A Bayesian Poisson specification with a conditionally autoregressive prior and a residual Morans coefficient minimization criterion for quantitating leptokurtic distributions in regression-based multi-drug resistant tuberculosis treatment protocols

Abstract

In this study, we employed an eigenfunction decomposition algorithm associated with a Moran’s coefficient to investigate district-level non-linearity in an empirical dataset of spatiotemporal-sampled MDR-TB parameter estimators sampled in San Juan de Lurigancho (SJL) Lima, Peru. The non-parametric technique attempted to remove the inherent autocorrelation in the model by introducing appropriate synthetic surrogate variants. We also constructed a robust Bayesian Poisson model to generate unbiased estimators for qualitatively assessing resistance to four commonly used drugs in TB treatment: isoniazid, rifampin, ethambutol, and streptomycin. Initially, data of residential addresses of individual patients with smear-positive MDR-TB were geocoded in ArcGIS. Next, the sampled data were matched automatically and interactively within the geodatabase. The MDR-TB data feature attributes were then calculated and digitally overlaid onto sub-meter resolution satellite data within a 1 km buffer of 31 georeferenced health centers using a 10 m2 grid-based algorithm. Global autocorrelation statistics were then generated by decomposing the sampled data into positive and negative spatial filter eigenvectors using the eigenfunction decomposition algorithm. Bayesian Poisson projections were then rendered employing normal priors for each of the sampled estimators. A Residual Moran’s coefficient (MC) minimization criterion was then applied to the clinical coefficients generated from the decomposition algorithm to detect any unaccounted latent autocorrelation error in the estimators. The model accounted for approximately 14% pseudo-replicated information and exhibited positive residual autocorrelation. Spatial statistics can elucidate the mechanics of MDR-TB transmission by prioritizing clinical covariates for identifying spatial distribution of high- risk populations and random heterogeneity in resistant strains. Key words: Multi-drug resistant tuberculosis, Bayesian Poisson, residual Moran’s coefficient (MC), minimization criterion, San Juan de Lurigancho (SJL) Lima, Peru.