Endogeneity in Logistic Regression Models

Menteshashvili O, et al. Pulmonary tuberculosis in prisons of the ex-USSR state Georgia: results of a nationwide prevalence survey among sentenced inmates. Antimicrobial prescribing patterns for respiratory diseases including tuberculosis in Russia: a possible role in drug resistance? Jpyridinium chloride is useful for isolation of Mycobacterium tuberculosis from sputa subjected to long-term storage. establishing DOTS-plus pilot projects for the management of multidrug-resistant tuberculosis (MDR-TB) 2000. [cited 2005 Jan 18]. To the Editor: Ethelberg et al. (1) report on a study of the determinants of hemolytic uremic syndrome resulting from Shiga toxin–producing Escherichia coli. The dataset is relatively small, and the authors use step-wise logistic regression models to detect small differences. This indicates that the authors were aware of the limitations of the statistical power of the study. Despite this, the study has an analytic flaw that seriously reduces the statistical power of the study. An often overlooked problem in building statistical models is that of endogeneity, a term arising from econometric analysis, in which the value of one independent variable is dependent on the value of other pre-dictor variables. Because of this endo-geneity, significant correlation can exist between the unobserved factors contributing to both the endogenous independent variable and the dependent variable, which results in biased estimators (incorrect regression coefficients) (2). Additionally, the correlation between the dependent variables can create significant multicollineari-ty, which violates the assumptions of standard regression models and results in inefficient estimators. This problem is shown by model-generated coefficient standard errors that are larger than true standard errors, which biases the interpretation towards the null hypothesis and increases the likelihood of a type II error. As a result, the power of the test of significance for an independent variable X 1 is reduced by a factor of (1-r 2 (1|2,3,….)), where r (1|2,3,….) is defined as the multiple correlation coefficient for the model X 1 = f(X 2 ,X 3 ,…), and all X i are independent variables in the larger model (3,4). The results of this study clearly show that the presence of bloody diarrhea is an endogenous variable in the model showing predictors of hemolyt-ic uremic syndrome, in that the diarrhea is shown to be predicted by, and therefore strongly correlated with, several other variables used to predict hemolytic uremic syndrome. Similarly, Shiga toxin 1 and 2 (stx1, stx2) genes are expected to be key predictors of the presence of bloody diarrhea, independent of strain, …