Pseudo R<SUP>2</SUP> Probablity Measures, Durbin Watson Diagnostic Statistics and Einstein Summations for Deriving Unbiased Frequentistic Inferences and Geoparameterizing Non-Zero First-Order Lag Autocorvariate Error in Regressed Multi-Drug Resistant Tuberculosis Time Series Estimators

Abstract

In randomized clinical trials using clustered multi-drug resistant tuberculosis (MDR-TB) data, groups of human population are routinely assigned to treatments; whereas, observations are taken on the individual subjects using clinically-oriented explanatory covariate coefficient estimates for identifying sites of hyperendemic transmission. Further, standard methods for data analyses of clinical MDR-TB data postulate models relating observational parameters to the response variables without accurately quantitating varying observational intra-cluster error coefficient effects. Implicit in this assumption is that the effect of these error coefficient estimates are identical. However, non-differentiation of varying and constant residual within-cluster covariate coefficient uncertainty effects in a time-series clinical MDR-TB endemic transmission model can lead to misspecified forecasted predictors of endemic transmission zones (e.g., mesoendemic). In this research we constructed multiple georeferenced autoregressive hierarchical models accompanied by non-generalized predictive residual uncertainty non-normal diagnostic tests employing multiple covariate coefficient estimates clinically-sampled in San Juan de Lurigancho Lima, Peru. Initially, a SAS-based hierarchical agglomerative polythetic clustering algorithm was employed to determine high and low MDR-TB clusters stratified by prevalence data. Univariate statistics and Poisson regression models were then generated in R and PROC NL MIXED, respectively. Durbin-Watson statistics were derived. A Bayesian probabilistic estimation matrix was then constructed employing normal priors for each of the error coefficient estimates which revealed both spatially structured (SSRE) and spatially unstructured effects (SURE). The residuals in the high MDR-TB explanatory prevalent cluster revealed two major uncertainty estimate interactions: 1) as the number of bedrooms in a house in which infected persons resided increased and the percentage of isoniazid-sensitive infected persons increased, the standardized rate of tuberculosis tended to decrease; and, (2) as the average working time and the percentage of streptomycin-sensitive persons increased, the standardized rate of MDR-TB tended to increase. In the low MDR-TB explanatory time series cluster single marital status and building material used for house construction were important predictors. Latent explanatory non-normal error probabilities in empirically regressed MDR-TB clinical-sampled covariate estimates can be robustly spatiotemporally quantitated employing a first-order autoregressive resdiualized model and a Bayesian diagnostic uncertainty estimation matrix.