Practical Large-Scale Spatio-Temporal Modeling of Particulate Matter Concentrations

The last two decades have seen intense scientific and regulatory interest in the health effects of particulate matter (PM). Influential epidemiological studies that characterize chronic exposure of individuals rely on monitoring data that are sparse in space and time, so they often assign the same exposure to participants in large geographic areas and across time. We estimate monthly PM during 1988-2002 in a large spatial domain for use in studying health effects in the Nurses' Health Study. We develop a conceptually simple spatio-temporal model that uses a rich set of covariates. The model is used to estimate concentrations of PM10 for the full time period and PM2.5 for a subset of the period. For the earlier part of the period, 1988-1998, few PM2.5 monitors were operating, so we develop a simple extension to the model that represents PM2.5 conditionally on PM10 model predictions. In the epidemiological analysis, model predictions of PM10 are more strongly associated with health effects than when using simpler approaches to estimate exposure. Our modeling approach supports the application in estimating both fine-scale and large-scale spatial heterogeneity and capturing space-time interaction through the use of monthly-varying spatial surfaces. At the same time, the model is computationally feasible, implementable with standard software, and readily understandable to the scientific audience. Despite simplifying assumptions, the model has good predictive performance and uncertainty characterization.

A Pseudolikelihood Approach for Simultaneous Analysis of Array Comparative Genomic Hybridizations (aCGH)

DNA sequence copy number has been shown to be associated with cancer development and progression. Array-based Comparative Genomic Hybridization (aCGH) is a recent development that seeks to identify the copy number ratio at large numbers of markers across the genome. Due to experimental and biological variations across chromosomes and across hybridizations, current methods are limited to analyses of single chromosomes. We propose a more powerful approach that borrows strength across chromosomes and across hybridizations. We assume a Gaussian mixture model, with a hidden Markov dependence structure, and with random effects to allow for intertumoral variation, as well as intratumoral clonal variation. For ease of computation, we base estimation on a pseudolikelihood function. The method produces quantitative assessments of the likelihood of genetic alterations at each clone, along with a graphical display for simple visual interpretation. We assess the characteristics of the method through simulation studies and through analysis of a brain tumor aCGH data set. We show that the pseudolikelihood approach is superior to existing methods both in detecting small regions of copy number alteration and in accurately classifying regions of change when intratumoral clonal variation is present.

Underestimation of Standard Errors in Multi-Site Time Series Studies

Multi-site time series studies of air pollution and mortality and morbidity have figured prominently in the literature as comprehensive approaches for estimating acute effects of air pollution on health. Hierarchical models are generally used to combine site-specific information and estimate pooled air pollution effects taking into account both within-site statistical uncertainty, and across-site heterogeneity. Within a site, characteristics of time series data of air pollution and health (small pollution effects, missing data, highly correlated predictors, non linear confounding etc.) make modelling all sources of uncertainty challenging. One potential consequence is underestimation of the statistical variance of the site-specific effects to be combined. In this paper we investigate the impact of variance underestimation on the pooled relative rate estimate. We focus on two-stage normal-normal hierarchical models and on under- estimation of the statistical variance at the first stage. By mathematical considerations and simulation studies, we found that variance underestimation does not affect the pooled estimate substantially. However, some sensitivity of the pooled estimate to variance underestimation is observed when the number of sites is small and underestimation is severe. These simulation results are applicable to any two-stage normal-normal hierarchical model for combining information of site-specific results, and they can be easily extended to more general hierarchical formulations. We also examined the impact of variance underestimation on the national average relative rate estimate from the National Morbidity Mortality Air Pollution Study and we found that variance underestimation as much as 40% has little effect on the national average.

A Method for Visualizing Multivariate Time Series Data

Visualization and exploratory analysis is an important part of any data analysis and is made more challenging when the data are voluminous and high-dimensional. One such example is environmental monitoring data, which are often collected over time and at multiple locations, resulting in a geographically indexed multivariate time series. Financial data, although not necessarily containing a geographic component, present another source of high-volume multivariate time series data. We present the mvtsplot function which provides a method for visualizing multivariate time series data. We outline the basic design concepts and provide some examples of its usage by applying it to a database of ambient air pollution measurements in the United States and to a hypothetical portfolio of stocks.

A BAYESIAN HIERARCHICAL MODEL FOR CONSTRAINED DISTRIBUTED LAG FUNCTIONS: ESTIMATING THE TIME COURSE OF HOSPITALIZATION ASSOCIATED WITH AIR POLLUTION EXPOSURE

Numerous time series studies have provided strong evidence of an association between increased levels of ambient air pollution and increased levels of hospital admissions, typically at 0, 1, or 2 days after an air pollution episode. An important research aim is to extend existing statistical models so that a more detailed understanding of the time course of hospitalization after exposure to air pollution can be obtained. Information about this time course, combined with prior knowledge about biological mechanisms, could provide the basis for hypotheses concerning the mechanism by which air pollution causes disease. Previous studies have identified two important methodological questions: (1) How can we estimate the shape of the distributed lag between increased air pollution exposure and increased mortality or morbidity? and (2) How should we estimate the cumulative population health risk from short-term exposure to air pollution? Distributed lag models are appropriate tools for estimating air pollution health effects that may be spread over several days. However, estimation for distributed lag models in air pollution and health applications is hampered by the substantial noise in the data and the inherently weak signal that is the target of investigation. We introduce an hierarchical Bayesian distributed lag model that incorporates prior information about the time course of pollution effects and combines information across multiple locations. The model has a connection to penalized spline smoothing using a special type of penalty matrix. We apply the model to estimating the distributed lag between exposure to particulate matter air pollution and hospitalization for cardiovascular and respiratory disease using data from a large United States air pollution and hospitalization database of Medicare enrollees in 94 counties covering the years 1999-2002.

A unified approach to modeling multivariate binary data using copulas over partitions

Many seemingly disparate approaches for marginal modeling have been developed in recent years. We demonstrate that many current approaches for marginal modeling of correlated binary outcomes produce likelihoods that are equivalent to the proposed copula-based models herein. These general copula models of underlying latent threshold random variables yield likelihood based models for marginal fixed effects estimation and interpretation in the analysis of correlated binary data. Moreover, we propose a nomenclature and set of model relationships that substantially elucidates the complex area of marginalized models for binary data. A diverse collection of didactic mathematical and numerical examples are given to illustrate concepts.

A SURVEY OF THE LIKELIHOOD APPROACH TO BIOEQUIVALENCE TRIALS

Bioequivalence trials are abbreviated clinical trials whereby a generic drug or new formulation is evaluated to determine if it is "equivalent" to a corresponding previously approved brand-name drug or formulation. In this manuscript, we survey the process of testing bioequivalence and advocate the likelihood paradigm for representing the resulting data as evidence. We emphasize the unique conflicts between hypothesis testing and confidence intervals in this area - which we believe are indicative of the existence of the systemic defects in the frequentist approach - that the likelihood paradigm avoids. We suggest the direct use of profile likelihoods for evaluating bioequivalence and examine the main properties of profile likelihoods and estimated likelihoods under simulation. This simulation study shows that profile likelihoods are a reasonable alternative to the (unknown) true likelihood for a range of parameters commensurate with bioequivalence research. Our study also shows that the standard methods in the current practice of bioequivalence trials offers only weak evidence from the evidential point of view.

Nonparametric Estimation of the Bivariate Recurrence Time Distribution

This paper considers statistical models in which two different types of events, such as the diagnosis of a disease and the remission of the disease, occur alternately over time and are observed subject to right censoring. We propose nonparametric estimators for the joint distribution of bivariate recurrence times and the marginal distribution of the first recurrence time. In general, the marginal distribution of the second recurrence time cannot be estimated due to an identifiability problem, but a conditional distribution of the second recurrence time can be estimated non-parametrically. In literature, statistical methods have been developed to estimate the joint distribution of bivariate recurrence times based on data of the first pair of censored bivariate recurrence times. These methods are efficient in the current model because recurrence times of higher orders are not used. Asymptotic properties of the estimators are established. Numerical studies demonstrate the estimator performs well with practical sample sizes. We apply the proposed method to a Denmark psychiatric case register data set for illustration of the methods and theory.

Seasonal Analyses of Air Pollution and Mortality in 100 U.S. Cities

Time series models relating short-term changes in air pollution levels to daily mortality counts typically assume that the effects of air pollution on the log relative rate of mortality do not vary with time. However, these short-term effects might plausibly vary by season. Changes in the sources of air pollution and meteorology can result in changes in characteristics of the air pollution mixture across seasons. The authors develop Bayesian semi-parametric hierarchical models for estimating time-varying effects of pollution on mortality in multi-site time series studies. The methods are applied to the updated National Morbidity and Mortality Air Pollution Study database for the period 1987--2000, which includes data for 100 U.S. cities. At the national level, a 10 micro-gram/m3 increase in PM(10) at lag 1 is associated with a 0.15 (95% posterior interval: -0.08, 0.39),0.14 (-0.14, 0.42), 0.36 (0.11, 0.61), and 0.14 (-0.06, 0.34) percent increase in mortality for winter, spring, summer, and fall, respectively. An analysis by geographical regions finds a strong seasonal pattern in the northeast (with a peak in summer) and little seasonal variation in the southern regions of the country. These results provide useful information for understanding particle toxicity and guiding future analyses of particle constituent data.

MORTALITY IN THE MEDICARE POPULATION AND CHRONIC EXPOSURE TO FINE PARTICULATE AIR POLLUTION

Prospective cohort studies have provided evidence on longer-term mortality risks of fine particulate matter (PM2.5), but due to their complexity and costs, only a few have been conducted. By linking monitoring data to the U.S. Medicare system by county of residence, we developed a retrospective cohort study, the Medicare Air Pollution Cohort Study (MCAPS), comprising over 20 million enrollees in the 250 largest counties during 2000-2002. We estimated log-linear regression models having as outcome the age-specific mortality rate for each county and as the main predictor, the average level for the study period 2000. Area-level covariates were used to adjust for socio-economic status and smoking. We reported results under several degrees of adjustment for spatial confounding and with stratification into by eastern, central and western counties. We estimated that a 10 µg/m3 increase in PM25 is associated with a 7.6% increase in mortality (95% CI: 4.4 to 10.8%). We found a stronger association in the eastern counties than nationally, with no evidence of an association in western counties. When adjusted for spatial confounding, the estimated log-relative risks drop by 50%. We demonstrated the feasibility of using Medicare data to establish cohorts for follow-up for effects of air pollution. Particulate matter (PM) air pollution is a global public health problem (1). In developing countries, levels of airborne particles still reach concentrations at which serious health consequences are well-documented; in developed countries, recent epidemiologic evidence shows continued adverse effects, even though particle levels have declined in the last two decades (2-6). Increased mortality associated with higher levels of PM air pollution has been of particular concern, giving an imperative for stronger protective regulations (7). Evidence on PM and health comes from studies of acute and chronic adverse effects (6). The London Fog of 1952 provides dramatic evidence of the unacceptable short-term risk of extremely high levels of PM air pollution (8-10); multi-site time-series studies of daily mortality show that far lower levels of particles are still associated with short-term risk (5)(11-13). Cohort studies provide complementary evidence on the longer-term risks of PM air pollution, indicating the extent to which exposure reduces life expectancy. The design of these studies involves follow-up of cohorts for mortality over periods of years to decades and an assessment of mortality risk in association with estimated long-term exposure to air pollution (2-4;14-17). Because of the complexity and costs of such studies, only a small number have been conducted. The most rigorously executed, including the Harvard Six Cities Study and the American Cancer Society’s (ACS) Cancer Prevention Study II, have provided generally consistent evidence for an association of long- term exposure to particulate matter air pollution with increased all-cause and cardio-respiratory mortality (2,4,14,15). Results from these studies have been used in risk assessments conducted for setting the U.S. National Ambient Air Quality Standard (NAAQS) for PM and for estimating the global burden of disease attributable to air pollution (18,19). Additional prospective cohort studies are necessary, however, to confirm associations between long-term exposure to PM and mortality, to broaden the populations studied, and to refine estimates by regions across which particle composition varies. Toward this end, we have used data from the U.S. Medicare system, which covers nearly all persons 65 years of age and older in the United States. We linked Medicare mortality data to (particulate matter less than 2.5 µm in aerodynamic diameter) air pollution monitoring data to create a new retrospective cohort study, the Medicare Air Pollution Cohort Study (MCAPS), consisting of 20 million persons from 250 counties and representing about 50% of the US population of elderly living in urban settings. In this paper, we report on the relationship between longer-term exposure to PM2.5 and mortality risk over the period 2000 to 2002 in the MCAPS.

A polymorphism within the equine CRISP3 gene is associated with stallion fertility in Hanoverian warmblood horses

Fertility of stallions is of high economic importance, especially for large breeding organisations and studs. Breeding schemes with respect to fertility traits and selection of stallions at an early stage may be improved by including molecular genetic markers associated with traits. The genes coding for equine cysteine-rich secretory proteins (CRISPs) are promising candidate genes because previous studies have shown that CRISPs play a role in the fertilising ability of male animals. We have previously characterised the three equine CRISP genes and identified a non-synonymous polymorphism in the CRISP1 gene. In this study, we report one non-synonymous polymorphism in the CRISP2 gene and four non-synonymous polymorphisms in the CRISP3 gene. All six CRISP polymorphisms were genotyped in 107 Hanoverian breeding stallions. Insemination records of stallions were used to analyse the association between CRISP polymorphisms and fertility traits. Three statistical models were used to evaluate the influence of single mutations, genotypes and haplotypes of the polymorphisms. The CRISP3 AJ459965:c.+622G>A SNP leading to the amino acid substitution E208K was significantly associated with the fertility of stallions. Stallions heterozygous for the CRISP3 c.+622G>A SNP had lower fertility than homozygous stallions (P = 0.0234). The pregnancy rate per cycle in these stallions was estimated to be approximately 7% lower than in stallions homozygous at this position.

Primary care physician supply and other key determinants of health care utilisation: The case of Switzerland

Background The Swiss government decided to freeze new accreditations for physicians in private practice in Switzerland based on the assumption that demand-induced health care spending may be cut by limiting care offers. This legislation initiated an ongoing controversial public debate in Switzerland. The aim of this study is therefore the determination of socio-demographic and health system-related factors of per capita consultation rates with primary care physicians in the multicultural population of Switzerland. Methods The data were derived from the complete claims data of Swiss health insurers for 2004 and included 21.4 million consultations provided by 6564 Swiss primary care physicians on a fee-for-service basis. Socio-demographic data were obtained from the Swiss Federal Statistical Office. Utilisation-based health service areas were created and were used as observational units for statistical procedures. Multivariate and hierarchical models were applied to analyze the data. Results Models within the study allowed the definition of 1018 primary care service areas with a median population of 3754 and an average per capita consultation rate of 2.95 per year. Statistical models yielded significant effects for various geographical, socio-demographic and cultural factors. The regional density of physicians in independent practice was also significantly associated with annual consultation rates and indicated an associated increase 0.10 for each additional primary care physician in a population of 10,000 inhabitants. Considerable differences across Swiss language regions were observed with reference to the supply of ambulatory health resources provided either by primary care physicians, specialists, or hospital-based ambulatory care. Conclusion The study documents a large small-area variation in utilisation and provision of health care resources in Switzerland. Effects of physician density appeared to be strongly related to Swiss language regions and may be rooted in the different cultural backgrounds of the served populations.

Hospital use of young children in Switzerland: a nation-wide study based on a complete survey over 4 years

Background Young children are known to be the most frequent hospital users compared to older children and young adults. Therefore, they are an important population from economic and policy perspectives of health care delivery. In Switzerland complete hospitalization discharge records for children [<5 years] of four consecutive years [2002–2005] were evaluated in order to analyze variation in patterns of hospital use. Methods Stationary and outpatient hospitalization rates on aggregated ZIP code level were calculated based on census data provided by the Swiss federal statistical office (BfS). Thirty-seven hospital service areas for children [HSAP] were created with the method of "small area analysis", reflecting user-based health markets. Descriptive statistics and general linear models were applied to analyze the data. Results The mean stationary hospitalization rate over four years was 66.1 discharges per 1000 children. Hospitalizations for respiratory problem are most dominant in young children (25.9%) and highest hospitalization rates are associated with geographical factors of urban areas and specific language regions. Statistical models yielded significant effect estimates for these factors and a significant association between ambulatory/outpatient and stationary hospitalization rates. Conclusion The utilization-based approach, using HSAP as spatial representation of user-based health markets, is a valid instrument and allows assessing the supply and demand of children's health care services. The study provides for the first time estimates for several factors associated with the large variation in the utilization and provision of paediatric health care resources in Switzerland.

Validation of a new method for determination of cup orientation in THA

Our goal was to validate accuracy, consistency, and reproducibility/reliability of a new method for determining cup orientation in total hip arthroplasty (THA). This method allows matching the 3D-model from CT images or slices with the projected pelvis on an anteroposterior pelvic radiograph using a fully automated registration procedure. Cup orientation (inclination and anteversion) is calculated relative to the anterior pelvic plane, corrected for individual malposition of the pelvis during radiograph acquisition. Measurements on blinded and randomized radiographs of 80 cadaver and 327 patient hips were investigated. The method showed a mean accuracy of 0.7 +/- 1.7 degrees (-3.7 degrees to 4.0 degrees) for inclination and 1.2 +/- 2.4 degrees (-5.3 degrees to 5.6 degrees) for anteversion in the cadaver trials and 1.7 +/- 1.7 degrees (-4.6 degrees to 5.5 degrees) for inclination and 0.9 +/- 2.8 degrees (-5.2 degrees to 5.7 degrees) for anteversion in the clinical data when compared to CT-based measurements. No systematic errors in accuracy were detected with the Bland-Altman analysis. The software consistency and the reproducibility/reliability were very good. This software is an accurate, consistent, reliable, and reproducible method to measure cup orientation in THA using a sophisticated 2D/3D-matching technique. Its robust and accurate matching algorithm can be expanded to statistical models.

Hemodynamic variables and mortality in cardiogenic shock: a retrospective cohort study

INTRODUCTION: Despite the key role of hemodynamic goals, there are few data addressing the question as to which hemodynamic variables are associated with outcome or should be targeted in cardiogenic shock patients. The aim of this study was to investigate the association between hemodynamic variables and cardiogenic shock mortality. METHODS: Medical records and the patient data management system of a multidisciplinary intensive care unit (ICU) were reviewed for patients admitted because of cardiogenic shock. In all patients, the hourly variable time integral of hemodynamic variables during the first 24 hours after ICU admission was calculated. If hemodynamic variables were associated with 28-day mortality, the hourly variable time integral of drops below clinically relevant threshold levels was computed. Regression models and receiver operator characteristic analyses were calculated. All statistical models were adjusted for age, admission year, mean catecholamine doses and the Simplified Acute Physiology Score II (excluding hemodynamic counts) in order to account for the influence of age, changes in therapies during the observation period, the severity of cardiovascular failure and the severity of the underlying disease on 28-day mortality. RESULTS: One-hundred and nineteen patients were included. Cardiac index (CI) (P = 0.01) and cardiac power index (CPI) (P = 0.03) were the only hemodynamic variables separately associated with mortality. The hourly time integral of CI drops <3, 2.75 (both P = 0.02) and 2.5 (P = 0.03) L/min/m2 was associated with death but not that of CI drops <2 L/min/m2 or lower thresholds (all P > 0.05). The hourly time integral of CPI drops <0.5-0.8 W/m2 (all P = 0.04) was associated with 28-day mortality but not that of CPI drops <0.4 W/m2 or lower thresholds (all P > 0.05). CONCLUSIONS: During the first 24 hours after intensive care unit admission, CI and CPI are the most important hemodynamic variables separately associated with 28-day mortality in patients with cardiogenic shock. A CI of 3 L/min/m2 and a CPI of 0.8 W/m2 were most predictive of 28-day mortality. Since our results must be considered hypothesis-generating, randomized controlled trials are required to evaluate whether targeting these levels as early resuscitation endpoints can improve mortality in cardiogenic shock.