M-quantile regression shrinkage and selection via the Lasso and Elastic Net to assess the effect of meteorology and traffic on air quality.

In this work, we intersect data on size-selected particulate matter (PM) with vehicular traffic counts and a comprehensive set of meteorological covariates to study the effect of traffic on air quality. To this end, we develop an M-quantile regression model with Lasso and Elastic Net penalizations. This allows (i) to identify the best proxy for vehicular traffic via model selection, (ii) to investigate the relationship between fine PM concentration and the covariates at different M-quantiles of the conditional response distribution, and (iii) to be robust to the presence of outliers. Heterogeneity in the data is accounted by fitting a B-spline on the effect of the day of the year. Analytic and bootstrap-based variance estimates of the regression coefficients are provided, together with a numerical evaluation of the proposed estimation procedure. Empirical results show that atmospheric stability is responsible for the most significant effect on fine PM concentration: this effect changes at different levels of the conditional response distribution and is relatively weaker on the tails. On the other hand, model selection allows to identify the best proxy for vehicular traffic whose effect remains essentially the same at different levels of the conditional response distribution.

The Fay-Herriot model for multiply imputed data with an application to regional wealth estimation in Germany.

The increasing inequality of private income and wealth requires the redistribution of financial resources. Thus, several financial support schemes allocate budget across countries or regions. This work shows how to estimate private wealth at low regional levels by means of a modified Fay-Herriot approach that deals with (a) unit and item non-response, especially with used multiple imputation, (b) the skewness of the wealth distribution, and (c) inconsistencies of the regional estimates with the national direct estimate. One compelling example for financial redistribution is the promoted catching-up process of East Germany after the German reunification. This work shows that 25 years after the reunification differences are more diverse than just between the East and the West by estimating private wealth at two regional levels in Germany. The analysis is based on the Household Finance and Consumption Survey (HFCS) that the European Central Bank launched for all euro area countries in 2010. Although the application in this paper focuses particularly on Germany, the approach proposed is applicable to the other countries participating in the HFCS as well as to other surveys that make use of multiple imputation.

Generalised M-quantile random-effects model for discrete response: An application to the number of visits to physicians.

In this paper, we extend the linear M-quantile random intercept model (MQRE) to discrete data and use the proposed model to evaluate the effect of selected covariates on two count responses: the number of generic medical examinations and the number of specialised examinations for health districts in three regions of central Italy. The new approach represents an outlier-robust alternative to the generalised linear mixed model with Gaussian random effects and it allows estimating the effect of the covariates at various quantiles of the conditional distribution of the target variable. Results from a simulation experiment, as well as from real data, confirm that the method proposed here presents good robustness properties and can be in certain cases more efficient than other approaches.

Modelling the distribution of health-related quality of life of advanced melanoma patients in a longitudinal multi-centre clinical trial using M-quantile random effects regression.

Health-related quality of life assessment is important in the clinical evaluation of patients with metastatic disease that may offer useful information in understanding the clinical effectiveness of a treatment. To assess if a set of explicative variables impacts on the health-related quality of life, regression models are routinely adopted. However, the interest of researchers may be focussed on modelling other parts (e.g. quantiles) of this conditional distribution. In this paper, we present an approach based on quantile and M-quantile regression to achieve this goal. We applied the methodologies to a prospective, randomized, multi-centre clinical trial. In order to take into account the hierarchical nature of the data we extended the M-quantile regression model to a three-level random effects specification and estimated it by maximum likelihood.

Long-term outcome of inactive and active, low viraemic HBeAg-negative-hepatitis B virus infection: Benign course towards HBsAg clearance.

BACKGROUND & AIMS: The difference between the long-term outcome of low-viraemic (HBV-DNA≤20 000-IU/mL, LV-AC) and inactive HBsAg carriers (HBV-DNA≤2000-IU/mL, IC) remains to be defined. We studied prospectively 153 HBeAg-negative HBsAg-carriers with baseline HBV-DNA≤20 000-IU/mL and normal transaminases. METHODS: IC, LV-AC or chronic hepatitis B (CHB) (HBV-DNA persistently ≤2000-IU/mL, ≤20 000-IU/mL or >20 000-IU/mL respectively) were diagnosed after 1-year, 3-monthly monitoring. Thereafter IC and LV-AC were followed-up for additional 57.2 (8.5-158.3) months. HBV-DNA, HBsAg, HBV"core-related"Antigen (HBcrAg) and total-anti-HBc were quantified at baseline. RESULTS: After the 1st year diagnostic follow-up CHB [higher HBV-DNA (P=.005), total-anti-HBc (P=.012), ALT (P=.007) and liver-stiffness (P=.021)] was identified in 20 (13.1%) carriers; baseline HBsAg≤1000IU/HBV-DNA≤2000IU/mL excluded the presence of CHB (NPV-100%). Thereafter, during the long-term follow-up none of 87 IC reactivated, 19 (21.8%) cleared HBsAg [older-age (P=.004), lower HBsAg (P<.001), higher yearly HBsAg decline (P<.001)]. Twenty-five of 46 (54.3%) LV-AC remained stable, 20 (43.5%) became IC and 1 (2.2%) developed CHB. The best single-point CHB and IC diagnostic-accuracies were total-anti-HBc (84.2%, NPV-98.2%) and HBV-DNA/total-anti-HBc/HBcrAg combination (89.5%, 93%-sensitivity, 84.8%-specificity) respectively. CONCLUSIONS: Viraemia persistently ≤20 000-IU/mL predicts a benign clinical outcome: it was associated with transition to IC in 43% of LV-AC and to Occult HBV Infection in 20% of IC within 5-years. Nevertheless, 13.1% of individuals with low viraemia at presentation develops CHB within 1 year: 1-year HBV-DNA monitoring resulted the most accurate diagnostic approach that can be limited to at least a half of cases by the single point HBV-DNA/HBsAg quantification. The IC-diagnostic-accuracy combining HBV-DNA/total-anti-HBc/HBcrAg needs to be confirmed in further studies.

Longitudinal analysis of the strengths and difficulties questionnaire scores of the Millennium Cohort Study children in England using M-quantile random-effects regression.

Multilevel modelling is a popular approach for longitudinal data analysis. Statistical models conventionally target a parameter at the centre of a distribution. However, when the distribution of the data is asymmetric, modelling other location parameters, e.g. percentiles, may be more informative. We present a new approach, M-quantile random-effects regression, for modelling multilevel data. The proposed method is used for modelling location parameters of the distribution of the strengths and difficulties questionnaire scores of children in England who participate in the Millennium Cohort Study. Quantile mixed models are also considered. The analyses offer insights to child psychologists about the differential effects of risk factors on children's outcomes.

Robust small area prediction for counts.

A new semiparametric approach to model-based small area prediction for counts is proposed and used for estimating the average number of visits to physicians for Health Districts in Central Italy. The proposed small area predictor can be viewed as an outlier robust alternative to the more commonly used empirical plug-in predictor that is based on a Poisson generalized linear mixed model with Gaussian random effects. Results from the real data application and from a simulation experiment confirm that the proposed small area predictor has good robustness properties and in some cases can be more efficient than alternative small area approaches.

Disease mapping via negative binomial regression M-quantiles.

We introduce a semi-parametric approach to ecological regression for disease mapping, based on modelling the regression M-quantiles of a negative binomial variable. The proposed method is robust to outliers in the model covariates, including those due to measurement error, and can account for both spatial heterogeneity and spatial clustering. A simulation experiment based on the well-known Scottish lip cancer data set is used to compare the M-quantile modelling approach with a disease mapping approach based on a random effects model. This suggests that the M-quantile approach leads to predicted relative risks with smaller root mean square error. The paper concludes with an illustrative application of the M-quantile approach, mapping low birth weight incidence data for English Local Authority Districts for the years 2005-2010.

Semiparametric M-quantile regression for count data.

Lung cancer incidence over 2005-2010 for 326 Local Authority Districts in England is investigated by ecological regression. Motivated from mis-specification of a Negative Binomial additive model, a semiparametric Negative Binomial M-quantile regression model is introduced. The additive part relates to those univariate or bivariate smoothing components, which are included in the model to capture nonlinearities in the predictor or to account for spatial dependence. All such components are estimated using penalized splines. The results show the capability of the semiparametric Negative Binomial M-quantile regression model to handle data with a strong spatial structure.

Outlier robust model-assisted small area estimation.

Small area estimation with M-quantile models was proposed by Chambers and Tzavidis (). The key target of this approach to small area estimation is to obtain reliable and outlier robust estimates avoiding at the same time the need for strong parametric assumptions. This approach, however, does not allow for the use of unit level survey weights, making questionable the design consistency of the estimators unless the sampling design is self-weighting within small areas. In this paper, we adopt a model-assisted approach and construct design consistent small area estimators that are based on the M-quantile small area model. Analytic and bootstrap estimators of the design-based variance are discussed. The proposed estimators are empirically evaluated in the presence of complex sampling designs.