic longline fishery. In addition, we compare our proposal to a series of available alternatives by simulation. The results show that in all cases our methods perform better or as well as these alternatives.

Non-parametric adjustment for covariates when estimating a treatment effect

We consider a non-parametric model for estimating the effect of a binary treatment on an outcome variable while adjusting for an observed covariate. A naive procedure consists of performing two separate non-parametric regressions of the response on the covariate: one with the treated individuals and the other with the untreated. The treatment effect is then obtained by taking the difference between the two fitted regression functions. This article proposes a backfitting algorithm that uses all the data for the two abovementioned non-parametric regressions. We give finite sample theoretical results showing that the resulting estimator of the treatment effect can have lower variance. This improvement is not necessarily achieved at the cost of a larger bias. In all of the performed simulations, we observe that mean squared error is substantially lower for the proposed backfitting estimator. When more than one covariate is observed, our backfitting estimator can still be applied by using the propensity score (the probability of being treated for a given setup of the covariates). We illustrate the use of the backfitting estimator in a several-covariate situation with data on a training program for individuals having faced social and economic problems.

Robust inference in the negative binomial regression model with an application to falls data

A popular way to model overdispersed count data, such as the number of falls reported during intervention studies, is by means of the negative binomial (NB) distribution. Classical estimating methods are well-known to be sensitive to model misspecifications, taking the form of patients falling much more than expected in such intervention studies where the NB regression model is used. We extend in this article two approaches for building robust M-estimators of the regression parameters in the class of generalized linear models to the NB distribution. The first approach achieves robustness in the response by applying a bounded function on the Pearson residuals arising in the maximum likelihood estimating equations, while the second approach achieves robustness by bounding the unscaled deviance components. For both approaches, we explore different choices for the bounding functions. Through a unified notation, we show how close these approaches may actually be as long as the bounding functions are chosen and tuned appropriately, and provide the asymptotic distributions of the resulting estimators. Moreover, we introduce a robust weighted maximum likelihood estimator for the overdispersion parameter, specific to the NB distribution. Simulations under various settings show that redescending bounding functions yield estimates with smaller biases under contamination while keeping high efficiency at the assumed model, and this for both approaches. We present an application to a recent randomized controlled trial measuring the effectiveness of an exercise program at reducing the number of falls among people suffering from Parkinsons disease to illustrate the diagnostic use of such robust procedures and their need for reliable inference.

Robust Repeat Sales Indexes

Using single-family sales data for Louisville, Kentucky, we show the benefits of applying robust methods to down-weight problematic transactions in a repeat sales context. Robust estimators reduce the influence of outliers in repeat sales price changes that are due to data entry errors, quality changes or nonmarket transactions. In addition to comparing conventional and robust indexes, we also use simulated data, where the correct index is known, to show that robust methods control for the impacts of contaminated data. Finally, we demonstrate that robust methods reduce the magnitude and volatility of index revisions.

Saddlepoint tests for accurate and robust inference on overdispersed count data

Inference on regression coefficients when the response variable consists of overdispersed counts is traditionally based on Wald, score and likelihood ratio tests. As the accuracy of the p-values of such tests becomes questionable in small samples, three recently developed tests are adapted to the negative binomial regression model. The non-trivial computational aspects involved in their implementation, some of which remained obscure in the literature until now, are detailed for general M-estimators. Under regularity conditions, these tests feature a relative error property with respect to the asymptotic chi-squared distribution, thus yielding highly accurate p-values even in small samples. Extensive simulations show how these new tests outperform the traditional ones in terms of actual level with comparable power. Moreover, inference based on robust (bounded influence) versions of these tests remains reliable when the sample does not entirely conform to the model assumptions. The use of these procedures is illustrated with data coming from a recent randomized controlled trial, with a sample size of 52 observations. An R package implementing all tests is readily available.

Nonlinear Growth Curve Models

In the past three decades, the growth curve model (also known as latent curve model) has become a popular statistical methodology for the analysis of longitudinal or, more generally, repeated-measures data. Developed primarily within the latent variable modeling framework, the equivalent model emerged from other fields under the names of linear mixed-effects model, random-effects model, hierarchical linear model, and linear multilevel model. This methodology estimates the so-called growth parameters that describe individuals’ change trajectories across time and are related via linear combinations to the dependent variable. While satisfying in many research settings, oftentimes a linear relation between dependent variable and growth parameters cannot allow for meaningful interpretation of the growth parameters, parsimonious descriptions of the change phenomenon, good adjustment to the data across all values of the time predictor, and realistic extrapolations outside the empirical range of the time predictor. Consequently, nonlinear alternatives have been proposed, for which the growth parameters can be related to the dependent variable via any mathematical function (not just linear combinations). We discuss the theoretical foundations as well as practical implications of estimating nonlinear growth curve models. We also illustrate the methodology with an example from the psychological literature.