, Volume 21, Issue 2, pp 123-130

Evaluation of two microbiological diagnostic methods for pulmonary tuberculosis based on Bayes rule

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To evaluate two microbiological diagnostic methods with sputum samples for pulmonary tuberculosis, for quantifying the inherent errors in each method, based on Bayes rule.

Subject and methods

Diagnostic test results of 1,064 sputum samples were obtained by smear microscopy (Ziehl-Neelsen staining) or the smear test and with the other popular and assertive method, the culturing of samples on the Lowenstein-Jensen medium or the culture test. Results were subjected to a Bayesian analysis.


In the diagnostic analysis of 1,064 samples, there were 143 true-positives, 05 false-positives, 675 true-negatives and 241 false-negatives. Probability values of the analysis are given. The prevalence or a priori probability (the pre-test prevalence of disease in the targeted population) value = 0.3609; the sensitivity (true positive rate or probability of smear test positives among culture positives) was 0.3724, whereas the specificity (true negative rate or probability of smear test negatives among culture test negatives) was 0.9926. The false positive rate (probability of errors of the culture test) = 0.00735; the false negative rate (probability of errors of the smear test) = 0.6276; the positive predictivity (post-test probability of the disease that gave a positive result) and the negative predictivity (post-test probability of the disease that gave a negative result) values were 0.9662 and 0.7369, respectively. Computed values of other test statistics were: diagnostic accuracy (accuracy of diagnosing positivity/negativity of tests) = 0.7688; positive likelihood ratio (ratio of true positive rate and false positive rate) = 50.66; negative likelihood ratio (ratio of false negative rate and true negative rate) = 0.6322; and a posteriori probability (post-test arithmetic computation for diagnostic efficiency) = 0.5738. The area under the receiver operating characteristic (ROC curve or the AUC (post-test graphical analysis for diagnostic efficiency) was 0.648.


The prevalence of the disease was 36 %. The smear test was efficient by 37–97 % in arriving at a positive result with a sample, when its culture test was positive; alternately, it was efficient by 74–99 % for a negative result, when its culture test result was negative. As found by post-test analysis, both smear and culture tests were dependable by 57–65 % for pulmonary tuberculosis.