A Bayesian space varying parameter model applied to estimating fertility schedules

A Bayesian adaptive phase II clinical trial design accounting for spatial variation

Conventional phase II clinical trials evaluate the treatment effects under the assumption of patient homogeneity. However, due to inter-patient heterogeneity, the effect of a treatment may differ remarkably among subgroups of patients. Besides patient’s individual characteristics such as age, gender, and biomarker status, a substantial amount of this heterogeneity could be due to the spatial variation across geographic regions because of unmeasured or unknown spatially varying environmental and social exposures. In this article, we propose a hierarchical Bayesian adaptive design for two-arm randomized phase II clinical trials that accounts for the spatial variation as well as patient’s individual characteristics. We treat the treatment efficacy as an ordinal outcome and quantify the desirability of each possible category of the ordinal efficacy using a utility function. A cumulative probit mixed model is used to relate efficacy to patient-specific covariates and geographic region spatial effects. Spatial dependence between regions is induced through the conditional autoregressive priors on the spatial effects. A two-stage design is proposed to adaptively assign patients to desirable treatments according to each patient’s spatial information and individual covariates and make treatment recommendations at the end of the trial based on the overall treatment effect. Simulation studies show that our proposed design has good operating characteristics and significantly outperforms an alternative phase II trial design that ignores the spatial variation.

Revisiting crash spatial heterogeneity: A Bayesian spatially varying coefficients approach

This study was performed to investigate the spatially varying relationships between crash frequency and related risk factors. A Bayesian spatially varying coefficients model was elaborately introduced as a methodological alternative to simultaneously account for the unstructured and spatially structured heterogeneity of the regression coefficients in predicting crash frequencies. The proposed method was appealing in that the parameters were modeled via a conditional autoregressive prior distribution, which involved a single set of random effects and a spatial correlation parameter with extreme values corresponding to pure unstructured or pure spatially correlated random effects. A case study using a three-year crash dataset from the Hillsborough County, Florida, was conducted to illustrate the proposed model. Empirical analysis confirmed the presence of both unstructured and spatially correlated variations in the effects of contributory factors on severe crash occurrences. The findings also suggested that ignoring spatially structured heterogeneity may result in biased parameter estimates and incorrect inferences, while assuming the regression coefficients to be spatially clustered only is probably subject to the issue of over-smoothness.

Bayesian spatially dependent variable selection for small area health modeling

Statistical methods for spatial health data to identify the significant covariates associated with the health outcomes are of critical importance. Most studies have developed variable selection approaches in which the covariates included appear within the spatial domain and their effects are fixed across space. However, the impact of covariates on health outcomes may change across space and ignoring this behavior in spatial epidemiology may cause the wrong interpretation of the relations. Thus, the development of a statistical framework for spatial variable selection is important to allow for the estimation of the space-varying patterns of covariate effects as well as the early detection of disease over space. In this paper, we develop flexible spatial variable selection approaches to find the spatially-varying subsets of covariates with significant effects. A Bayesian hierarchical latent model framework is applied to account for spatially-varying covariate effects. We present a simulation example to examine the performance of the proposed models with the competing models. We apply our models to a county-level low birth weight incidence dataset in Georgia.

A Four Dimensional Spatio-Temporal Analysis of an Agricultural Dataset

While a variety of statistical models now exist for the spatio-temporal analysis of two-dimensional (surface) data collected over time, there are few published examples of analogous models for the spatial analysis of data taken over four dimensions: latitude, longitude, height or depth, and time. When taking account of the autocorrelation of data within and between dimensions, the notion of closeness often differs for each of the dimensions. Here, we consider a number of approaches to the analysis of such a dataset, which arises from an agricultural experiment exploring the impact of different cropping systems on soil moisture. The proposed models vary in their representation of the spatial correlation in the data, the assumed temporal pattern and choice of conditional autoregressive (CAR) and other priors. In terms of the substantive question, we find that response cropping is generally more effective than long fallow cropping in reducing soil moisture at the depths considered (100 cm to 220 cm). Thus, if we wish to reduce the possibility of deep drainage and increased groundwater salinity, the recommended cropping system is response cropping.

Bayesian latent structure models with space-time-dependent covariates

Spatial-temporal data requires flexible regression models which can model the dependence of responses on space- and time-dependent covariates. In this paper, we describe a semiparametric space-time model from a Bayesian perspective. Nonlinear time dependence of covariates and the interactions among the covariates are constructed by local linear and piecewise linear models, allowing for more flexible orientation and position of the covariate plane by using time-varying basis functions. Space-varying covariate linkage coefficients are also incorporated to allow for the variation of space structures across the geographical location. The formulation accommodates uncertainty in the number and locations of the piecewise basis functions to characterize the global effects, spatially structured and unstructured random effects in relation to covariates. The proposed approach relies on variable selection-type mixture priors for uncertainty in the number and locations of basis functions and in the space-varying linkage coefficients. A simulation example is presented to evaluate the performance of the proposed approach with the competing models. A real data example is used for illustration.

Bayesian statistics in medicine: a 25 year review

This review examines the state of Bayesian thinking as Statistics in Medicine was launched in 1982, reflecting particularly on its applicability and uses in medical research. It then looks at each subsequent five-year epoch, with a focus on papers appearing in Statistics in Medicine, putting these in the context of major developments in Bayesian thinking and computation with reference to important books, landmark meetings and seminal papers. It charts the growth of Bayesian statistics as it is applied to medicine and makes predictions for the future. From sparse beginnings, where Bayesian statistics was barely mentioned, Bayesian statistics has now permeated all the major areas of medical statistics, including clinical trials, epidemiology, meta-analyses and evidence synthesis, spatial modelling, longitudinal modelling, survival modelling, molecular genetics and decision-making in respect of new technologies.

The health status of southern children: a neglected regional disparity

PURPOSE

Great variations exist in child health outcomes among states in the United States, with southern states consistently ranked among the lowest in the country. Investigation of the geographical distribution of children's health status and the regional factors contributing to these outcomes has been neglected. We attempted to identify the degree to which region of residence may be linked to health outcomes for children with the specific aim of determining whether living in the southern region of the United States is adversely associated with children's health status.

METHODS

A child health index (CHI) that ranked each state in the United States was computed by using state-specific composite scores generated from outcome measures for a number of indicators of child health. Five indicators for physical health were chosen (percent low birth weight infants, infant mortality rate, child death rate, teen death rate, and teen birth rates) based on their historic and routine use to define health outcomes in children. Indicators were calculated as rates or percentages. Standard scores were calculated for each state for each health indicator by subtracting the mean of the measures for all states from the observed measure for each state. Indicators related to social and economic status were considered to be variables that impact physical health, as opposed to indicators of physical health, and therefore were not used to generate the composite child health score. These variables were subsequently examined in this study as potential confounding variables. Mapping was used to redefine regional groupings of states, and parametric tests (2-sample t test, analysis of means, and analysis-of-variance F tests) were used to compare the means of the CHI scores for the regional groupings and test for statistical significance. Multiple-regression analysis computed the relationship of region, social and economic indicators, and race to the CHI. Simple linear-regression analyses were used to assess the individual effect of each indicator.

RESULTS

A geographic region of contiguous states, characterized by their poor child health outcomes relative to other states and regions of the United States, exists within the "Deep South" (Mississippi, Louisiana, Arkansas, Tennessee, Alabama, Georgia, North Carolina, South Carolina, and Florida). This Deep-South region is statistically different in CHI scores from the US Census Bureau-defined grouping of states in the South. The mean of CHI scores for the Deep-South region was >1 SD below the mean of CHI scores for all states. In contrast, the CHI score means for each of the other 3 regions were all above the overall mean of CHI scores for all states. Regression analysis showed that living in the Deep-South region is a stronger predictor of poor child health outcomes than other consistently collected and reported variables commonly used to predict children's health.

CONCLUSIONS

The findings of this study indicate that region of residence in the United States is statistically related to important measures of children's health and may be among the most powerful predictors of child health outcomes and disparities. This clarification of the poorer health status of children living in the Deep South through spatial analysis is an essential first step for developing a better understanding of variations in the health of children. Similar to early epidemiology work linking geographic boundaries to disease, discovering the mechanisms/pathways/causes by which region influences health outcomes is a critical step in addressing disparities and inequities in child health and one that is an important and fertile area for future research. The reasons for these disparities may be complex and synergistically related to various economic, political, social, cultural, and perhaps even environmental (physical) factors in the region. This research will require the use and development of new approaches and applications of spatial analysis to develop insights into the societal, environmental, and historical determinants of child health that have been neglected in previous child health outcomes and policy research. The public policy implications of the findings in this study are substantial. Few, if any, policies identify these children as a high-risk group on the basis of their region of residence. A better understanding of the depth and breadth of disparities in health, education, and other social outcomes among and within regions of the United States is necessary for the generation of policies that enable policy makers to address and mitigate the factors that influence these disparities. Defining and clarifying the regional boundaries is also necessary to better inform public policy decisions related to resource allocation and the prevention and/or mitigation of the effects of region on child health. The identification of the Deep South as a clearly defined subregion of the Census Bureau's regional definition of the South suggests the need to use more culturally and socially relevant boundaries than the Census Bureau regions when analyzing regional data for policy development.