Second-order analysis of inhomogeneous spatial point processes using case-control data.

Methods for the statistical analysis of stationary spatial point process data are now well established, methods for nonstationary processes less so. One of many sources of nonstationary point process data is a case-control study in environmental epidemiology. In that context, the data consist of a realization of each of two spatial point processes representing the locations, within a specified geographical region, of individual cases of a disease and of controls drawn at random from the population at risk. In this article, we extend work by Baddeley, Møller, and Waagepetersen (2000, Statistica Neerlandica54, 329-350) concerning estimation of the second-order properties of a nonstationary spatial point process. First, we show how case-control data can be used to overcome the problems encountered when using the same data to estimate both a spatially varying intensity and second-order properties. Second, we propose a semiparametric method for adjusting the estimate of intensity so as to take account of explanatory variables attached to the cases and controls. Our primary focus is estimation, but we also propose a new test for spatial clustering that we show to be competitive with existing tests. We describe an application to an ecological study in which juvenile and surviving adult trees assume the roles of controls and cases.

Investigation of spatial clustering from individually matched case-control studies.

The paper demonstrates how existing theory to assess spatial clustering based on second-moment properties of a labelled point process can be adapted to matched case-control studies. The null hypothesis that cases are a random sample from the superposition of cases and controls is replaced by the hypothesis that each case is a random sample from the set consisting of itself and its k matched controls. We compare the proposed test with other tests of spatial clustering, and describe an application to data on childhood diabetes in Yorkshire, England.

A mixture model for sucking patterns of breast-fed infants.

Previous studies of sucking patterns have mainly been on bottle-fed babies and have assumed that the babies' sucks occur within bursts separated by gaps of predetermined minimum length which is fixed over the feed. This study considers babies that are breast-fed, a more complex and natural process than bottle-feeding, and develops a more sophisticated model for the pattern of bursts and gaps which allows the parameters of the process to vary over the feed. We consider data from four breast feeds of each of 32 babies. We develop a two-component mixture model based on an underlying Markov chain model for the switching between bursts and gaps. We use the model to provide summary statistics for each feed and give estimates of the normal range of each of the model's parameters.

Second-order analysis of space-time clustering.

We consider the problem of detecting and describing space-time interaction in point process data. We extend existing second-order methods for purely spatial point process data to the spatial-temporal setting. This extension allows us to estimate space-time interaction as a function of spatial and temporal separation, and provides a useful reinterpretation of a popular test, due to Knox, for space-time interaction. Applications to simulated and real data indicate the method's potential.

Second-order analysis of spatial clustering for inhomogeneous populations.

Motivated by recent interest in the possible spatial clustering of rare diseases, the paper develops an approach to the assessment of spatial clustering based on the second-moment properties of a labelled point process. The concept of no spatial clustering is identified with the hypothesis that in a realisation of a stationary spatial point process consisting of events of two qualitatively different types, the type 1 events are a random sample from the superposition of type 1 and type 2 events. A diagnostic plot for estimating the nature and physical scale of clustering effects is proposed. The availability of Monte Carlo tests of significance is noted. An application to published data on the spatial distribution of childhood leukaemia and lymphoma in North Humberside is described.