Hierarchical Bayes GLMs for the analysis of spatial data: An application to disease mapping

This paper considers estimation of cancer incidence rates for local areas. The raw estimates usually are based on small sample sizes, and hence are usually unreliable. A hierarchical Bayes generalized linear model approach is taken which connects the local areas, thereby enabling one to ‘borrow strength’. Random effects with pairwise difference priors model the spatial structure in the data. The methods are applied to cancer incidence estimation for census tracts in a certain region of the state of New York.     

Modelling map positional error to infer true feature location

The authors consider the issue of map positional error, or the difference between location as represented in a spatial database (i.e., a map) and the corresponding unobservable true location. They propose a fully model‐based approach that incorporates aspects of the map registration process commonly performed by users of geographic informations systems, including rubber‐sheeting. They explain how estimates of positional error can be obtained, hence estimates of true location. They show that with multiple maps of varying accuracy along with ground truthing data, suitable model averaging offers a strategy for using all of the maps to learn about true location.     

Direct parametric inference for the cumulative incidence function

Summary.  In survival data that are collected from phase III clinical trials on breast cancer, a patient may experience more than one event, including recurrence of the original cancer, new primary cancer and death. Radiation oncologists are often interested in comparing patterns of local or regional recurrences alone as first events to identify a subgroup of patients who need to be treated by radiation therapy after surgery. The cumulative incidence function provides estimates of the cumulative probability of locoregional recurrences in the presence of other competing events. A simple version of the Gompertz distribution is proposed to parameterize the cumulative incidence function directly. The model interpretation for the cumulative incidence function is more natural than it is with the usual cause-specific hazard parameterization. Maximum likelihood analysis is used to estimate simultaneously parametric models for cumulative incidence functions of all causes. The parametric cumulative incidence approach is applied to a data set from the National Surgical Adjuvant Breast and Bowel Project and compared with analyses that are based on parametric cause-specific hazard models and nonparametric cumulative incidence estimation.     

Exploring spatial dependence in area-level random effect model for disaggregate-level crop yield estimation

This paper describes an application of small area estimation (SAE) techniques under area-level spatial random effect models when only area (or district or aggregated) level data are available. In particular, the SAE approach is applied to produce district-level model-based estimates of crop yield for paddy in the state of Uttar Pradesh in India using the data on crop-cutting experiments supervised under the Improvement of Crop Statistics scheme and the secondary data from the Population Census. The diagnostic measures are illustrated to examine the model assumptions as well as reliability and validity of the generated model-based small area estimates. The results show a considerable gain in precision in model-based estimates produced applying SAE. Furthermore, the model-based estimates obtained by exploiting spatial information are more efficient than the one obtained by ignoring this information. However, both of these model-based estimates are more efficient than the direct survey estimate. In many districts, there is no survey data and therefore it is not possible to produce direct survey estimates for these districts. The model-based estimates generated using SAE are still reliable for such districts. These estimates produced by using SAE will provide invaluable information to policy-analysts and decision-makers.     

Small area estimation of proportions under a spatial dependent aggregated level random effects model

This paper describes small area estimation (SAE) of proportions under a spatial dependent generalized linear mixed model using aggregated level data. The SAE is also applied to produce reliable district level estimates and mapping of incidence of indebtedness in the State of Uttar Pradesh in India using debt and investment survey data collected by National Sample Survey Office (NSSO) and the secondary data from the Census. The results show a significant improvement in precision of model-based estimates generated by SAE as compared to direct estimates. The estimates generated by incorporating spatial information are more efficient than the one generated by ignoring this information.     

Multivariate meta-analysis for data consortia,individual patient meta-analysis,and pooling projects

We discuss maximum likelihood and estimating equations methods for combining results from multiple studies in pooling projects and data consortia using a meta-analysis model, when the multivariate estimates with their covariance matrices are available. The estimates to be combined are typically regression slopes, often from relative risk models in biomedical and epidemiologic applications. We generalize the existing univariate meta-analysis model and investigate the efficiency advantages of the multivariate methods, relative to the univariate ones. We generalize a popular univariate test for between-studies homogeneity to a multivariate test. The methods are applied to a pooled analysis of type of carotenoids in relation to lung cancer incidence from seven prospective studies. In these data, the expected gain in efficiency was evident, sometimes to a large extent. Finally, we study the finite sample properties of the estimators and compare the multivariate ones to their univariate counterparts.     

Methods for Quantitative Risk Assessment Using Occupational Studies

Although carcinogenic risk assessment is frequently based on animal bioassay data, occupational studies are generally considered the best source of data for quantitative risk estimation. The model selected for use with occupational study data is required to extrapolate on age, exposure level, and temporal exposure pattern. Relative and absolute risk models are examined, as are alternatives for the definition of a dose (exposure) variable. The models express disease incidence as a function of the chosen exposure variable and convert incidence into estimates of lifetime risk. In this form, predictions of the models can be compared. The methods are illustrated using three examples: arsenic exposure and respiratory cancer, leukemia associated with benzene exposure, and asbestos-induced mesothelioma.     

Spatial Modeling of Habitat Preferences of Biological Species using Markov Random Fields

Spatial modeling has gained interest in ecology during the past two decades, especially in the area of biodiversity, where reliable distribution maps are required. Several methods have been proposed to construct distribution maps, most of them acknowledging the presence of spatial interactions. In many cases, a key problem is the lack of true absence data. We present here a model suitable for use when true absence data are missing. The quality of the estimates obtained from the model is evaluated using ROC curve analysis as well as a quadratic cost function, computed from the false positive and false negative error rates. The model is also tested under random and clustered scattering of the presence records. We also present an application of the model to the construction of distribution maps of two endemic bird species in México.     

Influence of light level on the incidence of road casualties and the predicted effect of changing 'summertime'

Previous studies of the apparent influence of daylight level and hour changes on the incidence of road casualties are reviewed and refined, by analysis of official databases for Great Britain (1969–1973 and 1985–1994) and the USA (1991–1995). New statistical methods, based on precisely computed altitudes of the sun for each accident location, are used to model casualty frequencies aggregated by week and hour of day, and locally evaluated associations between individual casualty incidence and solar altitude. Estimates of the altitude factor are interpreted causally to give counterfactual estimates of the effect of different clock time schedules on countrywide casualty numbers.     

A Case for Better Graphics: The Unclassed Choropleth Map

In recent years a number of researchers have shown a strong interest in statistical graphics. One widely used graphical method is the “statistical map,” or what is better known in cartography as the choropleth map. A factor in the use of these maps has been the need to group data into classes, raising the obvious question of defining optimum class intervals. Computer technology now makes it possible to produce unclassed choropleth maps, minimizing quantization error. An example of the two methods is given using criminal justice statistics. The unclassed maps are more accurate with regard to quantization error and appear to be of superior visual quality     

Numerical experiments with the thin plate histospline

The thin plate volume matching and volume smoothing histosplines are described. These histosplines are suitable for estimating densities or incidence rates as a function of position on the plane when data is aggregated by area, for example by county. We give a numerical algorithm for the volume matching histospline and for the volume smoothing histospline using generalized cross validation to estimate the smoothing parameter. Some numerical experiments were performed using synthetic data, population data and SMR's (standardized mortality ratios) aggregated by county over the state of Wisconsin. The method turns out to be not particularly suited for obtaining population density maps where the population density can vary by two orders of magnitude, because the histospline can be negative in     

Generalised Variance Function Estimation for Binary Variables in Large‐Scale Sample Surveys

Generalised variance function (GVF) models are data analysis techniques often used in large‐scale sample surveys to approximate the design variance of point estimators for population means and proportions. Some potential advantages of the GVF approach include operational simplicity, more stable sampling errors estimates and providing a convenient method of summarising results when a high number of survey variables is considered. In this paper, several parametric and nonparametric methods for GVF estimation with binary variables are proposed and compared. The behavior of these estimators is analysed under heteroscedasticity and in the presence of outliers and influential observations. An empirical study based on the annual survey of living conditions in Galicia (a region in the northwest of Spain) illustrates the behaviour of the proposed estimators.     

Simple methods for ecological inference in 2×2 tables

This paper considers inference about the individual level relationship between two dichotomous variables based on aggregated data. It is known that such analyses suffer from 'ecological bias', caused by the lack of homogeneity of this relationship across the groups over which the aggregation occurs. Two new methods for overcoming this bias, one based on local smoothing and the other a simple semiparametric approach, are developed and evaluated. The local smoothing approach performs best when it is used with a covariate which accounts for some of the variation in the relationships across groups. The semiparametric approach performed well in our evaluation even without such auxiliary information     

The Risk of a Mortality Catastrophe

We develop a continuous-time model for analyzing and valuing catastrophe mortality contingent claims based on stochastic modeling of the force of mortality. We derive parameter estimates from a 105-year time series of U.S. population mortality data using a simulated maximum likelihood approach based on a particle filter. Relying on the resulting parameters, we calculate loss profiles for a representative catastrophe mortality transaction and compare them to the “official” loss profiles that are provided by the issuers to investors and rating agencies. We find that although the loss profiles are subject to great uncertainties, the official figures fall significantly below the corresponding risk statistics based on our model. In particular, we find that the annualized incidence probability of a mortality catastrophe, defined as a 15% increase in aggregated mortality probabilities, is about 1.4%—compared to about 0.1% according to the official loss profiles.     

Models for surveillance data under reporting delay: applications to US veteran first-time suicide attempters

Surveillance data provide a vital source of information for assessing the spread of a health problem or disease of interest and for planning for future health-care needs. However, the use of surveillance data requires proper adjustments of the reported caseload due to underreporting caused by reporting delays within a limited observation period. Although methods are available to address this classic statistical problem, they are largely focused on inference for the reporting delay distribution, with inference about caseload of disease incidence based on estimates for the delay distribution. This approach limits the complexity of models for disease incidence to provide reliable estimates and projections of incidence. Also, many of the available methods lack robustness since they require parametric distribution assumptions. We propose a new approach to overcome such limitations by allowing for separate models for the incidence and the reporting delay in a distribution-free fashion, but with joint inference for both modeling components, based on functional response models. In addition, we discuss inference about projections of future disease incidence to help identify significant shifts in temporal trends modeled based on the observed data. This latter issue on detecting ‘change points’ is not sufficiently addressed in the literature, despite the fact that such warning signs of potential outbreak are critically important for prevention purposes. We illustrate the approach with both simulated and real data, with the latter involving data for suicide attempts from the Veteran Healthcare Administration.     

Bayesian age-stratified joinpoint regression model: an application to lung and brain cancer mortality

Joinpoint regression model identifies significant changes in the trends of the incidence, mortality, and survival of a specific disease in a given population. The purpose of the present study is to develop an age-stratified Bayesian joinpoint regression model to describe mortality trend assuming that the observed counts are probabilistically characterized by the Poisson distribution. The proposed model is based on Bayesian model selection criteria with the smallest number of joinpoints that are sufficient to explain the Annual Percentage Change. The prior probability distributions are chosen in such a way that they are automatically derived from the model index contained in the model space. The proposed model and methodology estimates the age-adjusted mortality rates in different epidemiological studies to compare the trends by accounting the confounding effects of age. In developing the subject methods, we use the cancer mortality counts of adult lung and bronchus cancer, and brain and other Central Nervous System cancer patients obtained from the Surveillance Epidemiology and End Results data base of the National Cancer Institute.     

Random sliced inverse regression

Sliced Inverse Regression (SIR; 1991) is a dimension reduction method for reducing the dimension of the predictors without losing regression information. The implementation of SIR requires inverting the covariance matrix of the predictors—which has hindered its use to analyze high-dimensional data where the number of predictors exceed the sample size. We propose random sliced inverse regression (rSIR) by applying SIR to many bootstrap samples, each using a subset of randomly selected candidate predictors. The final rSIR estimate is obtained by aggregating these estimates. A simple variable selection procedure is also proposed using these bootstrap estimates. The performance of the proposed estimates is studied via extensive simulation. Application to a dataset concerning myocardial perfusion diagnosis from cardiac Single Proton Emission Computed Tomography (SPECT) images is presented.     

Small area estimates of labour force participation under a multinomial logit mixed model

Summary.  A new methodology is developed for estimating unemployment or employment characteristics in small areas, based on the assumption that the sample totals of unemployed and employed individuals follow a multinomial logit model with random area effects. The method is illustrated with UK labour force data aggregated by sex–age groups. For these data, the accuracy of direct estimates is poor in comparison with estimates that are derived from the multinomial logit model. Furthermore, two different estimators of the mean-squared errors are given: an analytical approximation obtained by Taylor linearization and an estimator based on bootstrapping. A simulation study for comparison of the two estimators shows the good performance of the bootstrap estimator.