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Background In large multiregional cohort studies, survival data is often collected at small geographical levels (such as counties) and aggregated at larger levels, leading to correlated patterns that are associated with location. Traditional studies typically analyze such data globally or locally by region, often neglecting the spatial information inherent in the data, which can introduce bias in effect estimates and potentially reduce statistical power. Method We propose a Geographically Weighted Accelerated Failure Time Model for spatial survival data to investigate spatial heterogeneity. We establish a weighting scheme and bandwidth selection based on quasi-likelihood information criteria. Theoretical properties of the proposed estimators are thoroughly examined. To demonstrate the efficacy of the model in various scenarios, we conduct a simulation study with different sample sizes and adherence to the proportional hazards assumption or not. Additionally, we apply the proposed method to analyze ovarian cancer survival data from the Surveillance, Epidemiology, and End Results cancer registry in the state of New Jersey. Results Our simulation results indicate that the proposed model exhibits superior performance in terms of four measurements compared to existing methods, including the geographically weighted Cox model, when the proportional hazards assumption is violated. Furthermore, in scenarios where the sample size per location is 20-25, the simulation data failed to fit the local model, while our proposed model still demonstrates satisfactory performance. In the empirical study, we identify clear spatial variations in the effects of all three covariates. Conclusion Our proposed model offers a novel approach to exploring spatial heterogeneity of survival data compared to global and local models, providing an alternative to geographically weighted Cox regression when the proportional hazards assumption is not met. It addresses the issue of certain counties' survival data being unable to fit the model due to limited samples, particularly in the context of rare diseases.

Survival data often contain small-area geographical or spatial information, such as the residence of individuals. In many cases, the impact of such spatial effects on hazard rates is of considerable substantive interest. Therefore, extensions of known survival or hazard rate models to spatial models have been suggested. Mostly, a spatial component is added to the usual linear predictor of the Cox model. In this article flexible continuous-time geoadditive models are proposed, extending the Cox model with respect to several aspects often needed in applications. The common linear predictor is generalized to an additive predictor, including nonparametric components for the log-baseline hazard, time-varying effects, and possibly nonlinear effects of continuous covariates or further time scales, and a spatial component for geographical effects. In addition, uncorrelated frailty effects or nonlinear two-way interactions can be incorporated. Inference is developed within a unified fully Bayesian framework. Penalized regression splines and Markov random fields are suggested as basic building blocks, and geostatistical (kriging) models are also considered. Posterior analysis uses computationally efficient Markov chain Monte Carlo sampling schemes. Smoothing parameters are an integral part of the model and are estimated automatically. Propriety of posteriors is shown under fairly general conditions, and practical performance is investigated through simulation studies. Our approach is applied to data from a case study in London and Essex that aims to estimate the effect of area of residence and further covariates on waiting times to coronary artery bypass grafting. Results provide clear evidence of nonlinear time-varying effects, and considerable spatial variability of waiting times to bypass grafting.

The global emergence of Batrachochytrium dendrobatidis (Bd) has caused the extinction of hundreds of amphibian species worldwide. It has become increasingly important to be able to precisely predict time to Bd arrival in a population. The data analyzed herein present a unique challenge in terms of modeling because there is a strong spatial component to Bd arrival time and the traditional proportional hazards assumption is grossly violated. To address these concerns, we develop a novel marginal Bayesian nonparametric survival model for spatially correlated right‐censored data. This class of models assumes that the logarithm of survival times marginally follow a mixture of normal densities with a linear‐dependent Dirichlet process prior as the random mixing measure, and their joint distribution is induced by a Gaussian copula model with a spatial correlation structure. To invert high‐dimensional spatial correlation matrices, we adopt a full‐scale approximation that can capture both large‐ and small‐scale spatial dependence. An efficient Markov chain Monte Carlo algorithm with delayed rejection is proposed for posterior computation, and an R package spBayesSurv is provided to fit the model. This approach is first evaluated through simulations, then applied to threatened frog populations in Sequoia‐Kings Canyon National Park.

The paper describes a Bayesian spatial discrete time survival model to estimate the effect of air pollution on the risk of preterm birth. The standard approach treats prematurity as a binary outcome and cannot effectively examine time varying exposures during pregnancy. Time varying exposures can arise either in short-term lagged exposures due to seasonality in air pollution or long-term cumulative exposures due to changes in length of exposure. Our model addresses this challenge by viewing gestational age as time-to-event data where each pregnancy becomes at risk at a prespecified time (e.g. the 28th week). The pregnancy is then followed until either a birth occurs before the 37th week (preterm), or it reaches the 37th week, and a full-term birth is expected. The model also includes a flexible spatially varying baseline hazard function to control for unmeasured spatial confounders and to borrow information across areal units. The approach proposed is applied to geocoded birth records in Mecklenburg County, North Carolina, for the period 2001–2005. We examine the risk of preterm birth that is associated with total cumulative and 4-week lagged exposure to ambient fine particulate matter.

There is an emerging interest in modeling spatially correlated survival data in biomedical and epidemiologic studies. In this article we propose a new class of semiparametric normal transformation models for right-censored spatially correlated survival data. This class of models assumes that survival outcomes marginally follow a Cox proportional hazard model with unspecified baseline hazard, and their joint distribution is obtained by transforming survival outcomes to normal random variables, whose joint distribution is assumed to be multivariate normal with a spatial correlation structure. A key feature of the class of semiparametric normal transformation models is that it provides a rich class of spatial survival models where regression coefficients have population average interpretation and the spatial dependence of survival times is conveniently modeled using the transformed variables by flexible normal random fields. We study the relationship of the spatial correlation structure of the transformed normal variables and the dependence measures of the original survival times. Direct nonparametric maximum likelihood estimation in such models is practically prohibited due to the high-dimensional intractable integration of the likelihood function and the infinite-dimensional nuisance baseline hazard parameter. We hence develop a class of spatial semiparametric estimating equations, which conveniently estimate the population-level regression coefficients and the dependence parameters simultaneously. We study the asymptotic properties of the proposed estimators and show that they are consistent and asymptotically normal. The proposed method is illustrated with an analysis of data from the East Boston Asthma Study, and its performance is evaluated using simulations.

While there is a considerable number of studies on the relationship between the risk of disease or death and direct exposure from the atomic bomb in Hiroshima, the risk for indirect exposure caused by residual radioactivity has not yet been fully evaluated. One of the reasons is that risk assessments have utilized estimated radiation doses, but that it is difficult to estimate indirect exposure. To evaluate risks for other causes, including indirect radiation exposure, as well as direct exposure, a statistical method is described here that evaluates risk with respect to individual location at the time of atomic bomb exposure instead of radiation dose. In addition, it is also considered to split the risks into separate risks due to direct exposure and other causes using radiation dose. The proposed method is applied to a cohort study of Hiroshima atomic bomb survivors. The resultant contour map suggests that the region west to the hypocenter has a higher risk compared to other areas. This in turn suggests that there exists an impact on risk that cannot be explained by direct exposure.

Background Tuberculosis (TB) transmission often occurs within a household or community, leading to heterogeneous spatial patterns. However, apparent spatial clustering of TB could reflect ongoing transmission or co-location of risk factors and can vary considerably depending on the type of data available, the analysis methods employed and the dynamics of the underlying population. Thus, we aimed to review methodological approaches used in the spatial analysis of TB burden. Methods We conducted a systematic literature search of spatial studies of TB published in English using Medline, Embase, PsycInfo, Scopus and Web of Science databases with no date restriction from inception to 15 February 2017. The protocol for this systematic review was prospectively registered with PROSPERO ( CRD42016036655 ). Results We identified 168 eligible studies with spatial methods used to describe the spatial distribution ( n  = 154), spatial clusters ( n  = 73), predictors of spatial patterns ( n  = 64), the role of congregate settings ( n  = 3) and the household ( n  = 2) on TB transmission. Molecular techniques combined with geospatial methods were used by 25 studies to compare the role of transmission to reactivation as a driver of TB spatial distribution, finding that geospatial hotspots are not necessarily areas of recent transmission. Almost all studies used notification data for spatial analysis (161 of 168), although none accounted for undetected cases. The most common data visualisation technique was notification rate mapping, and the use of smoothing techniques was uncommon. Spatial clusters were identified using a range of methods, with the most commonly employed being Kulldorff’s spatial scan statistic followed by local Moran’s I and Getis and Ord’s local Gi(d) tests. In the 11 papers that compared two such methods using a single dataset, the clustering patterns identified were often inconsistent. Classical regression models that did not account for spatial dependence were commonly used to predict spatial TB risk. In all included studies, TB showed a heterogeneous spatial pattern at each geographic resolution level examined. Conclusions A range of spatial analysis methodologies has been employed in divergent contexts, with all studies demonstrating significant heterogeneity in spatial TB distribution. Future studies are needed to define the optimal method for each context and should account for unreported cases when using notification data where possible. Future studies combining genotypic and geospatial techniques with epidemiologically linked cases have the potential to provide further insights and improve TB control.

Checkpoint blockade therapies that reactivate tumour-associated T cells can induce durable tumour control and result in the long-term survival of patients with advanced cancers 1 . Current predictive biomarkers for therapy response include high levels of intratumour immunological activity, a high tumour mutational burden and specific characteristics of the gut microbiota 2 , 3 . Although the role of T cells in antitumour responses has thoroughly been studied, other immune cells remain insufficiently explored. Here we use clinical samples of metastatic melanomas to investigate the role of B cells in antitumour responses, and find that the co-occurrence of tumour-associated CD8 + T cells and CD20 + B cells is associated with improved survival, independently of other clinical variables. Immunofluorescence staining of CXCR5 and CXCL13 in combination with CD20 reveals the formation of tertiary lymphoid structures in these CD8 + CD20 + tumours. We derived a gene signature associated with tertiary lymphoid structures, which predicted clinical outcomes in cohorts of patients treated with immune checkpoint blockade. Furthermore, B-cell-rich tumours were accompanied by increased levels of TCF7 + naive and/or memory T cells. This was corroborated by digital spatial-profiling data, in which T cells in tumours without tertiary lymphoid structures had a dysfunctional molecular phenotype. Our results indicate that tertiary lymphoid structures have a key role in the immune microenvironment in melanoma, by conferring distinct T cell phenotypes. Therapeutic strategies to induce the formation of tertiary lymphoid structures should be explored to improve responses to cancer immunotherapy. The co-occurrence of tumour-associated CD8 + T cells and CD20 + B cells, and the formation of tertiary lymphoid structures, are linked with improved survival in cohorts of patients with metastatic melanoma.

Background Large geographical variations in colorectal cancer (CRC) survival rates have been reported across regions. Poorer survival rates were mainly found in socioeconomically deprived areas, highly dense areas, and areas lacking healthcare accessibility. The objective of this study was to identify, compare, and contrast the spatial patterns of 5-year CRC-specific survival rates and identify high-priority areas by districts in Malaysia. Methods This retrospective cohort study utilized secondary data from the National Cancer Registry. CRC patients (ICD10 C18-21) diagnosed between 2013 and 2018 were selected. Patient addresses were geocoded into districts and states via geospatial data from the National Geospatial Centre, whereas district population density data were gathered from the Population Census of Malaysia. Kaplan‒Meier survival analysis and log-rank test were conducted to determine and compare the 5-year CRC-specific survival rates, and the spatial distribution of CRC survival by district was determined via ArcGIS software. Results A total of 18,513 CRC patients were registered from 143 districts, with 10,819 deaths occurring during follow-up. The national 5-year CRC-specific survival rate was 42%, with median survival time of 36 months (95% CI: 34.46, 37.54). The eastern region (Kelantan, Terengganu, and Pahang) had the lowest survival (38.0%). Among the 143 districts, eighty-one (56.6%) reported survival rates below the national average while thirty-six (25.2%) were identified as high-priority districts. Conclusion The differences in CRC survival rates were evident according to geographical location. Area-based targeted interventions to improve CRC detection, management, and access to healthcare are imperative to address cancer survival disparities and help effectively allocate resources.

The under-five mortality rate (U5MR) is a critical and widely available population health indicator. Both the MDGs and SDGs define targets for improvement in the U5MR, and the SDGs require spatial disaggregation of indicators. We estimate trends in the U5MR for Admin-1 subnational areas using 122 DHS surveys in 35 countries in Africa and assess progress toward the MDG target reductions for each subnational region and each country as a whole. In each country, direct weighted estimates of the U5MR from each survey are calculated and combined into a single estimate for each Admin-1 region across five-year periods. Our method fully accounts for the sample design of each survey. The region-time-specific estimates are smoothed using a Bayesian, space-time model that produces more precise estimates (when compared to the direct estimates) at a one-year scale that are consistent with each other in both space and time. The resulting estimated distributions of the U5MR are summarized and used to assess subnational progress toward the MDG 4 target of two-thirds reduction in the U5MR during 1990-2015. Our space-time modeling approach is tractable and can be readily applied to a large collection of sample survey data. Subnational, regional spatial heterogeneity in the levels and trends in the U5MR vary considerably across Africa. There is no generalizable pattern between spatial heterogeneity and levels or trends in the U5MR. Subnational, small-area estimates of the U5MR: (i) identify subnational regions where interventions are still necessary and those where improvement is well under way; and (ii) countries where there is very little spatial variation and others where there are important differences between subregions in both levels and trends. More work is necessary to improve both the data sources and methods necessary to adequately measure subnational progress toward the SDG child survival targets.