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.

Evolutionary demography of long-lived monocarpic perennials: a time-lagged integral projection model

1. The evolution of flowering strategies (when and at what size to flower) in monocarpic perennials is determined by balancing current reproduction with expected future reproduction, and these are largely determined by size-specific patterns of growth and survival. However, because of the difficulty in following long-lived individuals throughout their lives, this theory has largely been tested using short-lived species (< 5 years). 2. Here, we tested this theory using the long-lived monocarpic perennial Campanula thyrsoides which can live up to 16 years. We used a novel approach that combined permanent plot and herb chronology data from a 3-year field study to parameterize and validate integral projection models (IPMs). 3. Similar to other monocarpic species, the rosette leaves of C. thyrsoides wither over winter and so size cannot be measured in the year of flowering. We therefore extended the existing IPM framework to incorporate an additional time delay that arises because flowering demography must be predicted from rosette size in the year before flowering. 4. We found that all main demographic functions (growth, survival probability, flowering probability and fecundity) were strongly size-dependent and there was a pronounced threshold size of flowering. There was good agreement between the predicted distribution of flowering ages obtained from the IPMs and that estimated in the field. Mostly, there was good agreement between the IPM predictions and the direct quantitative field measurements regarding the demographic parameters lambda, R-0 and T. We therefore conclude that the model captures the main demographic features of the field populations. 5. Elasticity analysis indicated that changes in the survival and growth function had the largest effect (c. 80%) on lambda and this was considerably larger than in short-lived monocarps. We found only weak selection pressure operating on the observed flowering strategy which was close to the predicted evolutionary stable strategy. 6. Synthesis. The extended IPM accurately described the demography of a long-lived monocarpic perennial using data collected over a relatively short period. We could show that the evolution of flowering strategies in short- and long-lived monocarps seem to follow the same general rules but with a longevity-related emphasis on survival over fecundity.

Incorporating Latent Variables into Discrete Choice Models - A Simultaneous Estimation Approach Using SEM Software

Integrated choice and latent variable (ICLV) models represent a promising new class of models which merge classic choice models with the structural equation approach (SEM) for latent variables. Despite their conceptual appeal, applications of ICLV models in marketing remain rare. We extend previous ICLV applications by first estimating a multinomial choice model and, second, by estimating hierarchical relations between latent variables. An empirical study on travel mode choice clearly demonstrates the value of ICLV models to enhance the understanding of choice processes. In addition to the usually studied directly observable variables such as travel time, we show how abstract motivations such as power and hedonism as well as attitudes such as a desire for flexibility impact on travel mode choice. Furthermore, we show that it is possible to estimate such a complex ICLV model with the widely available structural equation modeling package Mplus. This finding is likely to encourage more widespread application of this appealing model class in the marketing field.

Prediction of PA12 melt viscosity in Laser Sintering by a Time and Temperature dependent rheological model

Ein auf Basis von Prozessdaten kalibriertes Viskositätsmodell wird vorgeschlagen und zur Vorhersage der Viskosität einer Polyamid 12 (PA12) Kunststoffschmelze als Funktion von Zeit, Temperatur und Schergeschwindigkeit angewandt. Im ersten Schritt wurde das Viskositätsmodell aus experimentellen Daten abgeleitet. Es beruht hauptsächlich auf dem drei-parametrigen Ansatz von Carreau, wobei zwei zusätzliche Verschiebungsfaktoren eingesetzt werden. Die Temperaturabhängigkeit der Viskosität wird mithilfe des Verschiebungsfaktors aT von Arrhenius berücksichtigt. Ein weiterer Verschiebungsfaktor aSC (Structural Change) wird eingeführt, der die Strukturänderung von PA12 als Folge der Prozessbedingungen beim Lasersintern beschreibt. Beobachtet wurde die Strukturänderung in Form einer signifikanten Viskositätserhöhung. Es wurde geschlussfolgert, dass diese Viskositätserhöhung auf einen Molmassenaufbau zurückzuführen ist und als Nachkondensation verstanden werden kann. Abhängig von den Zeit- und Temperaturbedingungen wurde festgestellt, dass die Viskosität als Folge des Molmassenaufbaus exponentiell gegen eine irreversible Grenze strebt. Die Geschwindigkeit dieser Nachkondensation ist zeit- und temperaturabhängig. Es wird angenommen, dass die Pulverbetttemperatur einen Molmassenaufbau verursacht und es damit zur Kettenverlängerung kommt. Dieser fortschreitende Prozess der zunehmenden Kettenlängen setzt molekulare Beweglichkeit herab und unterbindet die weitere Nachkondensation. Der Verschiebungsfaktor aSC drückt diese physikalisch-chemische Modellvorstellung aus und beinhaltet zwei zusätzliche Parameter. Der Parameter aSC,UL entspricht der oberen Viskositätsgrenze, wohingegen k0 die Strukturänderungsrate angibt. Es wurde weiterhin festgestellt, dass es folglich nützlich ist zwischen einer Fließaktivierungsenergie und einer Strukturänderungsaktivierungsenergie für die Berechnung von aT und aSC zu unterscheiden. Die Optimierung der Modellparameter erfolgte mithilfe eines genetischen Algorithmus. Zwischen berechneten und gemessenen Viskositäten wurde eine gute Übereinstimmung gefunden, so dass das Viskositätsmodell in der Lage ist die Viskosität einer PA12 Kunststoffschmelze als Folge eines kombinierten Lasersinter Zeit- und Temperatureinflusses vorherzusagen. Das Modell wurde im zweiten Schritt angewandt, um die Viskosität während des Lasersinter-Prozesses in Abhängigkeit von der Energiedichte zu berechnen. Hierzu wurden Prozessdaten, wie Schmelzetemperatur und Belichtungszeit benutzt, die mithilfe einer High-Speed Thermografiekamera on-line gemessen wurden. Abschließend wurde der Einfluss der Strukturänderung auf das Viskositätsniveau im Prozess aufgezeigt.

A reduced model clarifies the role of feedback loops and time delays in the Drosophila circadian oscillator.

Although several detailed models of molecular processes essential for circadian oscillations have been developed, their complexity makes intuitive understanding of the oscillation mechanism difficult. The goal of the present study was to reduce a previously developed, detailed model to a minimal representation of the transcriptional regulation essential for circadian rhythmicity in Drosophila. The reduced model contains only two differential equations, each with time delays. A negative feedback loop is included, in which PER protein represses per transcription by binding the dCLOCK transcription factor. A positive feedback loop is also included, in which dCLOCK indirectly enhances its own formation. The model simulated circadian oscillations, light entrainment, and a phase-response curve with qualitative similarities to experiment. Time delays were found to be essential for simulation of circadian oscillations with this model. To examine the robustness of the simplified model to fluctuations in molecule numbers, a stochastic variant was constructed. Robust circadian oscillations and entrainment to light pulses were simulated with fewer than 80 molecules of each gene product present on average. Circadian oscillations persisted when the positive feedback loop was removed. Moreover, elimination of positive feedback did not decrease the robustness of oscillations to stochastic fluctuations or to variations in parameter values. Such reduced models can aid understanding of the oscillation mechanisms in Drosophila and in other organisms in which feedback regulation of transcription may play an important role.

Time-dependent and somatically acquired mitochondrial DNA mutagenesis and respiratory chain dysfunction in a scleroderma model of lung fibrosis.

Reactive oxygen species (ROS) have been implemented in the etiology of pulmonary fibrosis (PF) in systemic sclerosis. In the bleomycin model, we evaluated the role of acquired mutations in mitochondrial DNA (mtDNA) and respiratory chain defects as a trigger of ROS formation and fibrogenesis. Adult male Wistar rats received a single intratracheal instillation of bleomycin and their lungs were examined at different time points. Ashcroft scores, collagen and TGFβ1 levels documented a delayed onset of PF by day 14. In contrast, increased malon dialdehyde as a marker of ROS formation was detectable as early as 24 hours after bleomycin instillation and continued to increase. At day 7, lung tissue acquired significant amounts of mtDNA deletions, translating into a significant dysfunction of mtDNA-encoded, but not nucleus-encoded respiratory chain subunits. mtDNA deletions and markers of mtDNA-encoded respiratory chain dysfunction significantly correlated with pulmonary TGFβ1 concentrations and predicted PF in a multivariate model.

From quantum to classical dynamics: The relativistic O ( N ) model in the framework of the real-time functional renormalization group

We investigate the transition from unitary to dissipative dynamics in the relativistic O(N) vector model with the λ(φ2)2 interaction using the nonperturbative functional renormalization group in the real-time formalism. In thermal equilibrium, the theory is characterized by two scales, the interaction range for coherent scattering of particles and the mean free path determined by the rate of incoherent collisions with excitations in the thermal medium. Their competition determines the renormalization group flow and the effective dynamics of the model. Here we quantify the dynamic properties of the model in terms of the scale-dependent dynamic critical exponent z in the limit of large temperatures and in 2≤d≤4 spatial dimensions. We contrast our results to the behavior expected at vanishing temperature and address the question of the appropriate dynamic universality class for the given microscopic theory.

Time-order errors and standard-position effects in duration discrimination: An experimental study and an analysis by the sensation-weighting model

Studies have shown that the discriminability of successive time intervals depends on the presentation order of the standard (St) and the comparison (Co) stimuli. Also, this order affects the point of subjective equality. The first effect is here called the standard-position effect (SPE); the latter is known as the time-order error. In the present study, we investigated how these two effects vary across interval types and standard durations, using Hellström’s sensation-weighting model to describe the results and relate them to stimulus comparison mechanisms. In Experiment 1, four modes of interval presentation were used, factorially combining interval type (filled, empty) and sensory modality (auditory, visual). For each mode, two presentation orders (St–Co, Co–St) and two standard durations (100 ms, 1,000 ms) were used; half of the participants received correctness feedback, and half of them did not. The interstimulus interval was 900 ms. The SPEs were negative (i.e., a smaller difference limen for St–Co than for Co–St), except for the filled-auditory and empty-visual 100-ms standards, for which a positive effect was obtained. In Experiment 2, duration discrimination was investigated for filled auditory intervals with four standards between 100 and 1,000 ms, an interstimulus interval of 900 ms, and no feedback. Standard duration interacted with presentation order, here yielding SPEs that were negative for standards of 100 and 1,000 ms, but positive for 215 and 464 ms. Our findings indicate that the SPE can be positive as well as negative, depending on the interval type and standard duration, reflecting the relative weighting of the stimulus information, as is described by the sensation-weighting model.

A Dynamic Stochastic Frontier Production Model with Time-Varying Efficiency

In this paper we introduce technical efficiency via the intercept that evolve over time as a AR(1) process in a stochastic frontier (SF) framework in a panel data framework. Following are the distinguishing features of the model. First, the model is dynamic in nature. Second, it can separate technical inefficiency from fixed firm-specific effects which are not part of inefficiency. Third, the model allows one to estimate technical change separate from change in technical efficiency. We propose the ML method to estimate the parameters of the model. Finally, we derive expressions to calculate/predict technical inefficiency (efficiency).

Mixture modeling for joint analysis of survival, discrete, and continuous data

Mixture modeling is commonly used to model categorical latent variables that represent subpopulations in which population membership is unknown but can be inferred from the data. In relatively recent years, the potential of finite mixture models has been applied in time-to-event data. However, the commonly used survival mixture model assumes that the effects of the covariates involved in failure times differ across latent classes, but the covariate distribution is homogeneous. The aim of this dissertation is to develop a method to examine time-to-event data in the presence of unobserved heterogeneity under a framework of mixture modeling. A joint model is developed to incorporate the latent survival trajectory along with the observed information for the joint analysis of a time-to-event variable, its discrete and continuous covariates, and a latent class variable. It is assumed that the effects of covariates on survival times and the distribution of covariates vary across different latent classes. The unobservable survival trajectories are identified through estimating the probability that a subject belongs to a particular class based on observed information. We applied this method to a Hodgkin lymphoma study with long-term follow-up and observed four distinct latent classes in terms of long-term survival and distributions of prognostic factors. Our results from simulation studies and from the Hodgkin lymphoma study demonstrated the superiority of our joint model compared with the conventional survival model. This flexible inference method provides more accurate estimation and accommodates unobservable heterogeneity among individuals while taking involved interactions between covariates into consideration.^

The number and timing of time -dependent covariate measurements for the Cox regression model

The problem of analyzing data with updated measurements in the time-dependent proportional hazards model arises frequently in practice. One available option is to reduce the number of intervals (or updated measurements) to be included in the Cox regression model. We empirically investigated the bias of the estimator of the time-dependent covariate while varying the effect of failure rate, sample size, true values of the parameters and the number of intervals. We also evaluated how often a time-dependent covariate needs to be collected and assessed the effect of sample size and failure rate on the power of testing a time-dependent effect.^ A time-dependent proportional hazards model with two binary covariates was considered. The time axis was partitioned into k intervals. The baseline hazard was assumed to be 1 so that the failure times were exponentially distributed in the ith interval. A type II censoring model was adopted to characterize the failure rate. The factors of interest were sample size (500, 1000), type II censoring with failure rates of 0.05, 0.10, and 0.20, and three values for each of the non-time-dependent and time-dependent covariates (1/4,1/2,3/4).^ The mean of the bias of the estimator of the coefficient of the time-dependent covariate decreased as sample size and number of intervals increased whereas the mean of the bias increased as failure rate and true values of the covariates increased. The mean of the bias of the estimator of the coefficient was smallest when all of the updated measurements were used in the model compared with two models that used selected measurements of the time-dependent covariate. For the model that included all the measurements, the coverage rates of the estimator of the coefficient of the time-dependent covariate was in most cases 90% or more except when the failure rate was high (0.20). The power associated with testing a time-dependent effect was highest when all of the measurements of the time-dependent covariate were used. An example from the Systolic Hypertension in the Elderly Program Cooperative Research Group is presented. ^

Three time-slice simulations of the Eemian (eem), the mid-Holocene (hol), and a pre-industrial (pri) control run with the coupled atmosphere-ocean-model ECHAM5/MPI-OM

Orbital forcing does not only exert direct insolation effects, but also alters climate indirectly through feedback mechanisms that modify atmosphere and ocean dynamics and meridional heat and moisture transfers. We investigate the regional effects of these changes by detailed analysis of atmosphere and ocean circulation and heat transports in a coupled atmosphere-ocean-sea ice-biosphere general circulation model (ECHAM5/JSBACH/MPI-OM). We perform long term quasi equilibrium simulations under pre-industrial, mid-Holocene (6000 years before present - yBP), and Eemian (125 000 yBP) orbital boundary conditions. Compared to pre-industrial climate, Eemian and Holocene temperatures show generally warmer conditions at higher and cooler conditions at lower latitudes. Changes in sea-ice cover, ocean heat transports, and atmospheric circulation patterns lead to pronounced regional heterogeneity. Over Europe, the warming is most pronounced over the north-eastern part in accordance with recent reconstructions for the Holocene. We attribute this warming to enhanced ocean circulation in the Nordic Seas and enhanced ocean-atmosphere heat flux over the Barents Shelf in conduction with retreat of sea ice and intensified winter storm tracks over northern Europe.

Lagrangian back-tracing results for Kohnen station; output of time dependent numerical experiment with a 3D nested Antarctic ice sheet model

A nested ice flow model was developed for eastern Dronning Maud Land to assist with the dating and interpretation of the EDML deep ice core. The model consists of a high-resolution higher-order ice dynamic flow model that was nested into a comprehensive 3-D thermomechanical model of the whole Antarctic ice sheet. As the drill site is on a flank position the calculations specifically take into account the effects of horizontal advection as deeper ice in the core originated from higher inland. First the regional velocity field and ice sheet geometry is obtained from a forward experiment over the last 8 glacial cycles. The result is subsequently employed in a Lagrangian backtracing algorithm to provide particle paths back to their time and place of deposition. The procedure directly yields the depth-age distribution, surface conditions at particle origin, and a suite of relevant parameters such as initial annual layer thickness. This paper discusses the method and the main results of the experiment, including the ice core chronology, the non-climatic corrections needed to extract the climatic part of the signal, and the thinning function. The focus is on the upper 89% of the ice core (appr. 170 kyears) as the dating below that is increasingly less robust owing to the unknown value of the geothermal heat flux. It is found that the temperature biases resulting from variations of surface elevation are up to half of the magnitude of the climatic changes themselves.

X-ray fluorescence scanning of discrete samples on the Schwalbenberg II loess-paleosol sequence, raw data, magnetic susceptibility, organic carbon and U-ratio as grainsize index

The Schwalbenberg II loess-paleosol sequence (LPS) denotes a key site for Marine Isotope Stage (MIS 3) in Western Europe owing to eight succeeding cambisols, which primarily constitute the Ahrgau Subformation. Therefore, this LPS qualifies as a test candidate for the potential of temporal high-resolution geochemical data obtained X-ray fluorescence (XRF) scanning of discrete samplesproviding a fast and non-destructive tool for determining the element composition. The geochemical data is first contextualized to existing proxy data such as magnetic susceptibility (MS) and organic carbon (Corg) and then aggregated to element log ratios characteristic for weathering intensity [LOG (Ca/Sr), LOG (Rb/Sr), LOG (Ba/Sr), LOG (Rb/K)] and dust provenance [LOG (Ti/Zr), LOG (Ti/Al), LOG (Si/Al)]. Generally, an interpretation of rock magnetic particles is challenged in western Europe, where not only magnetic enhancement but also depletion plays a role. Our data indicates leaching and top-soil erosion induced MS depletion at the Schwalbenberg II LPS. Besides weathering, LOG (Ca/Sr) is susceptible for secondary calcification. Thus, also LOG (Rb/Sr) and LOG (Ba/Sr) are shown to be influenced by calcification dynamics. Consequently, LOG (Rb/K) seems to be the most suitable weathering index identifying the Sinzig Soils S1 and S2 as the most pronounced paleosols for this site. Sinzig Soil S3 is enclosed by gelic gleysols and in contrast to S1 and S2 only initially weathered pointing to colder climate conditions. Also the Remagen Soils are characterized by subtle to moderate positive excursions in the weathering indices. Comparing the Schwalbenberg II LPS with the nearby Eifel Lake Sediment Archive (ELSA) and other more distant German, Austrian and Czech LPS while discussing time and climate as limiting factors for pedogenesis, we suggest that the lithologically determined paleosols are in-situ soil formations. The provenance indices document a Zr-enrichment at the transition from the Ahrgau to the Hesbaye Subformation. This is explained by a conceptual model incorporating multiple sediment recycling and sorting effects in eolian and fluvial domains.