Forecasting waved daily COVID-19 death count series with a novel combination of segmented Poisson model and ARIMA models.

Autoregressive Integrated Moving Average (ARIMA) models have been widely used to forecast and model the development of various infectious diseases including COVID-19 outbreaks; however, such use of ARIMA models does not respect the count nature of the pandemic development data. For example, the daily COVID-19 death count series data for Canada and the United States (USA) are generally skewed with lots of low counts. In addition, there are generally waved patterns with turning points influenced by government major interventions against the spread of COVID-19 during different periods and seasons. In this study, we propose a novel combination of the segmented Poisson model and ARIMA models to handle these features and correlation structures in a two-stage process. The first stage of this process is a generalization of trend analysis of time series data. Our approach is illustrated with forecasting and modeling of daily COVID-19 death count series data for Canada and the USA.

Tweedie Compound Poisson Models with Covariate-Dependent Random Effects for Multilevel Semicontinuous Data.

Multilevel semicontinuous data occur frequently in medical, environmental, insurance and financial studies. Such data are often measured with covariates at different levels; however, these data have traditionally been modelled with covariate-independent random effects. Ignoring dependence of cluster-specific random effects and cluster-specific covariates in these traditional approaches may lead to ecological fallacy and result in misleading results. In this paper, we propose Tweedie compound Poisson model with covariate-dependent random effects to analyze multilevel semicontinuous data where covariates at different levels are incorporated at relevant levels. The estimation of our models has been developed based on the orthodox best linear unbiased predictor of random effect. Explicit expressions of random effects predictors facilitate computation and interpretation of our models. Our approach is illustrated through the analysis of the basic symptoms inventory study data where 409 adolescents from 269 families were observed at varying number of times from 1 to 17 times. The performance of the proposed methodology was also examined through the simulation studies.

Analysis of Longitudinal Binomial Data with Positive Association between the Number of Successes and the Number of Failures: An Application to Stock Instability Study.

Numerous methods have been developed for longitudinal binomial data in the literature. These traditional methods are reasonable for longitudinal binomial data with a negative association between the number of successes and the number of failures over time; however, a positive association may occur between the number of successes and the number of failures over time in some behaviour, economic, disease aggregation and toxicological studies as the numbers of trials are often random. In this paper, we propose a joint Poisson mixed modelling approach to longitudinal binomial data with a positive association between longitudinal counts of successes and longitudinal counts of failures. This approach can accommodate both a random and zero number of trials. It can also accommodate overdispersion and zero inflation in the number of successes and the number of failures. An optimal estimation method for our model has been developed using the orthodox best linear unbiased predictors. Our approach not only provides robust inference against misspecified random effects distributions, but also consolidates the subject-specific and population-averaged inferences. The usefulness of our approach is illustrated with an analysis of quarterly bivariate count data of stock daily limit-ups and limit-downs.

Linking dynamic patterns of COVID-19 spreads in Italy with regional characteristics: a two level longitudinal modelling approach.

The current statistical modeling of coronavirus (COVID-19) spread has mainly focused on spreading patterns and forecasting of COVID-19 development; these patterns have been found to vary among locations. As the survival time of coronaviruses on surfaces depends on temperature, some researchers have explored the association of daily confirmed cases with environmental factors. Furthermore, some researchers have studied the link between daily fatality rates with regional factors such as health resources, but found no significant factors. As the spreading patterns of COVID-19 development vary a lot among locations, fitting regression models of daily confirmed cases or fatality rates directly with regional factors might not reveal important relationships. In this study, we investigate the link between regional spreading patterns of COVID-19 development in Italy and regional factors in two steps. First, we characterize regional spreading patterns of COVID-19 daily confirmed cases by a special patterned Poisson regression model for longitudinal count; the varying growth and declining patterns as well as turning points among regions in Italy have been well captured by regional regression parameters. We then associate these regional regression parameters with regional factors. The effects of regional factors on spreading patterns of COVID-19 daily confirmed cases have been effectively evaluated.

Predicting turning point, duration and attack rate of COVID-19 outbreaks in major Western countries.

In this paper, we employed a segmented Poisson model to analyze the available daily new cases data of the COVID-19 outbreaks in the six Western countries of the Group of Seven, namely, Canada, France, Germany, Italy, UK and USA. We incorporated the governments' interventions (stay-at-home advises/orders, lockdowns, quarantines and social distancing) against COVID-19 into consideration. Our analysis allowed us to make a statistical prediction on the turning point (the time that the daily new cases peak), the duration (the period that the outbreak lasts) and the attack rate (the percentage of the total population that will be infected over the course of the outbreak) for these countries.

A Joint Poisson State-Space Modelling Approach to Analysis of Binomial Series with Random Cluster Sizes.

Serially correlation binomial data with random cluster sizes occur frequently in environmental and health studies. Such data series have traditionally been analyzed using binomial state-space or hidden Markov models without appropriately accounting for the randomness in the cluster sizes. To characterize correlation and extra-variation arising from the random cluster sizes properly, we introduce a joint Poisson state-space modelling approach to analysis of binomial series with random cluster sizes. This approach enables us to model the marginal counts and binomial proportions simultaneously. An optimal estimation of our model has been developed using the orthodox best linear unbiased predictors. This estimation method is computationally efficient and robust since it depends only on the first- and second- moment assumptions of unobserved random effects. Our proposed approach is illustrated with analysis of birth delivery data.

Tweedie family of generalized linear models with distribution-free random effects for skewed longitudinal data.

Generalized linear mixed models have played an important role in the analysis of longitudinal data; however, traditional approaches have limited flexibility in accommodating skewness and complex correlation structures. In addition, the existing estimation approaches generally rely heavily on the specifications of random effects distributions; therefore, the corresponding inferences are sometimes sensitive to the choice of random effect distributions under certain circumstance. In this paper, we incorporate serially dependent distribution-free random effects into Tweedie generalized linear models to accommodate a wide range of skewness and covariance structures for discrete and continuous longitudinal data. An optimal estimation of our model has been developed using the orthodox best linear unbiased predictors of random effects. Our approach unifies population-averaged and subject-specific inferences. Our method is illustrated through the analyses of patient-controlled analgesia data and Framingham cholesterol data.

Probing Laser-Induced Heterogeneous Microenvironment Changes in Room-Temperature Ionic Liquids.

Modulating the heterogeneous microenvironment in room-temperature ionic liquids (RTILs) by external stimuli is an important approach for understanding and designing external field-induced chemical reactions in natural and applied systems. Here, we report for the first time the redistribution of oxygen molecules related to microstructure changes in RTILs induced by an external laser field, which is probed simultaneously by the triplet-state dynamics of porphyrin. A remarkably long-lived triplet state of porphyrin is observed with changes of microstructures after irradiation, suggesting that charge-shifted O2 molecules are induced by the external field and/or rearranged intrinsic ions move from nonpolar domains into the polar domains of RTILs through electrostatic interactions. The results suggest that heterogeneous systems like ionic liquids in the presence of external stimuli can be designed for reaction systems associated with not only O2 but also for CO2 , CS2 , etc. and many other similar solvent molecules for many promising applications.

Intramolecular Charge Transfer and Solvation of Photoactive Molecules with Conjugated Push-Pull Structures.

A comparative investigation on the photophysical properties and solvation-related ICT dynamics of three push-pull compounds containing different donors including carbazole, triphenylamine and phenothiazine, was performed. The steady-state spectra and theoretical calculations show the charge transfers from the central donors to the acceptors at each side. The characterization of the extent of charge transfer was determined by various means, including estimation of the dipole moment, the electron density distribution of HOMO and LUMO, CDD and change in Gibb's free energy, which show the charge transfer strength to be in the order PDHP > BDHT > PDHC. This suggests that the electron-donating ability of the donor groups plays a crucial role in the charge transfer in these compounds. The TA data show the excited-state relaxation dynamics follow a sequential model: FC→ICT→ICT'→S0 , and are affected by the solvent polarity. The results presented here demonstrate that the compound with a higher degree of ICT characteristic interacts more strongly with stronger polar solvent molecules, which can accelerate the solvation and spectral evolution to lower energy levels. The A-π-D-π-A architectures with prominent ICT characteristics based on carbazole, triphenylamine and phenothiazine might be potential scaffolds for light-harvesting and photovoltaic devices. These results are of value for understanding structure-property relationships and the rational design of functional materials for photoelectric applications.

Enhanced fluorescence of [[5'-(4-hydroxyphenyl)[2,2'-bithiophen]-5-yl]methylene]-propanedinitrile (NIAD-4): solvation induced micro-viscosity enhancement.

Excited state solvation plays a very important role in modulating the emission behavior of fluorophores upon excitation. Here, the solvation effects on the local micro-environment around a fluorophore are proposed by investigating the fantastic emission behavior of a novel amyloid fibril marker, NIAD-4, in different alcoholic and aprotic solvents. In alcoholic solvents, high solvent viscosity causes an obvious enhancement of fluorescence because of the restriction of torsion of NIAD-4, where the formation of a non-fluorescent twist intramolecular charge transfer (TICT) state is suppressed. In aprotic solvents, high solvent polarity leads to a remarkable redshift of the emission spectra suggesting strong solvation. Surprisingly, an abnormal fluorescence enhancement of NIAD-4 is observed with increasing solvent polarity of the aprotic solvents, whereas solvent viscosity plays little role in influencing the fluorescence intensity. We conclude that such an abnormal phenomenon is originated from a solvation induced micro-viscosity enhancement around the fluorophore upon excitation which restricts the torsion of NIAD-4. Femtosecond transient absorption results further prove such a micro-viscosity increasing mechanism. We believe that this solvation induced micro-viscosity enhancement effect on fluorescence could widely exist for most donor-π-acceptor (D-π-A) compounds in polar solvents, which should be carefully taken into consideration when probing the micro-viscosity in polar environments, especially in complex bioenvironments.

Pattern-mixture zero-inflated mixed models for longitudinal unbalanced count data with excessive zeros.

Analysis of longitudinal data with excessive zeros has gained increasing attention in recent years; however, current approaches to the analysis of longitudinal data with excessive zeros have primarily focused on balanced data. Dropouts are common in longitudinal studies; therefore, the analysis of the resulting unbalanced data is complicated by the missing mechanism. Our study is motivated by the analysis of longitudinal skin cancer count data presented by Greenberg, Baron, Stukel, Stevens, Mandel, Spencer, Elias, Lowe, Nierenberg, Bayrd, Vance, Freeman, Clendenning, Kwan, and the Skin Cancer Prevention Study Group[New England Journal of Medicine 323, 789-795]. The data consist of a large number of zero responses (83% of the observations) as well as a substantial amount of dropout (about 52% of the observations). To account for both excessive zeros and dropout patterns, we propose a pattern-mixture zero-inflated model with compound Poisson random effects for the unbalanced longitudinal skin cancer data. We also incorporate an autoregressive of order 1 correlation structure in the model to capture longitudinal correlation of the count responses. A quasi-likelihood approach has been developed in the estimation of our model. We illustrated the method with analysis of the longitudinal skin cancer data.

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

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.

Modelling heterogeneity in clustered count data with extra zeros using compound Poisson random effect.

In medical and health studies, heterogeneities in clustered count data have been traditionally modeled by positive random effects in Poisson mixed models; however, excessive zeros often occur in clustered medical and health count data. In this paper, we consider a three-level random effects zero-inflated Poisson model for health-care utilization data where data are clustered by both subjects and families. To accommodate zero and positive components in the count response compatibly, we model the subject level random effects by a compound Poisson distribution. Our model displays a variance components decomposition which clearly reflects the hierarchical structure of clustered data. A quasi-likelihood approach has been developed in the estimation of our model. We illustrate the method with analysis of the health-care utilization data. The performance of our method is also evaluated through simulation studies.

Spatial analysis of air pollution and mortality in Los Angeles.

BACKGROUND: The assessment of air pollution exposure using only community average concentrations may lead to measurement error that lowers estimates of the health burden attributable to poor air quality. To test this hypothesis, we modeled the association between air pollution and mortality using small-area exposure measures in Los Angeles, California. METHODS: Data on 22,905 subjects were extracted from the American Cancer Society cohort for the period 1982-2000 (5,856 deaths). Pollution exposures were interpolated from 23 fine particle (PM2.5) and 42 ozone (O3) fixed-site monitors. Proximity to expressways was tested as a measure of traffic pollution. We assessed associations in standard and spatial multilevel Cox regression models. RESULTS: After controlling for 44 individual covariates, all-cause mortality had a relative risk (RR) of 1.17 (95% confidence interval=1.05-1.30) for an increase of 10 mug/m PM2.5 and a RR of 1.11 (0.99-1.25) with maximal control for both individual and contextual confounders. The RRs for mortality resulting from ischemic heart disease and lung cancer deaths were elevated, in the range of 1.24-1.6, depending on the model used. These PM results were robust to adjustments for O3 and expressway exposure. CONCLUSION: Our results suggest the chronic health effects associated with within-city gradients in exposure to PM2.5 may be even larger than previously reported across metropolitan areas. We observed effects nearly 3 times greater than in models relying on comparisons between communities. We also found specificity in cause of death, with PM2.5 associated more strongly with ischemic heart disease than with cardiopulmonary or all-cause mortality.

Spatial regression models for large-cohort studies linking community air pollution and health.

Cohort study designs are often used to assess the association between community-based ambient air pollution concentrations and health outcomes, such as mortality, development and prevalence of disease, and pulmonary function. Typically, a large number of subjects are enrolled in the study in each of a small number of communities. Fixed-site monitors are used to determine long-term exposure to ambient pollution. The association between community average pollution levels and health is determined after controlling for risk factors of the health outcome measured at the individual level (i.e., smoking). We present a new spatial regression model linking spatial variation in ambient air pollution to health. Health outcomes can be measured as continuous variables (pulmonary function), binary variables (prevalence of disease), or time-to-event data (survival or development of disease). The model incorporates risk factors measured at the individual level, such as smoking, and at the community level, such as air pollution. We demonstrate that the spatial autocorrelation in community health outcomes, an indication of not fully characterizing potentially confounding risk factors to the air pollution--health association, can be accounted for through the inclusion of location in the deterministic component of the model assessing the effects of air pollution on health or through a distance-decay spatial autocorrelation function in the stochastic component of the model, or both. We present a statistical approach that can be implemented for very large cohort studies. Our methods are illustrated with an analysis of the American Cancer Society cohort to determine whether the prevalence of heart disease is associated with concentrations of sulfate particles. From a statistical point of view, it appears that a location surface in the deterministic component of the model was preferred to a distance-decay autocorrelation structure in the model's stochastic component.