We conducted an extended follow-up and spatial analysis of the American Cancer Society (ACS) Cancer Prevention Study II (CPS-II) cohort in order to further examine associations between long-term exposure to particulate air pollution and mortality in large U.S. cities. The current study sought to clarify outstanding scientific issues that arose from our earlier HEI-sponsored Reanalysis of the original ACS study data (the Particle Epidemiology Reanalysis Project). Specifically, we examined (1) how ecologic covariates at the community and neighborhood levels might confound and modify the air pollution-mortality association; (2) how spatial autocorrelation and multiple levels of data (e.g., individual and neighborhood) can be taken into account within the random effects Cox model; (3) how using land-use regression to refine measurements of air pollution exposure to the within-city (or intra-urban) scale might affect the size and significance of health effects in the Los Angeles and New York City regions; and (4) what exposure time windows may be most critical to the air pollution-mortality association. The 18 years of follow-up (extended from 7 years in the original study [Pope et al. 1995]) included vital status data for the CPS-II cohort (approximately 1.2 million participants) with multiple cause-of-death codes through December 31, 2000 and more recent exposure data from air pollution monitoring sites for the metropolitan areas. In the Nationwide Analysis, the influence of ecologic covariate data (such as education attainment, housing characteristics, and level of income; data obtained from the 1980 U.S. Census; see Ecologic Covariates sidebar on page 14) on the air pollution-mortality association were examined at the Zip Code area (ZCA) scale, the metropolitan statistical area (MSA) scale, and by the difference between each ZCA value and the MSA value (DIFF). In contrast to previous analyses that did not directly include ecologic covariates at the ZCA scale, risk estimates increased when ecologic covariates were included at all scales. The ecologic covariates exerted their greatest effect on mortality from ischemic heart disease (IHD), which was also the health outcome most strongly related with exposure to PM2.5 (particles 2.5 microm or smaller in aerodynamic diameter), sulfate (SO4(2-)), and sulfur dioxide (SO2), and the only outcome significantly associated with exposure to nitrogen dioxide (NO2). When ecologic covariates were simultaneously included at both the MSA and DIFF levels, the hazard ratio (HR) for mortality from IHD associated with PM2.5 exposure (average concentration for 1999-2000) increased by 7.5% and that associated with SO4(2-) exposure (average concentration for 1990) increased by 12.8%. The two covariates found to exert the greatest confounding influence on the PM2.5-mortality association were the percentage of the population with a grade 12 education and the median household income. Also in the Nationwide Analysis, complex spatial patterns in the CPS-II data were explored with an extended random effects Cox model (see Glossary of Statistical Terms at end of report) that is capable of clustering up to two geographic levels of data. Using this model tended to increase the HR estimate for exposure to air pollution and also to inflate the uncertainty in the estimates. Including ecologic covariates decreased the variance of the results at both the MSA and ZCA scales; the largest decrease was in residual variation based on models in which the MSA and DIFF levels of data were included together, which suggests that partitioning the ecologic covariates into between-MSA and within-MSA values more completely captures the sources of variation in the relationship between air pollution, ecologic covariates, and mortality. Intra-Urban Analyses were conducted for the New York City and Los Angeles regions. The results of the Los Angeles spatial analysis, where we found high exposure contrasts within the Los Angeles region, showed that air pollution-mortality risks were nearly 3 times greater than those reported from earlier analyses. This suggests that chronic health effects associated with intra-urban gradients in exposure to PM2.5 may be even larger between ZCAs within an MSA than the associations between MSAs that have been previously reported. However, in the New York City spatial analysis, where we found very little exposure contrast between ZCAs within the New York region, mortality from all causes, cardiopulmonary disease (CPD), and lung cancer was not elevated. A positive association was seen for PM2.5 exposure and IHD, which provides evidence of a specific association with a cause of death that has high biologic plausibility. These results were robust when analyses controlled (1) the 44 individual-level covariates (from the ACS enrollment questionnaire in 1982; see 44 Individual-Level Covariates sidebar on page 22) and (2) spatial clustering using the random effects Cox model. Effects were mildly lower when unemployment at the ZCA scale was included. To examine whether there is a critical exposure time window that is primarily responsible for the increased mortality associated with ambient air pollution, we constructed individual time-dependent exposure profiles for particulate and gaseous air pollutants (PM2.5 and SO2) for a subset of the ACS CPS-II participants for whom residence histories were available. The relevance of the three exposure time windows we considered was gauged using the magnitude of the relative risk (HR) of mortality as well as the Akaike information criterion (AIC), which measures the goodness of fit of the model to the data. For PM2.5, no one exposure time window stood out as demonstrating the greatest HR; nor was there any clear pattern of a trend in HR going from recent to more distant windows or vice versa. Differences in AIC values among the three exposure time windows were also small. The HRs for mortality associated with exposure to SO2 were highest in the most recent time window (1 to 5 years), although none of these HRs were significantly elevated. Identifying critical exposure time windows remains a challenge that warrants further work with other relevant data sets. This study provides additional support toward developing cost-effective air quality management policies and strategies. The epidemiologic results reported here are consistent with those from other population-based studies, which collectively have strongly supported the hypothesis that long-term exposure to PM2.5 increases mortality in the general population. Future research using the extended Cox-Poisson random effects methods, advanced geostatistical modeling techniques, and newer exposure assessment techniques will provide additional insight.

/pdf/extended-follow-up-and-spatial-analysis-of-the-american-4gnmhravlu.pdf

Extended follow-up and spatial analysis of the American Cancer Society study linking particulate air pollution and mortality.

Particle filters for dynamic state-space models handling unknown static parameters are discussed. The approach is based on marginalizing the static parameters out of the posterior distribution such that only the state vector needs to be considered. Such a marginalization can always be applied. However, real-time applications are only possible when the distribution of the unknown parameters given both observations and the hidden state vector depends on some low-dimensional sufficient statistics. Such sufficient statistics are present in many of the commonly used state-space models. Marginalizing the static parameters avoids the problem of impoverishment, which typically occurs when static parameters are included as part of the state vector. The filters are tested on several different models, with promising results.

/pdf/particle-filters-for-state-space-models-with-the-presence-of-29wjm1wyzq.pdf

Particle filters for state-space models with the presence of unknown static parameters

The analysis of non-Gaussian time series by using state space models is considered from both classical and Bayesian perspectives. The treatment in both cases is based on simulation using importance sampling and antithetic variables; Markov chain Monte Carlo methods are not employed. Non-Gaussian disturbances for the state equation as well as for the observation equation are considered. Methods for estimating conditional and posterior means of functions of the state vector given the observations, and the mean-square errors of their estimates, are developed. These methods are extended to cover the estimation of conditional and posterior densities and distribution functions. The choice of importance sampling densities and antithetic variables is discussed. The techniques work well in practice and are computationally efficient. Their use is illustrated by applying them to a univariate discrete time series, a series with outliers and a volatility series.

/pdf/time-series-analysis-of-non-gaussian-observations-based-on-2wrtl7p2o1.pdf

Time series analysis of non‐Gaussian observations based on state space models from both classical and Bayesian perspectives

Longitudinal experiments often involve multiple outcomes measured repeatedly within a set of study participants. While many questions can be answered by modeling the various outcomes separately, some questions can only be answered in a joint analysis of all of them. In this article, we will present a review of the many approaches proposed in the statistical literature. Four main model families will be presented, discussed and compared. Focus will be on presenting advantages and disadvantages of the different models rather than on the mathematical or computational details.

/pdf/the-analysis-of-multivariate-longitudinal-data-a-review-1z4rcr2pke.pdf

The analysis of multivariate longitudinal data: a review.

A framework for the statistical analysis of counts from infectious disease surveillance databases is proposed. In its simplest form, the model can be seen as a Poisson branching process model with immigration. Extensions to include seasonal effects, time trends and overdispersion are outlined. The model is shown to provide an adequate fit and reliable one-step-ahead prediction intervals for a typical infectious disease time series. In addition, a multivariate formulation is proposed, which is well suited to capture space-time dependence caused by the spatial spread of a disease over time. An analysis of two multivariate time series is described. All analyses have been done using general optimization routines, where ML estimates and corresponding standard errors are readily available.

A statistical framework for the analysis of multivariate infectious disease surveillance counts

SUMMARY We propose a nonstationary state space model for multivariate longitudinal count data driven by a latent gamma Markov process. The Poisson counts are assumed to be conditionally independent given the latent process, both over time and across categories. We consider a regression model where time-varying covariates may enter via either the Poisson model or the latent gamma process. Estimation is based on the Kalman smoother, and we consider analysis of residuals from both the Poisson model and the latent process. A reanalysis of Zeger's (1988) polio data shows that the choice between a stationary and nonstationary model is crucial for the correct assessment of the evidence of a long-term decrease in the rate of U.S. polio infection.

A state-space model for multivariate longitudinal count data

We propose a class of state-space models for multivariate longitudinal data where the components of the response vector may have different distributions. The approach is based on the class of Tweedie exponential dispersion models, which accommodates a wide variety of discrete, continuous and mixed data. The latent process is assumed to be a Markov process, and the observations are conditionally independent given the latent process, over time as well as over the components of the response vector. This provides a fully parametric alternative to the quasilikelihood approach of Liang and Zeger. We estimate the regression parameters for time-varying covariates entering either via the observation model or via the latent process, based on an estimating equation derived from the Kalman smoother. We also consider analysis of residuals from both the observation model and the latent process.



Nous proposons une classe de modeles pour des donnees longitudinales multivariees dont les composantes du vecteur de reponse peuvent avoir differentes distributions. L'approche est basee sur la classe des modeles exponentiels de dispersion de Tweedie, qui s'adapte a une grande variete de donnees, soit discretes, soit continues, soit mixtes. On suppose que le processus sous-jacent est markovien et que, en conditionnant sur ce processus, les observations sont independantes, a la fois dans le temps et dans les composantes du vecteur de reponse. Ceci constitue une alternative totalement parametrique a l'approche de quasi-vraisemblance de Liang et Zeger. Nous estimons les parametres de regression pour les covariables, qui varient dans le temps et qui interviennent dans le modele d'observation ainsi que dans le processus sous-jacent. Cette estimation est basee sur une equation derivee du regularisateur de Kalman. Nous etudions agalement les residus, pour le modele d'observation et pour le processus sous-jacent.

State‐space models for multivariate longitudinal data of mixed types

A new method for regression analysis of longitudinal counts is applied to data from Prince George, British Columbia, previously analysed by Knight et al. The data consist of daily recordings of the number of emergency room visits for each of four categories of respiratory diseases, along with measurements of meteorological variables and air pollution. We use a state-space model assuming conditionally independent Poisson counts for the four categories given a latent morbidity process, the latent process being a gamma Markov process. The main objective of the investigation was to examine the relationship between air pollution and respiratory morbidity, taking into account seasonality and meteorological conditions. We found that total reduced sulphur significantly influences the expected number of emergency room visits for the four disease categories, in agreement with the conclusion by Knight et al. However, our final model is simpler than theirs; in particular we found no evidence of seasonal variation beyond that explained by the meteorological variables.

A longitudinal study of emergency room visits and air pollution for Prince George, British Columbia

Correction: Longitudinal study of emergency room visits and air pollution for Prince George, British Columbia (Statistics in Medicine (1996) 15 (823-836))

. We study tail risk dynamics in high-frequency ﬁnancial markets and their connection with trading activity and market uncertainty. We introduce a dynamic extreme value regression model ac-commodating both stationary and local unit-root predictors to appropriately capture the time-varying behaviour of the distribution of high-frequency extreme losses. To characterize trading activity and market uncertainty, we consider several volatility and liquidity predictors, and propose a two-step adaptive L 1 -regularized maximum likelihood estimator to select the most appropriate ones. We establish the oracle property of the proposed estimator for selecting both stationary and local unit-root predictors, and show its good ﬁnite sample properties in an extensive simulation study. Studying the high-frequency extreme losses of nine large liquid U.S. stocks using 42 liquidity and volatility predictors, we ﬁnd the severity of extreme losses to be well predicted by low levels of price impact in period of high volatility of liquidity and volatility.

Li Sun

Papers

A state-space model for multivariate longitudinal count data

State‐space models for multivariate longitudinal data of mixed types

A longitudinal study of emergency room visits and air pollution for Prince George, British Columbia

Correction: Longitudinal study of emergency room visits and air pollution for Prince George, British Columbia (Statistics in Medicine (1996) 15 (823-836))

Measuring tail risk at high-frequency: An $L_1$-regularized extreme value regression approach with unit-root predictors