Multiple testing in spatial epidemiology: a Bayesian approach

In this work we aim to propose a new approach for preliminary epidemiological studies on Standardized Mortality Ratios (SMR) collected in many spatial regions. A preliminary study on SMRs aims to formulate hypotheses to be investigated via individual epidemiological studies that avoid bias carried on by aggregated analyses. Starting from collecting disease counts and calculating expected disease counts by means of reference population disease rates, in each area an SMR is derived as the MLE under the Poisson assumption on each observation. Such estimators have high standard errors in small areas, i.e. where the expected count is low either because of the low population underlying the area or the rarity of the disease under study. Disease mapping models and other techniques for screening disease rates among the map aiming to detect anomalies and possible high-risk areas have been proposed in literature according to the classic and the Bayesian paradigm. Our proposal is approaching this issue by a decision-oriented method, which focus on multiple testing control, without however leaving the preliminary study perspective that an analysis on SMR indicators is asked to. We implement the control of the FDR, a quantity largely used to address multiple comparisons problems in the eld of microarray data analysis but which is not usually employed in disease mapping. Controlling the FDR means providing an estimate of the FDR for a set of rejected null hypotheses. The small areas issue arises diculties in applying traditional methods for FDR estimation, that are usually based only on the p-values knowledge (Benjamini and Hochberg, 1995; Storey, 2003). Tests evaluated by a traditional p-value provide weak power in small areas, where the expected number of disease cases is small. Moreover tests cannot be assumed as independent when spatial correlation between SMRs is expected, neither they are identical distributed when population underlying the map is heterogeneous. The Bayesian paradigm oers a way to overcome the inappropriateness of p-values based methods. Another peculiarity of the present work is to propose a hierarchical full Bayesian model for FDR estimation in testing many null hypothesis of absence of risk.We will use concepts of Bayesian models for disease mapping, referring in particular to the Besag York and Mollié model (1991) often used in practice for its exible prior assumption on the risks distribution across regions. The borrowing of strength between prior and likelihood typical of a hierarchical Bayesian model takes the advantage of evaluating a singular test (i.e. a test in a singular area) by means of all observations in the map under study, rather than just by means of the singular observation. This allows to improve the power test in small areas and addressing more appropriately the spatial correlation issue that suggests that relative risks are closer in spatially contiguous regions. The proposed model aims to estimate the FDR by means of the MCMC estimated posterior probabilities b i's of the null hypothesis (absence of risk) for each area. An estimate of the expected FDR conditional on data (\FDR) can be calculated in any set of b i's relative to areas declared at high-risk (where thenull hypothesis is rejected) by averaging the b i's themselves. The\FDR can be used to provide an easy decision rule for selecting high-risk areas, i.e. selecting as many as possible areas such that the\FDR is non-lower than a prexed value; we call them\FDR based decision (or selection) rules. The sensitivity and specicity of such rule depend on the accuracy of the FDR estimate, the over-estimation of FDR causing a loss of power and the under-estimation of FDR producing a loss of specicity. Moreover, our model has the interesting feature of still being able to provide an estimate of relative risk values as in the Besag York and Mollié model (1991). A simulation study to evaluate the model performance in FDR estimation accuracy, sensitivity and specificity of the decision rule, and goodness of estimation of relative risks, was set up. We chose a real map from which we generated several spatial scenarios whose counts of disease vary according to the spatial correlation degree, the size areas, the number of areas where the null hypothesis is true and the risk level in the latter areas. In summarizing simulation results we will always consider the FDR estimation in sets constituted by all b i's selected lower than a threshold t. We will show graphs of the\FDR and the true FDR (known by simulation) plotted against a threshold t to assess the FDR estimation. Varying the threshold we can learn which FDR values can be accurately estimated by the practitioner willing to apply the model (by the closeness between\FDR and true FDR). By plotting the calculated sensitivity and specicity (both known by simulation) vs the\FDR we can check the sensitivity and specicity of the corresponding\FDR based decision rules. For investigating the over-smoothing level of relative risk estimates we will compare box-plots of such estimates in high-risk areas (known by simulation), obtained by both our model and the classic Besag York Mollié model. All the summary tools are worked out for all simulated scenarios (in total 54 scenarios). Results show that FDR is well estimated (in the worst case we get an overestimation, hence a conservative FDR control) in small areas, low risk levels and spatially correlated risks scenarios, that are our primary aims. In such scenarios we have good estimates of the FDR for all values less or equal than 0.10. The sensitivity of\FDR based decision rules is generally low but specicity is high. In such scenario the use of\FDR = 0:05 or\FDR = 0:10 based selection rule can be suggested. In cases where the number of true alternative hypotheses (number of true high-risk areas) is small, also FDR = 0:15 values are well estimated, and \FDR = 0:15 based decision rules gains power maintaining an high specicity. On the other hand, in non-small areas and non-small risk level scenarios the FDR is under-estimated unless for very small values of it (much lower than 0.05); this resulting in a loss of specicity of a\FDR = 0:05 based decision rule. In such scenario\FDR = 0:05 or, even worse,\FDR = 0:1 based decision rules cannot be suggested because the true FDR is actually much higher. As regards the relative risk estimation, our model achieves almost the same results of the classic Besag York Molliè model. For this reason, our model is interesting for its ability to perform both the estimation of relative risk values and the FDR control, except for non-small areas and large risk level scenarios. A case of study is nally presented to show how the method can be used in epidemiology.

Subject-specific musculoskeletal models of the lower limbs for the prediction of skeletal loads during motion

The determination of skeletal loading conditions in vivo and their relationship to the health of bone tissues, remain an open question. Computational modeling of the musculoskeletal system is the only practicable method providing a valuable approach to muscle and joint loading analyses, although crucial shortcomings limit the translation process of computational methods into the orthopedic and neurological practice. A growing attention focused on subject-specific modeling, particularly when pathological musculoskeletal conditions need to be studied. Nevertheless, subject-specific data cannot be always collected in the research and clinical practice, and there is a lack of efficient methods and frameworks for building models and incorporating them in simulations of motion. The overall aim of the present PhD thesis was to introduce improvements to the state-of-the-art musculoskeletal modeling for the prediction of physiological muscle and joint loads during motion. A threefold goal was articulated as follows: (i) develop state-of-the art subject-specific models and analyze skeletal load predictions; (ii) analyze the sensitivity of model predictions to relevant musculotendon model parameters and kinematic uncertainties; (iii) design an efficient software framework simplifying the effort-intensive phases of subject-specific modeling pre-processing. The first goal underlined the relevance of subject-specific musculoskeletal modeling to determine physiological skeletal loads during gait, corroborating the choice of full subject-specific modeling for the analyses of pathological conditions. The second goal characterized the sensitivity of skeletal load predictions to major musculotendon parameters and kinematic uncertainties, and robust probabilistic methods were applied for methodological and clinical purposes. The last goal created an efficient software framework for subject-specific modeling and simulation, which is practical, user friendly and effort effective. Future research development aims at the implementation of more accurate models describing lower-limb joint mechanics and musculotendon paths, and the assessment of an overall scenario of the crucial model parameters affecting the skeletal load predictions through probabilistic modeling.

Prediction of psychosis in adolescents and young adults at high risk: results from the prospective European prediction of psychosis study

Indicated prevention is currently regarded as the most promising strategy to attenuate, delay, or even avert psychosis. Existing criteria need improvement in terms of specificity and individual risk assessment to allow for better targeted and earlier interventions.

Real-time adaptive models for the personalized prediction of glycemic profile in type 1 diabetes patients

Prediction of glycemic profile is an important task for both early recognition of hypoglycemia and enhancement of the control algorithms for optimization of insulin infusion rate. Adaptive models for glucose prediction and recognition of hypoglycemia based on statistical and artificial intelligence techniques are presented.

Prognostic clinical prediction rules to identify a low-risk pulmonary embolism: a systematic review and meta-analysis

Prognostic assessment is important for the management of patients with a pulmonary embolism (PE). A number of clinical prediction rules (CPRs) have been proposed for stratifying PE mortality risk. The aim of this systematic review was to assess the performance of prognostic CPRs in identifying a low-risk PE.

Prediction of psychosis in clinical high-risk patients by the Schizotypal Personality Questionnaire. Results of the EPOS project

OBJECTIVE: Schizotypal features indicate proneness to psychosis in the general population. It is also possible that they increase transition to psychosis (TTP) among clinical high-risk patients (CHR). Our aim was to investigate whether schizotypal features predict TTP in CHR patients. METHODS: In the EPOS (European Prediction of Psychosis Study) project, 245 young help-seeking CHR patients were prospectively followed for 18 months and their TTP was identified. At baseline, subjects were assessed with the Schizotypal Personality Questionnaire (SPQ). Associations between SPQ items and its subscales with the TTP were analysed in Cox regression analysis. RESULTS: The SPQ subscales and items describing ideas of reference and lack of close interpersonal relationships were found to correlate significantly with TTP. The co-occurrence of these features doubled the risk of TTP. CONCLUSIONS: Presence of ideas of reference and lack of close interpersonal relations increase the risk of full-blown psychosis among CHR patients. This co-occurrence makes the risk of psychosis very high.

Prediction of hip fracture risk by quantitative ultrasound in more than 7000 Swiss women > or =70 years of age: comparison of three technologically different bone ultrasound devices in the SEMOF study

To compare the prediction of hip fracture risk of several bone ultrasounds (QUS), 7062 Swiss women > or =70 years of age were measured with three QUSs (two of the heel, one of the phalanges). Heel QUSs were both predictive of hip fracture risk, whereas the phalanges QUS was not. INTRODUCTION: As the number of hip fracture is expected to increase during these next decades, it is important to develop strategies to detect subjects at risk. Quantitative bone ultrasound (QUS), an ionizing radiation-free method, which is transportable, could be interesting for this purpose. MATERIALS AND METHODS: The Swiss Evaluation of the Methods of Measurement of Osteoporotic Fracture Risk (SEMOF) study is a multicenter cohort study, which compared three QUSs for the assessment of hip fracture risk in a sample of 7609 elderly ambulatory women > or =70 years of age. Two QUSs measured the heel (Achilles+; GE-Lunar and Sahara; Hologic), and one measured the heel (DBM Sonic 1200; IGEA). The Cox proportional hazards regression was used to estimate the hazard of the first hip fracture, adjusted for age, BMI, and center, and the area under the ROC curves were calculated to compare the devices and their parameters. RESULTS: From the 7609 women who were included in the study, 7062 women 75.2 +/- 3.1 (SD) years of age were prospectively followed for 2.9 +/- 0.8 years. Eighty women reported a hip fracture. A decrease by 1 SD of the QUS variables corresponded to an increase of the hip fracture risk from 2.3 (95% CI, 1.7, 3.1) to 2.6 (95% CI, 1.9, 3.4) for the three variables of Achilles+ and from 2.2 (95% CI, 1.7, 3.0) to 2.4 (95% CI, 1.8, 3.2) for the three variables of Sahara. Risk gradients did not differ significantly among the variables of the two heel QUS devices. On the other hand, the phalanges QUS (DBM Sonic 1200) was not predictive of hip fracture risk, with an adjusted hazard risk of 1.2 (95% CI, 0.9, 1.5), even after reanalysis of the digitalized data and using different cut-off levels (1700 or 1570 m/s). CONCLUSIONS: In this elderly women population, heel QUS devices were both predictive of hip fracture risk, whereas the phalanges QUS device was not.

Evaluating Prediction Rules for t-Year Survivors With Censored Regression Models

Suppose that we are interested in establishing simple, but reliable rules for predicting future t-year survivors via censored regression models. In this article, we present inference procedures for evaluating such binary classification rules based on various prediction precision measures quantified by the overall misclassification rate, sensitivity and specificity, and positive and negative predictive values. Specifically, under various working models we derive consistent estimators for the above measures via substitution and cross validation estimation procedures. Furthermore, we provide large sample approximations to the distributions of these nonsmooth estimators without assuming that the working model is correctly specified. Confidence intervals, for example, for the difference of the precision measures between two competing rules can then be constructed. All the proposals are illustrated with two real examples and their finite sample properties are evaluated via a simulation study.

Bayesian Hierarchical Distributed Lag Models for Summer Ozone Exposure and Cardio-Respiratory Mortality

In this paper, we develop Bayesian hierarchical distributed lag models for estimating associations between daily variations in summer ozone levels and daily variations in cardiovascular and respiratory (CVDRESP) mortality counts for 19 U.S. large cities included in the National Morbidity Mortality Air Pollution Study (NMMAPS) for the period 1987 - 1994. At the first stage, we define a semi-parametric distributed lag Poisson regression model to estimate city-specific relative rates of CVDRESP associated with short-term exposure to summer ozone. At the second stage, we specify a class of distributions for the true city-specific relative rates to estimate an overall effect by taking into account the variability within and across cities. We perform the calculations with respect to several random effects distributions (normal, t-student, and mixture of normal), thus relaxing the common assumption of a two-stage normal-normal hierarchical model. We assess the sensitivity of the results to: 1) lag structure for ozone exposure; 2) degree of adjustment for long-term trends; 3) inclusion of other pollutants in the model;4) heat waves; 5) random effects distributions; and 6) prior hyperparameters. On average across cities, we found that a 10ppb increase in summer ozone level for every day in the previous week is associated with 1.25 percent increase in CVDRESP mortality (95% posterior regions: 0.47, 2.03). The relative rate estimates are also positive and statistically significant at lags 0, 1, and 2. We found that associations between summer ozone and CVDRESP mortality are sensitive to the confounding adjustment for PM_10, but are robust to: 1) the adjustment for long-term trends, other gaseous pollutants (NO_2, SO_2, and CO); 2) the distributional assumptions at the second stage of the hierarchical model; and 3) the prior distributions on all unknown parameters. Bayesian hierarchical distributed lag models and their application to the NMMAPS data allow us estimation of an acute health effect associated with exposure to ambient air pollution in the last few days on average across several locations. The application of these methods and the systematic assessment of the sensitivity of findings to model assumptions provide important epidemiological evidence for future air quality regulations.

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.

Modeling multilevel sleep transitional data via Poisson log-linear multilevel models

This paper proposes Poisson log-linear multilevel models to investigate population variability in sleep state transition rates. We specifically propose a Bayesian Poisson regression model that is more flexible, scalable to larger studies, and easily fit than other attempts in the literature. We further use hierarchical random effects to account for pairings of individuals and repeated measures within those individuals, as comparing diseased to non-diseased subjects while minimizing bias is of epidemiologic importance. We estimate essentially non-parametric piecewise constant hazards and smooth them, and allow for time varying covariates and segment of the night comparisons. The Bayesian Poisson regression is justified through a re-derivation of a classical algebraic likelihood equivalence of Poisson regression with a log(time) offset and survival regression assuming piecewise constant hazards. This relationship allows us to synthesize two methods currently used to analyze sleep transition phenomena: stratified multi-state proportional hazards models and log-linear models with GEE for transition counts. An example data set from the Sleep Heart Health Study is analyzed.

Reduced Bayesian Hierarchical Models: Estimating Health Effects of Simultaneous Exposure to Multiple Pollutants

Quantifying the health effects associated with simultaneous exposure to many air pollutants is now a research priority of the US EPA. Bayesian hierarchical models (BHM) have been extensively used in multisite time series studies of air pollution and health to estimate health effects of a single pollutant adjusted for potential confounding of other pollutants and other time-varying factors. However, when the scientific goal is to estimate the impacts of many pollutants jointly, a straightforward application of BHM is challenged by the need to specify a random-effect distribution on a high-dimensional vector of nuisance parameters, which often do not have an easy interpretation. In this paper we introduce a new BHM formulation, which we call "reduced BHM", aimed at analyzing clustered data sets in the presence of a large number of random effects that are not of primary scientific interest. At the first stage of the reduced BHM, we calculate the integrated likelihood of the parameter of interest (e.g. excess number of deaths attributed to simultaneous exposure to high levels of many pollutants). At the second stage, we specify a flexible random-effect distribution directly on the parameter of interest. The reduced BHM overcomes many of the challenges in the specification and implementation of full BHM in the context of a large number of nuisance parameters. In simulation studies we show that the reduced BHM performs comparably to the full BHM in many scenarios, and even performs better in some cases. Methods are applied to estimate location-specific and overall relative risks of cardiovascular hospital admissions associated with simultaneous exposure to elevated levels of particulate matter and ozone in 51 US counties during the period 1999-2005.

Price risk management in the copper market using commodity derivatives and options strategies

Metals price risk management is a key issue related to financial risk in metal markets because of uncertainty of commodity price fluctuation, exchange rate, interest rate changes and huge price risk either to metals’ producers or consumers. Thus, it has been taken into account by all participants in metal markets including metals’ producers, consumers, merchants, banks, investment funds, speculators, traders and so on. Managing price risk provides stable income for both metals’ producers and consumers, so it increases the chance that a firm will invest in attractive projects. The purpose of this research is to evaluate risk management strategies in the copper market. The main tools and strategies of price risk management are hedging and other derivatives such as futures contracts, swaps and options contracts. Hedging is a transaction designed to reduce or eliminate price risk. Derivatives are financial instruments, whose returns are derived from other financial instruments and they are commonly used for managing financial risks. Although derivatives have been around in some form for centuries, their growth has accelerated rapidly during the last 20 years. Nowadays, they are widely used by financial institutions, corporations, professional investors, and individuals. This project is focused on the over-the-counter (OTC) market and its products such as exotic options, particularly Asian options. The first part of the project is a description of basic derivatives and risk management strategies. In addition, this part discusses basic concepts of spot and futures (forward) markets, benefits and costs of risk management and risks and rewards of positions in the derivative markets. The second part considers valuations of commodity derivatives. In this part, the options pricing model DerivaGem is applied to Asian call and put options on London Metal Exchange (LME) copper because it is important to understand how Asian options are valued and to compare theoretical values of the options with their market observed values. Predicting future trends of copper prices is important and would be essential to manage market price risk successfully. Therefore, the third part is a discussion about econometric commodity models. Based on this literature review, the fourth part of the project reports the construction and testing of an econometric model designed to forecast the monthly average price of copper on the LME. More specifically, this part aims at showing how LME copper prices can be explained by means of a simultaneous equation structural model (two-stage least squares regression) connecting supply and demand variables. A simultaneous econometric model for the copper industry is built: {█(Q_t^D=e^((-5.0485))∙P_((t-1))^((-0.1868) )∙〖GDP〗_t^((1.7151) )∙e^((0.0158)∙〖IP〗_t ) @Q_t^S=e^((-3.0785))∙P_((t-1))^((0.5960))∙T_t^((0.1408))∙P_(OIL(t))^((-0.1559))∙〖USDI〗_t^((1.2432))∙〖LIBOR〗_((t-6))^((-0.0561))@Q_t^D=Q_t^S )┤ P_((t-1))^CU=e^((-2.5165))∙〖GDP〗_t^((2.1910))∙e^((0.0202)∙〖IP〗_t )∙T_t^((-0.1799))∙P_(OIL(t))^((0.1991))∙〖USDI〗_t^((-1.5881))∙〖LIBOR〗_((t-6))^((0.0717) Where, Q_t^D and Q_t^Sare world demand for and supply of copper at time t respectively. P(t-1) is the lagged price of copper, which is the focus of the analysis in this part. GDPt is world gross domestic product at time t, which represents aggregate economic activity. In addition, industrial production should be considered here, so the global industrial production growth that is noted as IPt is included in the model. Tt is the time variable, which is a useful proxy for technological change. A proxy variable for the cost of energy in producing copper is the price of oil at time t, which is noted as POIL(t ) . USDIt is the U.S. dollar index variable at time t, which is an important variable for explaining the copper supply and copper prices. At last, LIBOR(t-6) is the 6-month lagged 1-year London Inter bank offering rate of interest. Although, the model can be applicable for different base metals' industries, the omitted exogenous variables such as the price of substitute or a combined variable related to the price of substitutes have not been considered in this study. Based on this econometric model and using a Monte-Carlo simulation analysis, the probabilities that the monthly average copper prices in 2006 and 2007 will be greater than specific strike price of an option are defined. The final part evaluates risk management strategies including options strategies, metal swaps and simple options in relation to the simulation results. The basic options strategies such as bull spreads, bear spreads and butterfly spreads, which are created by using both call and put options in 2006 and 2007 are evaluated. Consequently, each risk management strategy in 2006 and 2007 is analyzed based on the day of data and the price prediction model. As a result, applications stemming from this project include valuing Asian options, developing a copper price prediction model, forecasting and planning, and decision making for price risk management in the copper market.

Risk assessment for invasive exotic plants using multi-criteria risk models

Invasive exotic plants have altered natural ecosystems across much of North America. In the Midwest, the presence of invasive plants is increasing rapidly, causing changes in ecosystem patterns and processes. Early detection has become a key component in invasive plant management and in the detection of ecosystem change. Risk assessment through predictive modeling has been a useful resource for monitoring and assisting with treatment decisions for invasive plants. Predictive models were developed to assist with early detection of ten target invasive plants in the Great Lakes Network of the National Park Service and for garlic mustard throughout the Upper Peninsula of Michigan. These multi-criteria risk models utilize geographic information system (GIS) data to predict the areas at highest risk for three phases of invasion: introduction, establishment, and spread. An accuracy assessment of the models for the ten target plants in the Great Lakes Network showed an average overall accuracy of 86.3%. The model developed for garlic mustard in the Upper Peninsula resulted in an accuracy of 99.0%. Used as one of many resources, the risk maps created from the model outputs will assist with the detection of ecosystem change, the monitoring of plant invasions, and the management of invasive plants through prioritized control efforts.