Carmen D.S. André

The minimum sum of absolute errors regression: a robust alternative to the least squares regression

This paper concerns the minimum sum of absolute errors regression. It is a more robust alternative to the popular least squares regression whenever there are outliers in the values of the response variable, or the errors follow a long tailed distribution, or the loss function is proportional to the absolute errors rather than their squared values. We use data from a study of interstitial lung disease to illustrate the method, interpret the findings, and contrast with least squares regression. We point out some of the problems with the least squares analysis and show how to avoid these with the minimum sum of absolute errors analysis.

Cardiac Arrhythmias and Atrioventricular Block in a Cohort of Asymptomatic Individuals without Heart Disease

Aims: To evaluate cardiac arrhythmias and rhythm disturbances on 24 h ambulatory electrocardiographic monitoring in a cohort of asymptomatic healthy individuals with normal clinical examination. Methods and Results: 625 asymptomatic healthy individuals, in the age range 15–83 (mean 42, SD 11.9) years; 276 (44.2%) men and 349 (55.8%) women were submitted to 24-hour ambulatory electrocardiographic monitoring. Statistical analysis was performed with likelihood ratio test and automatic backward logistic regression. The frequency of atrial arrhythmias (p < 0.0001; OR 1.059; 95% CI 1.050–1068) and of ventricular arrhythmias (p < 0.0001; OR 1.023; 95% CI 1.017–1.029) increased for each age increase of 1 year; neither atrial nor ventricular arrhythmias demonstrated a statistically significant difference relative to gender. Transient second-degree atrioventricular block (Mobitz I) was observed in 14 (2.2%) individuals and was more frequent in individuals with resting heart rate <60 bpm (p = 0.006; OR 6.7, 95% CI 1.7–25.5). Conclusion: The frequency of atrial and ventricular arrhythmias increased with age and did not demonstrate a significant difference relative to gender. Transient atrioventricular block was more frequent in individuals with lower resting heart rate.

Influence measure for the L1 regression

Because outliers and leverage observations unduly affect the least squares regression, the identification of influential observations is considered an important and integrai part of the analysis. However, very few techniques have been developed for the residual analysis and diagnostics for the minimum sum of absolute errors, L1 regression. Although the L1 regression is more resistant to the outliers than the least squares regression, it appears that outliers (leverage) in the predictor variables may affect it. In this paper, our objective is to develop an influence measure for the L1 regression based on the likelihood displacement function. We illustrate the proposed influence measure with examples.

Coefficients of determinations for variable selection in the msae regression

Our objective is to modify a robust coefficient of determination for the minimum sum of absolute errors MSAE regression proposed by McKean and Sievers (1987) so that it satisfies all the desirable properties. We also propose an adjusted coefficient of determination that is appropriate for comparing several models with different number of variables. Further, it has the property that if it decreases with the addition of predictor variables to the model, then the contribution of these variables is statistically non-significant. We illustrate the results with an example.

pH in exhaled breath condensate and nasal lavage as a biomarker of air pollution-related inflammation in street traffic-controllers and office-workers

OBJECTIVE: To utilize low-cost and simple methods to assess airway and lung inflammation biomarkers related to air pollution. METHODS: A total of 87 male, non-smoking, healthy subjects working as street traffic-controllers or office-workers were examined to determine carbon monoxide in exhaled breath and to measure the pH in nasal lavage fluid and exhaled breath condensate. Air pollution exposure was measured by particulate matter concentration, and data were obtained from fixed monitoring stations (8-h work intervals per day, during the 5 consecutive days prior to the study). RESULTS: Exhaled carbon monoxide was two-fold greater in traffic-controllers than in office-workers. The mean pH values were 8.12 in exhaled breath condensate and 7.99 in nasal lavage fluid in office-workers; these values were lower in traffic-controllers (7.80 and 7.30, respectively). Both groups presented similar cytokines concentrations in both substrates, however, IL-1β and IL-8 were elevated in nasal lavage fluid compared with exhaled breath condensate. The particulate matter concentration was greater at the workplace of traffic-controllers compared with that of office-workers. CONCLUSION: The pH values of nasal lavage fluid and exhaled breath condensate are important, robust, easy to measure and reproducible biomarkers that can be used to monitor occupational exposure to air pollution. Additionally, traffic-controllers are at an increased risk of airway and lung inflammation during their occupational activities compared with office-workers.

An algorithm for the MSAE estimation of the multistage dose-response model

Abstract The least squares procedure is often used to estimate the parameters of the multistage dose-response model. However. these estimates are unduly affected by outliers in a data set. The minimum sum of absolute errors. MSAE estimates are more resistant to outliers than the least squares estimates. Algorithms to compute the MSAE estimates can be tedious and computationally burdensome. We propose a linear approximation for the dose-response model that can be used to find the MSAE estimates by a simple and computationally less intensive algorithm. A few illustrative examples show that we get comparable values of the MSAE estimates of the parameters in a dose-response model using the exact model and the linear approximation.

Atmospheric Pollution and Mortality in São Paulo

Regression models are largely used to assess the health implications of air pollution exposure in studies involving daily counts of mortality or morbidity (response variable) and daily measures of pollutant concentrations as well as temperature and other possible confounders (explanatory variables). Model specification, however, is not a simple task since it may depend on several characteristics, as the presence of trends and seasonality in the time series, the choice of the confounding variables, the lag between an increase in pollutant concentration and outcome, the choice of the response variable distribution, over dispersion, multicollinearity and autocorrelation. We illustrate these issues via the analysis of data from the metropolitan area of Sao Paulo. The importance of a sensitivity analysis and the need to develop robust methods is also emphasized since the expected small magnitude of the effects may be influenced by the presence of outliers.

Asymptotic properties of the minimum sum of absolute errors estimators in a dose-response model

The multistage dose response model is frequently used in practical applications. The minimum sum of absolute errors MSAE criterion is more resistant to outliers than the popular least squares procedure. Efficient algorithms have been proposed to compute the MSAE estimates of the parameters of the model. However, the properties of these estimators are not known. In this paper, our objective is to study asymptotic properties of these estimators. We also give an approximate expression for the variance of these estimators when their asymptotic distribution is multinormal.

An iterative procedure for the estimation of parameters in a dose-response model

The least squares estimates of the parameters in the multistage dose-response model are unduly affected by outliers in a data set whereas the minimum sum of absolute errors, MSAE estimates are more resistant to outliers. Algorithms to compute the MSAE estimates can be tedious and computationally burdensome. We propose a linear approximation for the dose-response model that can be used to find the MSAE estimates by a simple and computationally less intensive algorithm. A few illustrative ex-amples and a Monte Carlo study show that we get comparable values of the MSAE estimates of the parameters in a dose-response model using the exact model and the linear approximation.