Estimating Individual-Level Risk in Spatial Epidemiology Using Spatially Aggregated Information on the Population at Risk

Multivariate Temporal Point Process Regression

Point process modeling is gaining increasing attention, as point process type data are emerging in a large variety of scientific applications. In this article, motivated by a neuronal spike trains study, we propose a novel point process regression model, where both the response and the predictor can be a high-dimensional point process. We model the predictor effects through the conditional intensities using a set of basis transferring functions in a convolutional fashion. We organize the corresponding transferring coefficients in the form of a three-way tensor, then impose the low-rank, sparsity, and subgroup structures on this coefficient tensor. These structures help reduce the dimensionality, integrate information across different individual processes, and facilitate the interpretation. We develop a highly scalable optimization algorithm for parameter estimation. We derive the large sample error bound for the recovered coefficient tensor, and establish the subgroup identification consistency, while allowing the dimension of the multivariate point process to diverge. We demonstrate the efficacy of our method through both simulations and a cross-area neuronal spike trains analysis in a sensory cortex study.

At-risk-measure Sampling in Case-Control Studies with Aggregated Data

Transient exposures are difficult to measure in epidemiologic studies, especially when both the status of being at risk for an outcome and the exposure change over time and space, as when measuring built-environment risk on transportation injury. Contemporary "big data" generated by mobile sensors can improve measurement of transient exposures. Exposure information generated by these devices typically only samples the experience of the target cohort, so a case-control framework may be useful. However, for anonymity, the data may not be available by individual, precluding a case-crossover approach. We present a method called at-risk-measure sampling. Its goal is to estimate the denominator of an incidence rate ratio (exposed to unexposed measure of the at-risk experience) given an aggregated summary of the at-risk measure from a cohort. Rather than sampling individuals or locations, the method samples the measure of the at-risk experience. Specifically, the method as presented samples person-distance and person-events summarized by location. It is illustrated with data from a mobile app used to record bicycling. The method extends an established case-control sampling principle: sample the at-risk experience of a cohort study such that the sampled exposure distribution approximates that of the cohort. It is distinct from density sampling in that the sample remains in the form of the at-risk measure, which may be continuous, such as person-time or person-distance. This aspect may be both logistically and statistically efficient if such a sample is already available, for example from big-data sources like aggregated mobile-sensor data.

Comparison of Models Analyzing a Small Number of Observed Meningitis Cases in Navrongo, Ghana

The "meningitis belt" is a region in sub-Saharan Africa where annual outbreaks of meningitis occur, with epidemics observed cyclically. While we know that meningitis is heavily dependent on seasonal trends, the exact pathways for contracting the disease are not fully understood and warrant further investigation. Most previous approaches have used large sample inference to assess impacts of weather on meningitis rates. However, in the case of rare events, the validity of such assumptions is uncertain. This work examines the meningitis trends in the context of rare events, with the specific objective of quantifying the underlying seasonal patterns in meningitis rates. We compare three main classes of models: the Poisson generalized linear model, the Poisson generalized additive model, and a Bayesian hazard model extended to accommodate count data and a changing at-risk population. We compare the accuracy and robustness of the models through the bias, RMSE, and standard deviation of the estimators, and also provide a detailed case study of meningitis patterns for data collected in Navrongo, Ghana.

Point pattern analysis with spatially varying covariate effects, applied to the study of cerebrovascular deaths

This article proposes a modeling approach for handling spatial heterogeneity present in the study of the geographical pattern of deaths due to cerebrovascular disease.The framework involvesa point pattern analysis with components exhibiting spatial variation. Preliminary studies indicate that mortality of this disease and the effect of relevant covariates do not exhibit uniform geographic distribution. Our model extends a previously proposed model in the literature that uses spatial and non-spatial variables by allowing for spatial variation of the effect of non-spatial covariates. A number of relative risk indicators are derived by comparing different covariate levels, different geographic locations, or both. The methodology is applied to the study of the geographical death pattern of cerebrovascular deaths in the city of Rio de Janeiro. The results compare well against existing alternatives, including fixed covariate effects. Our model is able to capture and highlight important data information that would not be noticed otherwise, providing information that is required for appropriate health decision-making.

Disease risk estimation by combining case-control data with aggregated information on the population at risk

We propose a novel statistical framework by supplementing case-control data with summary statistics on the population at risk for a subset of risk factors. Our approach is to first form two unbiased estimating equations, one based on the case-control data and the other on both the case data and the summary statistics, and then optimally combine them to derive another estimating equation to be used for the estimation. The proposed method is computationally simple and more efficient than standard approaches based on case-control data alone. We also establish asymptotic properties of the resulting estimator, and investigate its finite-sample performance through simulation. As a substantive application, we apply the proposed method to investigate risk factors for endometrial cancer, by using data from a recently completed population-based case-control study and summary statistics from the Behavioral Risk Factor Surveillance System, the Population Estimates Program of the US Census Bureau, and the Connecticut Department of Transportation.

A new estimation approach for combining epidemiological data from multiple sources

We propose a novel two-step procedure to combine epidemiological data obtained from diverse sources with the aim to quantify risk factors affecting the probability that an individual develops certain disease such as cancer. In the first step we derive all possible unbiased estimating functions based on a group of cases and a group of controls each time. In the second step, we combine these estimating functions efficiently in order to make full use of the information contained in data. Our approach is computationally simple and flexible. We illustrate its efficacy through simulation and apply it to investigate pancreatic cancer risks based on data obtained from the Connecticut Tumor Registry, a population-based case-control study, and the Behavioral Risk Factor Surveillance System which is a state-based system of health surveys.

Second-order analysis of semiparametric recurrent event processes

A typical recurrent event dataset consists of an often large number of recurrent event processes, each of which contains multiple event times observed from an individual during a follow-up period. Such data have become increasingly available in medical and epidemiological studies. In this article, we introduce novel procedures to conduct second-order analysis for a flexible class of semiparametric recurrent event processes. Such an analysis can provide useful information regarding the dependence structure within each recurrent event process. Specifically, we will use the proposed procedures to test whether the individual recurrent event processes are all Poisson processes and to suggest sensible alternative models for them if they are not. We apply these procedures to a well-known recurrent event dataset on chronic granulomatous disease and an epidemiological dataset on meningococcal disease cases in Merseyside, United Kingdom to illustrate their practical value.