Item response theory analysis of the Dysfunctional Beliefs and Attitudes about Sleep-16 (DBAS-16) scale in a university student sample.

Unhelpful beliefs about sleep have been shown to exacerbate distress associated with sleep-related difficulties. University students are particularly vulnerable to experiencing sleep-related problems. The Dysfunctional Beliefs and Attitudes about Sleep-16 (DBAS-16) scale is a widely used instrument that assesses for sleep-disruptive cognitions. Although psychometric support for the DBAS-16 is available, Item Response Theory (IRT) analysis is needed to examine its properties at the item level. Psychometric investigation in non-clinical samples can help identify people who may be at risk for developing sleep problems. We examined the DBAS-16 using IRT on a sample of 759 university students. Our results identified items and subscales that adequately/inadequately differentiated between students who held unhelpful beliefs about sleep and those who did not. The DBAS-16 is a valuable instrument to assess unhelpful beliefs about sleep. We outline recommendations to improve the discriminatory ability of the instrument. Future investigations should establish cross-validation with a clinical sample.

Adaptive Gaussian Markov random field spatiotemporal models for infectious disease mapping and forecasting.

Recent disease mapping literature presents adaptively parameterized spatiotemporal (ST) autoregressive (AR) or conditional autoregressive (CAR) models for Bayesian prediction of COVID-19 infection risks. These models were motivated to capture complex spatiotemporal dynamics and heterogeneities of infection risks. In the present paper, we synthesize, generalize, and unify the ST AR and CAR model constructions for models augmented by adaptive Gaussian Markov random fields, with an emphasis on disease forecasting. A general convolution construction is presented, with illustrative models motivated to (i) characterize local risk dependencies and influences over both spatial and temporal dimensions, (ii) model risk heterogeneities and discontinuities, and (iii) predict and forecast areal-level disease risks and occurrences. The broadened constructions allow rich options of intuitive parameterization for disease mapping and spatial regression. Illustrative parameterizations are presented for Bayesian hierarchical models of Poisson, zero-inflated Poisson, and Bernoulli data models, respectively. They are also discussed in the context of quantifying time-varying or time-invariant effects of (omitted) covariates, with application to prediction and forecasting areal-level COVID-19 infection occurrences and probabilities of zero-infection. The model constructions presented herein have much wider scope in offering a flexible framework for modelling complex spatiotemporal data and for estimation, learning, and forecasting purposes.

Revisiting Gaussian Markov random fields and Bayesian disease mapping.

We revisit several conditionally formulated Gaussian Markov random fields, known as the intrinsic conditional autoregressive model, the proper conditional autoregressive model, and the Leroux et al. conditional autoregressive model, as well as convolution models such as the well known Besag, York and Mollie model, its (adaptive) re-parameterization, and its scaled alternatives, for their roles of modelling underlying spatial risks in Bayesian disease mapping. Analytic and simulation studies, with graphic visualizations, and disease mapping case studies, present insights and critique on these models for their nature and capacities in characterizing spatial dependencies, local influences, and spatial covariance and correlation functions, and in facilitating stabilized and efficient posterior risk prediction and inference. It is illustrated that these models are Gaussian (Markov) random fields of different spatial dependence, local influence, and (covariance) correlation functions and can play different and complementary roles in Bayesian disease mapping applications.

Bayesian disease mapping: Past, present, and future.

On the occasion of the Spatial Statistics' 10th Anniversary, I reflect on the past and present of Bayesian disease mapping and look into its future. I focus on some key developments of models, and on recent evolution of multivariate and adaptive Gaussian Markov random fields and their impact and importance in disease mapping. I reflect on Bayesian disease mapping as a subject of spatial statistics that has advanced to date, and continues to grow, in scope and complexity alongside increasing needs of analytic tools for contemporary health science research, such as spatial epidemiology, population and public health, and medicine. I illustrate (potential) utility and impact of some of the disease mapping models and methods for analysing and monitoring communicable disease such as the COVID-19 infection risks during an ongoing pandemic.

Bayesian estimation of multivariate Gaussian Markov random fields with constraint.

This article concerns with conditionally formulated multivariate Gaussian Markov random fields (MGMRF) for modeling multivariate local dependencies with unknown dependence parameters subject to positivity constraint. In the context of Bayesian hierarchical modeling of lattice data in general and Bayesian disease mapping in particular, analytic and simulation studies provide new insights into various approaches to posterior estimation of dependence parameters under "hard" or "soft" positivity constraint, including the well-known strictly diagonal dominance criterion and options of hierarchical priors. Hierarchical centering is examined as a means to gain computational efficiency in Bayesian estimation of multivariate generalized linear mixed effects models in the presence of spatial confounding and weakly identified model parameters. Simulated data on irregular or regular lattice, and three datasets from the multivariate and spatiotemporal disease mapping literature, are used for illustration. The present investigation also sheds light on the use of deviance information criterion for model comparison, choice, and interpretation in the context of posterior risk predictions judged by borrowing-information and bias-precision tradeoff. The article concludes with a summary discussion and directions of future work. Potential applications of MGMRF in spatial information fusion and image analysis are briefly mentioned.

The Experience of Family Physicians and Home Health Staff Involved in an Intervention to Increase Patient-Related Collaboration.

Les médecins de famille (MF) et le personnel de soins de santé à domicile (PSD) canadiens rencontrent d'importants obstacles lorsqu'ils doivent collaborer pour la prestation de soins aux patients qu'ils ont en commun. Cette étude à méthodologie mixte visait à évaluer la qualité et la viabilité de l'utilisation de l'audioconférence sécurisée dans une optique d'amélioration de la planification des soins pour ces patients. Les données primaires incluaient les résultats d'un sondage réalisé avant et après l'intervention, ainsi que des entretiens semi-structurés et des groupes de discussion post-intervention. Des méthodes statistiques non paramétriques ont été utilisées pour analyser les résultats du sondage, et les données qualitatives ont fait l'objet d'une analyse thématique de contenu. Les résultats des analyses quantitatives et qualitatives ont ensuite été intégrés afin de faire ressortir les inférences reflétant les approches des MF et du PSD relatives aux obstacles et aux avantages de la planification interdisciplinaire des soins. Les MF et le PSD ont montré que des obstacles structurels limitent leur capacité à collaborer. Le PSD et les MF ont également convenu que les rencontres entre les intervenants des deux services étaient bénéfiques pour les patients et que l'utilisation de l'audioconférence constituait une méthode efficiente de planification collaborative des soins. Les limites comprenaient la petite taille de l'échantillon et la courte période d'intervention, compte tenu de l'ampleur des changements attendus.Canadian family physicians (FPs) and home health staff (HHS) experience significant barriers to patient-related collaboration about patients they share. This mixed-methods study sought to determine the quality and sustainability of secure audio conferencing as a way to increase care planning about shared patients. Primary data sources included pre-and post-study administration of a published survey and post-study semi-structured interviews and focus groups. Non-parametric statistical procedures were used to analyze survey results and thematic content analysis was undertaken for qualitative data. Results from both quantitative and qualitative analysis were integrated into the overall analysis, in order to draw inferences reflecting both approaches to barriers and benefits of collaborative care planning for FPs and HHS. Both FPs and HHS provided evidence that structural barriers impede their ability to collaborate. HHS and FPs also agreed that joint conferences were beneficial for patients, and that the use of audio conferencing provided an efficient method of collaborative care planning. Limitations included a small sample size and short timeline for the intervention period, given the magnitude of the expected change.

Contextual influences on pain communication in couples with and without a partner with chronic pain.

This is an experimental study of pain communication in couples. Despite evidence that chronic pain in one partner impacts both members of the dyad, dyadic influences on pain communication have not been sufficiently examined and are typically studied based on retrospective reports. Our goal was to directly study contextual influences (ie, presence of chronic pain, gender, relationship quality, and pain catastrophizing) on self-reported and nonverbal (ie, facial expressions) pain responses. Couples with (n = 66) and without (n = 65) an individual with chronic pain (ICP) completed relationship and pain catastrophizing questionnaires. Subsequently, one partner underwent a pain task (pain target, PT), while the other partner observed (pain observer, PO). In couples with an ICP, the ICP was assigned to be the PT. Pain intensity and PO perceived pain intensity ratings were recorded at multiple intervals. Facial expressions were video recorded throughout the pain task. Pain-related facial expression was quantified using the Facial Action Coding System. The most consistent predictor of either partner's pain-related facial expression was the pain-related facial expression of the other partner. Pain targets provided higher pain ratings than POs and female PTs reported and showed more pain, regardless of chronic pain status. Gender and the interaction between gender and relationship satisfaction were predictors of pain-related facial expression among PTs, but not POs. None of the examined variables predicted self-reported pain. Results suggest that contextual variables influence pain communication in couples, with distinct influences for PTs and POs. Moreover, self-report and nonverbal responses are not displayed in a parallel manner.

Linear models of coregionalization for multivariate lattice data: Order-dependent and order-free cMCARs.

This paper concerns with multivariate conditional autoregressive models defined by linear combination of independent or correlated underlying spatial processes. Known as linear models of coregionalization, the method offers a systematic and unified approach for formulating multivariate extensions to a broad range of univariate conditional autoregressive models. The resulting multivariate spatial models represent classes of coregionalized multivariate conditional autoregressive models that enable flexible modelling of multivariate spatial interactions, yielding coregionalization models with symmetric or asymmetric cross-covariances of different spatial variation and smoothness. In the context of multivariate disease mapping, for example, they facilitate borrowing strength both over space and cross variables, allowing for more flexible multivariate spatial smoothing. Specifically, we present a broadened coregionalization framework to include order-dependent, order-free, and order-robust multivariate models; a new class of order-free coregionalized multivariate conditional autoregressives is introduced. We tackle computational challenges and present solutions that are integral for Bayesian analysis of these models. We also discuss two ways of computing deviance information criterion for comparison among competing hierarchical models with or without unidentifiable prior parameters. The models and related methodology are developed in the broad context of modelling multivariate data on spatial lattice and illustrated in the context of multivariate disease mapping. The coregionalization framework and related methods also present a general approach for building spatially structured cross-covariance functions for multivariate geostatistics.

A Gaussian random field model for similarity-based smoothing in Bayesian disease mapping.

Conditionally specified Gaussian Markov random field (GMRF) models with adjacency-based neighbourhood weight matrix, commonly known as neighbourhood-based GMRF models, have been the mainstream approach to spatial smoothing in Bayesian disease mapping. In the present paper, we propose a conditionally specified Gaussian random field (GRF) model with a similarity-based non-spatial weight matrix to facilitate non-spatial smoothing in Bayesian disease mapping. The model, named similarity-based GRF, is motivated for modelling disease mapping data in situations where the underlying small area relative risks and the associated determinant factors do not vary systematically in space, and the similarity is defined by "similarity" with respect to the associated disease determinant factors. The neighbourhood-based GMRF and the similarity-based GRF are compared and accessed via a simulation study and by two case studies, using new data on alcohol abuse in Portugal collected by the World Mental Health Survey Initiative and the well-known lip cancer data in Scotland. In the presence of disease data with no evidence of positive spatial correlation, the simulation study showed a consistent gain in efficiency from the similarity-based GRF, compared with the adjacency-based GMRF with the determinant risk factors as covariate. This new approach broadens the scope of the existing conditional autocorrelation models.

Linear models of coregionalization for multivariate lattice data: a general framework for coregionalized multivariate CAR models.

We present a general coregionalization framework for developing coregionalized multivariate Gaussian conditional autoregressive (cMCAR) models for Bayesian analysis of multivariate lattice data in general and multivariate disease mapping data in particular. This framework is inclusive of cMCARs that facilitate flexible modelling of spatially structured symmetric or asymmetric cross-variable local interactions, allowing a wide range of separable or non-separable covariance structures, and symmetric or asymmetric cross-covariances, to be modelled. We present a brief overview of established univariate Gaussian conditional autoregressive (CAR) models for univariate lattice data and develop coregionalized multivariate extensions. Classes of cMCARs are presented by formulating precision structures. The resulting conditional properties of the multivariate spatial models are established, which cast new light on cMCARs with richly structured covariances and cross-covariances of different spatial ranges. The related methods are illustrated via an in-depth Bayesian analysis of a Minnesota county-level cancer data set. We also bring a new dimension to the traditional enterprize of Bayesian disease mapping: estimating and mapping covariances and cross-covariances of the underlying disease risks. Maps of covariances and cross-covariances bring to light spatial characterizations of the cMCARs and inform on spatial risk associations between areas and diseases. Copyright © 2016 John Wiley & Sons, Ltd.

Bayesian hierarchical modelling of noisy spatial rates on a modestly large and discontinuous irregular lattice.

We present Bayesian hierarchical spatial model development motivated from a recent analysis of noisy small area response rate data, named the Booster data. The Booster data are postcode-level aggregates from a recent mail-out recruitment for a physical exercise intervention in deprived urban neighbourhoods in Sheffield, UK. Bayesian hierarchical Bernoulli-binomial spatial mixture zero-inflated Binomial models were developed for modelling overdispersion and for separation of systematic and random variations in the noisy and mostly low crude response rates. We present methods that enabled us to explore the underlying spatial rate variation, clustering of low or high response rate areas and neighbourhood characteristics that were associated with variations and patterns of invitation mail-outs, zero-response and response rates. Three spatial prior formulations, the intrinsic conditional autoregressive or (iCAR), the Besag-York-Mollié (BYM) and the modified BYM models, were explored for their performance on modelling sparse data on a modestly large and discontinuous irregular lattice. An in-depth Bayesian analysis of the Booster data is presented, with the resulting posterior estimation and inference implemented via Markov chain Monte Carlo simulation in WinBUGS. With increasing availability of spatial data referenced at fine spatial scales such as the postcode, the sparse-data situation and the Bayesian models and methods discussed herein should have considerable relevance to small area disease and health mapping and to spatial regression.

On identification in Bayesian disease mapping and ecological-spatial regression models.

We discuss identification of structural characteristics of the underlying relative risks ensemble for posterior relative risks inference within Bayesian generalized linear mixed model framework for small-area disease mapping and ecological-spatial regression. We revisit conditionally specified and locally characterized Gaussian Markov random field risks ensemble priors in univariate disease mapping and communicate insight into Gaussian Markov random field variance-covariance characteristics for representing disease risks variability and spatial risks interactions and for structural identification with respect to risks ensemble prior choices. Illustrative examples of identification in Bayesian disease mapping and ecological-spatial regression models are presented for Bayesian hierarchical generalized linear mixed Poisson models and zero-inflated Poisson models.

Mapping gender variation in the spatial pattern of alcohol-related mortality: a Bayesian analysis using data from South Yorkshire, United Kingdom.

Gender variation in the spatial pattern of alcohol-related deaths in South Yorkshire, UK for the period 1999 and 2003 was explored using two Bayesian modelling approaches. Firstly, separate models were fitted to male and female deaths, each with a fixed effect deprivation covariate and a random effect with unstructured and spatially structured terms. In a modification to the initial models, covariates were assumed estimated with error rather than known with certainty. In the second modelling approach male and female deaths were modelled jointly with a shared component for random effects. A range of different unstructured and spatially structured specifications for the shared and gender-specific random effects were fitted. In the best fitting shared component model a spatially structured prior was assumed for the shared component, while gender-specific components were assumed unstructured. Deprivation coefficients and random effect standard deviations were very similar between the gender-specific and shared component models. In each case the effect of deprivation was observed to be greater in males than in females, and slightly larger in the measurement error models than in the fixed covariate models. Greater variation was observed in the spatially smoothed estimates of risk for males versus females in both gender-specific and shared component models. The shared component explained a greater proportion of the male risk than it did the female risk. The analysis approach reveals the residual (unexplained by deprivation) gender-specific and shared risk surfaces, information which may be useful for guiding public health action.

Unemployment and mortality: a comparative study of Germany and the United States.

OBJECTIVES: We examined the relationship between unemployment and mortality in Germany, a coordinated market economy, and the United States, a liberal market economy. METHODS: We followed 2 working-age cohorts from the German Socio-economic Panel and the US Panel Study of Income Dynamics from 1984 to 2005. We defined unemployment as unemployed at the time of survey. We used discrete-time survival analysis, adjusting for potential confounders. RESULTS: There was an unemployment-mortality association among Americans (relative risk [RR]=2.4; 95% confidence interval [CI]=1.7, 3.4), but not among Germans (RR=1.4; 95% CI=1.0, 2.0). In education-stratified models, there was an association among minimum-skilled (RR=2.6; 95% CI=1.4, 4.7) and medium-skilled (RR=2.4; 95% CI=1.5, 3.8) Americans, but not among minimum- and medium-skilled Germans. There was no association among high-skilled Americans, but an association among high-skilled Germans (RR=3.0; 95% CI=1.3, 7.0), although this was limited to those educated in East Germany. Minimum- and medium-skilled unemployed Americans had the highest absolute risks of dying. CONCLUSIONS: The higher risk of dying for minimum- and medium-skilled unemployed Americans, not found among Germans, suggests that the unemployment-mortality relationship may be mediated by the institutional and economic environment.

Preclosure fluid resuscitation influences outcome in gastroschisis.

Optimal preclosure fluid resuscitation in gastroschisis (GS) is unknown. The purpose of our study was to evaluate effects of preclosure intravenous fluid resuscitation on GS outcome. Cases were accrued from a national GS database. Risk variables analyzed included gestational age (GA), birth weight (BW), neonatal illness severity score, and bolus fluid administration within 6 hours of neonatal intensive care unit admission. Outcomes analyzed included closure success, days of ventilation/total parenteral nutrition (TPN), and bacteremic episodes. Linear and logistic regression analyses were performed. Four hundred seven live-born GS cases were identified (362 with complete resuscitative fluids data). Mean BW, GA, and Score for Neonatal Acute Physiology-II score were 2562 ± 539 g, 36.17 ± 1.95 weeks, and 9.97 ± 12.65, respectively. One hundred sixty-two patients received no supplemental fluid, and 200 patients received a mean of 21.49 (0.81 to 134.81) mL/kg of intravenous fluid. Multivariate outcomes analyses demonstrated a significant, direct relationship between resuscitative volume and days of postclosure ventilation, TPN, length of hospital stay, and bacteremic episodes; specifically, every 17 mL/kg of fluid predicted one additional ventilation day (p = 0.002), TPN day (p = 0.01), and hospital day (p = 0.01) and 0.02 odds increase of an episode of bacteremia (p = 0.03). Judicious, preclosure fluid resuscitation is essential in early GS management. Excessive fluid is associated with several adverse survival outcomes.

Three measures of forest fire smoke exposure and their associations with respiratory and cardiovascular health outcomes in a population-based cohort.

BACKGROUND: During the summer of 2003 numerous fires burned in British Columbia, Canada. OBJECTIVES: We examined the associations between respiratory and cardiovascular physician visits and hospital admissions, and three measures of smoke exposure over a 92-day study period (1 July to 30 September 2003). METHODS: A population-based cohort of 281,711 residents was identified from administrative data. Spatially specific daily exposure estimates were assigned to each subject based on total measurements of particulate matter (PM) ≤ 10 µm in aerodynamic diameter (PM10) from six regulatory tapered element oscillating microbalance (TEOM) air quality monitors, smoke-related PM10 from a CALPUFF dispersion model run for the study, and a SMOKE exposure metric for plumes visible in satellite images. Logistic regression with repeated measures was used to estimate associations with each outcome. RESULTS: The mean (± SD) exposure based on TEOM-measured PM10 was 29 ± 31 µg/m3, with an interquartile range of 14-31 µg/m3. Correlations between the TEOM, smoke, and CALPUFF metrics were moderate (0.37-0.76). Odds ratios (ORs) for a 30-µg/m3 increase in TEOM-based PM10 were 1.05 [95% confidence interval (CI), 1.03-1.06] for all respiratory physician visits, 1.16 (95% CI, 1.09-1.23) for asthma-specific visits, and 1.15 (95% CI, 1.00-1.29) for respiratory hospital admissions. Associations with cardiovascular outcomes were largely null. CONCLUSIONS: Overall we found that increases in TEOM-measured PM10 were associated with increased odds of respiratory physician visits and hospital admissions, but not with cardiovascular health outcomes. Results indicating effects of fire smoke on respiratory outcomes are consistent with previous studies, as are the null results for cardiovascular outcomes. Some agreement between TEOM and the other metrics suggests that exposure assessment tools that are independent of air quality monitoring may be useful with further refinement.

Birth outcomes among older mothers in rural versus urban areas: a residence-based approach.

PURPOSE: We examined the association between rural residence and birth outcomes in older mothers, the effect of parity on this association, and the trend in adverse birth outcomes in relation to the distance to the nearest hospital with cesarean-section capacity. METHODS: A population-based retrospective cohort study, including all singleton births to 35+ year-old women in British Columbia (Canada), 1999-2003. We compared birth outcomes in rural versus urban areas, and between 3 distance categories to a hospital (<50, 50-150, >150 km). Outcomes included labor induction, cesarean section, stillbirth, perinatal death, preterm birth (<37 weeks), small-for-gestational-age, large-for-gestational-age, and neonatal intensive care unit admission. We used multivariate regression to obtain adjusted odds ratios (ORs) and 95% confidence intervals (CIs). FINDINGS: Among the 29,698 subjects, 11.5% lived in rural areas; 5% lived within 50-150 km; and 1.1% lived >150 km from a hospital. Rural women were at lower risk of primary and repeat cesarean section (OR = 0.9, CI: 0.9-1.0; OR = 0.7, CI: 0.6-0.9) and small-for-gestational-age (OR = 0.8, CI: 0.7-0.9) births; they were at increased risk for perinatal death (OR = 1.5, CI: 1.1-2.1) and large-for-gestational-age (OR = 1.1, CI: 1.1-1.2) births. The association was stronger among multiparous versus primiparous women. No differences in emergency cesarean section, preterm birth, or neonatal intensive care admission were found, regardless of parity. Perinatal mortality increased with distance from hospital; OR = 1.5 (CI: 1.1-2.1) per distance category. CONCLUSIONS: Older women in rural versus urban areas had a lower rate of cesarean section and increased risk of perinatal death. The risk of perinatal death increased with the distance to hospital. Further studies need to evaluate the contribution of underlying perinatal risks, access to care, and decision making regarding referral and transport.

On Gaussian Markov random fields and Bayesian disease mapping.

We discuss the nature of Gaussian Markov random fields (GMRFs) as they are typically formulated via full conditionals, also named conditional autoregressive or CAR formulations, to represent small area relative risks ensemble priors within a Bayesian hierarchical model framework for statistical inference in disease mapping and spatial regression. We present a partial review on GMRF/CAR and multivariate GMRF prior formulations in univariate and multivariate disease mapping models and communicate insights into various prior characteristics for representing disease risks variability and 'spatial interaction.' We also propose convolution prior modifications to the well known BYM model for attainment of identifiability and Bayesian robustness in univariate and multivariate disease mapping and spatial regression. Several illustrative examples of disease mapping and spatial regression are presented.

Water and sewage systems, socio-demographics, and duration of residence associated with endemic intestinal infectious diseases: a cohort study.

BACKGROUND: Studies of water-related gastrointestinal infections are usually directed at outbreaks. Few have examined endemic illness or compared rates across different water supply and sewage disposal systems. We conducted a cohort study of physician visits and hospitalizations for endemic intestinal infectious diseases in a mixed rural and urban community near Vancouver, Canada, with varied and well-characterized water and sewage systems. METHODS: Cohort members and their disease events were defined via universal health insurance data from 1995 through 2003. Environmental data were derived from municipal, provincial, and federal government sources. Logistic regression was used to examine associations between disease events and water and sewage systems, socio-demographic characteristics, and temporal factors. RESULTS: The cohort included 126,499 individuals and approximately 190,000,000 person-days. Crude incidence rates were 1,353 physician visits and 33.8 hospitalizations for intestinal infectious diseases per 100,000 person-years. Water supply chlorination was associated with reduced physician visit incidence (OR: 0.92, 95% CI 0.85-1.0). Two water systems with the highest proportions of surface water had increased incidence (ORs: 1.57, 95% CI 1.39-1.78; and 1.45, 95% CI 1.28-1.64). Private well water and well depth were not associated with increased risk, likely because of residents' awareness of and attention to water quality. There was increased crude incidence with increasing precipitation in the population served by surface water supplies, but this trend did not remain with adjustment for other variables. Municipal sewer systems were associated with increased risk (OR: 1.26, 95% CI 1.14-1.38). Most socio-demographic variables had predicted associations with risk: higher rates in females, in the very young and the elderly, and in residents of low income areas. Increased duration of area residence was associated with reduced risk (OR, duration ≥ 6 years: 0.69, 95% CI 0.60-0.80 vs. < 1 year: 1.16, 95% CI 1.03-1.30). CONCLUSIONS: This large cohort study, with objective data on exposures and outcomes, demonstrated associations between endemic infectious intestinal diseases and factors related to water supply, sewage disposal, socio-demographics, and duration of residency. The results did not always follow prior expectations based on studies examining outbreaks and single systems, and underscore the importance of studying factors associated with endemic disease across water and sewage system types.