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The bivariate combined model for spatial data analysis.

ABSTRACT: To describe the spatial distribution of diseases, a number of methods have been proposed to model relative risks within areas. Most models use Bayesian hierarchical methods, in which one models both spatially structured and unstructured extra-Poisson variance present in the data. For modelling a single disease, the conditional autoregressive (CAR) convolution model has been very popular. More recently, a combined model was proposed that 'combines' ideas from the CAR convolution model and the well-known Poisson-gamma model. The combined model was shown to be a good alternative to the CAR convolution model when there was a large amount of uncorrelated extra-variance in the data. Less solutions exist for modelling two diseases simultaneously or modelling a disease in two sub-populations simultaneously. Furthermore, existing models are typically based on the CAR convolution model. In this paper, a bivariate version of the combined model is proposed in which the unstructured heterogeneity term is split up into terms that are shared and terms that are specific to the disease or subpopulation, while spatial dependency is introduced via a univariate or multivariate Markov random field. The proposed method is illustrated by analysis of disease data in Georgia (USA) and Limburg (Belgium) and in a simulation study. We conclude that the bivariate combined model constitutes an interesting model when two diseases are possibly correlated. As the choice of the preferred model differs between data sets, we suggest to use the new and existing modelling approaches together and to choose the best model via goodness-of-fit statistics. Copyright © 2016 John Wiley & Sons, Ltd.

SUBMITTER: Neyens T

PROVIDER: S-EPMC4935601 | biostudies-other | 2016 Aug

REPOSITORIES: biostudies-other

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Project description:BACKGROUND: A useful application of flow cytometry is the investigation of cell receptor-ligand interactions. However such analyses are often compromised due to problems interpreting changes in ligand binding where the receptor expression is not constant. Commonly, problems are encountered due to cell treatments resulting in altered receptor expression levels, or when cell lines expressing a transfected receptor with variable expression are being compared. To overcome this limitation we have developed a Microsoft Excel spreadsheet that aims to automatically and effectively simplify flow cytometric data and perform statistical tests in order to provide a clearer graphical representation of results. RESULTS: To demonstrate the use and advantages of this new spreadsheet method we have investigated the binding of the transmembrane adhesion receptor CD44 to its ligand hyaluronan. In the first example, phorbol ester treatment of cells results in both increased CD44 expression and increased hyaluronan binding. By applying the spreadsheet method we effectively demonstrate that this increased ligand binding results from receptor activation. In the second example we have compared AKR1 cells transfected either with wild type CD44 (WT CD44) or a mutant with a truncated cytoplasmic domain (CD44-T). These two populations do not have equivalent receptor expression levels but by using the spreadsheet method hyaluronan binding could be compared without the need to generate single cell clones or FACS sorting the cells for matching CD44 expression. By this method it was demonstrated that hyaluronan binding requires a threshold expression of CD44 and that this threshold is higher for CD44-T. However, at high CD44-T expression, binding was equivalent to WT CD44 indicating that the cytoplasmic domain has a role in presenting the receptor at the cell surface in a form required for efficient hyaluronan binding rather than modulating receptor activity. CONCLUSION: Using the attached spreadsheets and instructions, a simple post-acquisition method for analysing bivariate flow cytometry data is provided. This method constitutes a straightforward improvement over the standard graphical output of flow cytometric data and has the significant advantage that ligand binding can be compared between cell populations irrespective of receptor expression levels.

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The bivariate combined model for spatial data analysis.

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