Christine Choirat

Air Pollution and Mortality in the Medicare Population

BACKGROUND Studies have shown that long‐term exposure to air pollution increases mortality. However, evidence is limited for air‐pollution levels below the most recent National Ambient Air Quality Standards. Previous studies involved predominantly urban populations and did not have the statistical power to estimate the health effects in underrepresented groups. METHODS We constructed an open cohort of all Medicare beneficiaries (60,925,443 persons) in the continental United States from the years 2000 through 2012, with 460,310,521 person‐years of follow‐up. Annual averages of fine particulate matter (particles with a mass median aerodynamic diameter of less than 2.5 μm [PM2.5]) and ozone were estimated according to the ZIP Code of residence for each enrollee with the use of previously validated prediction models. We estimated the risk of death associated with exposure to increases of 10 μg per cubic meter for PM2.5 and 10 parts per billion (ppb) for ozone using a two‐pollutant Cox proportional‐hazards model that controlled for demographic characteristics, Medicaid eligibility, and area‐level covariates. RESULTS Increases of 10 μg per cubic meter in PM2.5 and of 10 ppb in ozone were associated with increases in all‐cause mortality of 7.3% (95% confidence interval [CI], 7.1 to 7.5) and 1.1% (95% CI, 1.0 to 1.2), respectively. When the analysis was restricted to person‐years with exposure to PM2.5 of less than 12 μg per cubic meter and ozone of less than 50 ppb, the same increases in PM2.5 and ozone were associated with increases in the risk of death of 13.6% (95% CI, 13.1 to 14.1) and 1.0% (95% CI, 0.9 to 1.1), respectively. For PM2.5, the risk of death among men, blacks, and people with Medicaid eligibility was higher than that in the rest of the population. CONCLUSIONS In the entire Medicare population, there was significant evidence of adverse effects related to exposure to PM2.5 and ozone at concentrations below current national standards. This effect was most pronounced among self‐identified racial minorities and people with low income. (Supported by the Health Effects Institute and others.)

The Analytic Hierarchy Process and the Theory of Measurement

The analytic hierarchy process (AHP) is a decision-making procedure widely used in management for establishing priorities in multicriteria decision problems. Underlying the AHP is the theory of ratio-scale measures developed in psychophysics since the middle of the last century. It is, however, well known that classical ratio-scaling approaches have several problems. We reconsider the AHP in the light of the modern theory of measurement based on the so-called separable representations recently axiomatized in mathematical psychology. We provide various theoretical and empirical results on the extent to which the AHP can be considered a reliable decision-making procedure in terms of the modern theory of subjective measurement.

Empirical Properties of Group Preference Aggregation Methods Employed in AHP: Theory and Evidence

We study various methods of aggregating individual judgments and individual priorities in group decision making with the AHP. The focus is on the empirical properties of the various methods, mainly on the extent to which the various aggregation methods represent an accurate approximation of the priority vector of interest. We identify five main classes of aggregation procedures which provide identical or very similar empirical expressions for the vectors of interest. We also propose a method to decompose in the AHP response matrix distortions due to random errors and perturbations caused by cognitive bias predicted by the mathematical psychology literature. We test the decomposition with experimental data and find that perturbations in group decision making caused by cognitive distortions are more important than those caused by random errors. We propose methods to correct systematic distortions.

Association of Short-term Exposure to Air Pollution With Mortality in Older Adults

Importance The US Environmental Protection Agency is required to reexamine its National Ambient Air Quality Standards (NAAQS) every 5 years, but evidence of mortality risk is lacking at air pollution levels below the current daily NAAQS in unmonitored areas and for sensitive subgroups. Objective To estimate the association between short-term exposures to ambient fine particulate matter (PM2.5) and ozone, and at levels below the current daily NAAQS, and mortality in the continental United States. Design, Setting, and Participants Case-crossover design and conditional logistic regression to estimate the association between short-term exposures to PM2.5 and ozone (mean of daily exposure on the same day of death and 1 day prior) and mortality in 2-pollutant models. The study included the entire Medicare population from January 1, 2000, to December 31, 2012, residing in 39 182 zip codes. Exposures Daily PM2.5 and ozone levels in a 1-km × 1-km grid were estimated using published and validated air pollution prediction models based on land use, chemical transport modeling, and satellite remote sensing data. From these gridded exposures, daily exposures were calculated for every zip code in the United States. Warm-season ozone was defined as ozone levels for the months April to September of each year. Main Outcomes and Measures All-cause mortality in the entire Medicare population from 2000 to 2012. Results During the study period, there were 22 433 862 million case days and 76 143 209 control days. Of all case and control days, 93.6% had PM2.5 levels below 25 &mgr;g/m3, during which 95.2% of deaths occurred (21 353 817 of 22 433 862), and 91.1% of days had ozone levels below 60 parts per billion, during which 93.4% of deaths occurred (20 955 387 of 22 433 862). The baseline daily mortality rates were 137.33 and 129.44 (per 1 million persons at risk per day) for the entire year and for the warm season, respectively. Each short-term increase of 10 &mgr;g/m3 in PM2.5 (adjusted by ozone) and 10 parts per billion (10−9) in warm-season ozone (adjusted by PM2.5) were statistically significantly associated with a relative increase of 1.05% (95% CI, 0.95%-1.15%) and 0.51% (95% CI, 0.41%-0.61%) in daily mortality rate, respectively. Absolute risk differences in daily mortality rate were 1.42 (95% CI, 1.29-1.56) and 0.66 (95% CI, 0.53-0.78) per 1 million persons at risk per day. There was no evidence of a threshold in the exposure-response relationship. Conclusions and Relevance In the US Medicare population from 2000 to 2012, short-term exposures to PM2.5 and warm-season ozone were significantly associated with increased risk of mortality. This risk occurred at levels below current national air quality standards, suggesting that these standards may need to be reevaluated.

Quadrature rules and distribution of points on manifolds

We study the error in quadrature rules on a compact manifold. Our estimates are in the same spirit of the Koksma-Hlawka inequality and they depend on a sort of discrepancy of the sampling points and a generalized variation of the function. In particular, we give sharp quantitative estimates for quadrature rules of functions in Sobolev classes.

Estimation in Discrete Parameter Models

In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points. In this case, we speak of discrete parameter models. Even though the problem is quite old and has interesting connections with testing and model selection, asymptotic theory for these models has hardly ever been studied. Therefore, we discuss consistency, asymptotic distribu- tion theory, information inequalities and their relations with efficiency and superefficiency for a general class of m-estimators.

Measurement by subjective estimation: Testing for separable representations

Studying how individuals compare two given quantitative stimuli, sayd 1 andd 2 , is a fundamental problem. One very common way to address it is throughratio estimation, that is to ask individuals not to give values tod 1 andd 2 , but rather to give their estimates of the ratiop=d 1 /d 2 . Several psychophysical theories (the best known being Stevens’ power-law) claim that this ratio cannot be known directly and that there are cognitive distortions on the apprehension of the different quantities. These theories result in the so-calledseparable representations[Luce, R. D. (2002). A psychophysical theory of intensity proportions, joint presentations, and matches.Psychological Review, 109, 520‐532; Narens, L. (1996). A theory of ratio magnitude estimation.Journal of Mathematical Psychology, 40, 109‐788], which include Stevens’ model as a special case. In this paper we propose a general statistical framework that allows for testing in a rigorous way whether the separable representation theory is grounded or not. We conclude in favor of it, but reject Stevens’ model. As a byproduct, we provide estimates of the psychophysical functions of interest. c

Bootstrap confidence sets for the Aumann mean of a random closed set

The objective is to develop a reliable method to build confidence sets for the Aumann mean of a random closed set as estimated through the Minkowski empirical mean. First, a general definition of the confidence set for the mean of a random set is provided. Then, a method using a characterization of the confidence set through the support function is proposed and a bootstrap algorithm is described, whose performance is investigated in Monte Carlo simulations.

Approximation of Stochastic Programming Problems

In Stochastic Programming, the aim is often the optimization of a criterion function that can be written as an integral or mean functional with respect to a probability measure \(\mathbb{P}\). When this functional cannot be computed in closed form, it is customary to approximate it through an empirical mean functional based on a random Monte Carlo sample. Several improved methods have been proposed, using quasi-Monte Carlo samples, quadrature rules, etc. In this paper, we propose a result on the epigraphical approximation of an integral functional through an approximate one. This result allows us to deal with Monte Carlo, quasi-Monte Carlo and quadrature methods. We propose an application to the epi-convergence of stochastic programs approximated through the empirical measure based on an asymptotically mean stationary (ams) sequence. Because of the large scope of applications of ams measures in Applied Probability, this result turns out to be relevant for approximation of stochastic programs through real data.

Numerical properties of generalized discrepancies on spheres of arbitrary dimension

Quantifying uniformity of a configuration of points on the sphere is an interesting topic that is receiving growing attention in numerical analysis. An elegant solution has been provided by Cui and Freeden [J. Cui, W. Freeden, Equidistribution on the sphere, SIAM J. Sci. Comput. 18 (2) (1997) 595-609], where a class of discrepancies, called generalized discrepancies and originally associated with pseudodifferential operators on the unit sphere in R^3, has been introduced. The objective of this paper is to extend to the sphere of arbitrary dimension this class of discrepancies and to study their numerical properties. First we show that generalized discrepancies are diaphonies on the hypersphere. This allows us to completely characterize the sequences of points for which convergence to zero of these discrepancies takes place. Then we discuss the worst-case error of quadrature rules and we derive a result on tractability of multivariate integration on the hypersphere. At last we provide several versions of Koksma-Hlawka type inequalities for integration of functions defined on the sphere.