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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.

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.

Background: Many patients with primary biliary cirrhosis (PBC) are asymptomatic at the time of diagnosis. However, because most studies of asymptomatic PBC have been small and from tertiary centres, asymptomatic PBC remains poorly characterised. Aims: To describe the features and progression of initially asymptomatic PBC patients. Methods: Follow up by interview and note review of a large geographically and temporally defined cohort of patients with PBC, collected by multiple methods. Results: Of a total of 770 patients, 469 (61%) were asymptomatic at diagnosis. These patients had biochemically and histologically less advanced disease than initially symptomatic patients. Median survival was similar in both groups (9.6 v 8.0 years, respectively) possibly due to excess of non-liver related deaths in asymptomatic patients (31% v 57% of deaths related to liver disease). Survival in initially asymptomatic patients was not affected by subsequent symptom development. By the end of follow up, 20% of initially asymptomatic patients had died of liver disease or required liver transplantation. The majority of initially asymptomatic patients developed symptoms of liver disease if they were followed up for long enough (Kaplan-Meier estimate of proportion developing symptoms: 50% after five years, 95% after 20 years). However, 45% of patients remained asymptomatic at the time of death. Conclusions: Although asymptomatic PBC is less severe at diagnosis than symptomatic disease, it is not associated with a better prognosis, possibly due to an increase in non-hepatic deaths. The reasons for this are unclear but may reflect confounding by other risk factors or surveillance bias. These findings have important implications for future treatment strategies.

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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.

OBJECTIVEThe aim if the study was to investigate whether children born to older mothers have an increased risk of type 1 diabetes by performing a pooled analysis of previous studies using individual patient data to adjust for recognized confounders.RESEARCH DESIGN AND METHODSRelevant studies published before June 2009 were identified from MEDLINE, Web of Science, and EMBASE. Authors of studies were contacted and asked to provide individual patient data or conduct prespecified analyses. Risk estimates of type 1 diabetes by maternal age were calculated for each study, before and after adjustment for potential confounders. Meta-analysis techniques were used to derive combined odds ratios and to investigate heterogeneity among studies.RESULTSData were available for 5 cohort and 25 case-control studies, including 14,724 cases of type 1 diabetes. Overall, there was, on average, a 5% (95% CI 2–9) increase in childhood type 1 diabetes odds per 5-year increase in maternal age (P = 0.006), but there was heterogeneity among studies (heterogeneity I2 = 70%). In studies with a low risk of bias, there was a more marked increase in diabetes odds of 10% per 5-year increase in maternal age. Adjustments for potential confounders little altered these estimates.CONCLUSIONSThere was evidence of a weak but significant linear increase in the risk of childhood type 1 diabetes across the range of maternal ages, but the magnitude of association varied between studies. A very small percentage of the increase in the incidence of childhood type 1 diabetes in recent years could be explained by increases in maternal age.