Pseudo R² 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

Benjamin G. Jacob^1, , Daniel Mendoza², Mario Ponce³, Semiha Caliskan¹, Ali Moradi⁴, Eduardo Gotuzzo³, Daniel A. Griffith⁵ and Robert J. Novak¹

¹Department of Global Health, College of Public Health, University of South Florida, Tampa Fl

²Department of Environmental and Occupational Health, College of Public Health, University of South Florida, Tampa Fl

³Instituto de Medicina Tropical Alexander Von Humboldt-Universidad Peruana Cayetano Heredia, Lima, Peru

⁴LECOM School of Medicine 5000 Lakewood Ranch Blvd Bradenton, FL

⁵School of Economic, Political and Policy Sciences, The University of Texas at Dallas, 800 West Campbell Road, Richardson, TX

Cite this paper:
Benjamin G. Jacob, Daniel Mendoza, Mario Ponce, Semiha Caliskan, Ali Moradi, Eduardo Gotuzzo, Daniel A. Griffith and Robert J. Novak. Pseudo R² 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. American Journal of Applied Mathematics and Statistics. 2014; 2(5):252-301. doi: 10.12691/ajams-2-5-1

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.

Keywords:
Multi-Drug Resistant Tuberculosis (MDR-TB) Durbin-Watson statistics Bayesian San Juan de Lurigancho

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