Regression B‐spline smoothing in Bayesian disease mapping: with an application to patient safety surveillance

Abstract

In the context of Bayesian disease mapping, recent literature presents generalized linear mixed models that engender spatial smoothing. The methods assume spatially varying random effects as a route to partially pooling data and 'borrowing strength' in small-area estimation. When spatiotemporal disease rates are available for sequential risk mapping of several time periods, the 'smoothing' issue may be explored by considering spatial smoothing, temporal smoothing and spatiotemporal interaction. In this paper, these considerations are motivated and explored through development of a Bayesian semiparametric disease mapping model framework which facilitates temporal smoothing of rates and relative risks via regression B-splines with mixed-effect representation of coefficients. Specifically, we develop spatial priors such as multivariate Gaussian Markov random fields and non-spatial priors such as unstructured multivariate Gaussian distributions and illustrate how time trends in small-area relative risks may be explored by splines which vary in either a spatially structured or unstructured manner. In particular, we show that with suitable prior specifications for the random effects ensemble, small-area relative risk trends may be fit by 'spatially varying' or randomly varying B-splines. A recently developed Bayesian hierarchical model selection criterion, the deviance information criterion, is used to assess the trade-off between goodness-of-fit and smoothness and to select the number of knots. The methodological development aims to provide reliable information about the patterns (both over space and time) of disease risks and to quantify uncertainty. The study offers a disease and health outcome surveillance methodology for flexible and efficient exploration and assessment of emerging risk trends and clustering. The methods are motivated and illustrated through a Bayesian analysis of adverse medical events (also known as iatrogenic injuries) among hospitalized elderly patients in British Columbia, Canada.

Joint Modeling of Multiple Crimes: A Bayesian Spatial Approach

“…The scale matrix, Ω, is often set to be a scaled identify matrix with a scaling factor (see [45][46][47], for example).…”

“…In our analysis, we chose 0.01 as the scaling factor, i.e., setting Ω 's diagonal entries to Ω ii = 0.01, a specification adopted to run sensitivity analysis for the precision matrix of a multivariate normal distribution [45]. The parameter d, the degrees of freedom, was set equal to 2 in order to make the prior on ∑ u −1 minimally informative [48,49].…”

“…It is the intrinsic version of the Multivariate Conditional Autoregressive (MCAR) model [51] and has been used in spatial analysis [46,52]. Similar to the specification of ∑ u , we adopted the same approach to determine ∑ S ; a Wishart distribution was chosen for its inverse ∑ s −1 [45,48,49]:…”

“…It yielded a DIC with a difference of 5.077 (1349.786 versus 1344.709). For the multivariate model, we selected the two-dimensional identity matrix, an uninformative prior often used in practice, for Ω and R [45,47]. It yielded a DIC with a difference of 4.198 (1330.190 versus 1325.992).…”

Semiparametric M-quantile regression for count data

“…[2][3][4][5][6][7] Such models aim to cope with various types of drawbacks that could lead to a misspecification, for example:…”