^{a}Department of Microbiology, IMS & Sum Hospital Medical College, Siksha ‘O’ Anusandhan University, Kalinga Nagar, Bhubaneswar, Odisha, ^{}India.
^{b}Department of Pharmacology, IMS & Sum Hospital Medical College, Siksha ‘O’ Anusandhan University, Kalinga Nagar, Bhubaneswar, Odisha, ^{}India.
^{c}Central Research Laboratory, IMS & Sum Hospital Medical College, Siksha ‘O’ Anusandhan University, Kalinga Nagar, Bhubaneswar 751003, Odisha, ^{}India.
Copyright ©2013, Korea Centers for Disease Control and Prevention
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The sensitivity (TP rate) is the proportion of people with the disease who will have positive smear test results, computed by [TP/(TP + FN)]. This value is the ability of the smear test to detect the infection status, when it is truly present, i.e., it is the probability of a positive test result, given that the samples were taken from sick individuals.
The specificity (TN rate) is the proportion of people without the disease who will have negative smear test results, obtained by [TN/(FP + TN)]. This value is the ability of the smear test to yield a negative result with samples from disease-free individuals, i.e., it is the probability of a negative test result.
The FP rate is the probability of errors in the culture test, computed as [FP/(FP + TN)].
The FN rate is the probability of errors in the smear test, computed as FN/(TP + FN).
The positive predictivity is the posttest probability of the disease that yielded a positive test result, or the probability of the portion of people with positive test results who actually had the disease, computed as [TP/(TP + FP)].
The negative predictivity is the posttest probability of the disease that gave a negative test result, or the probability of the proportion of people with negative test results who actually did not have the disease, computed as [TN/(FN + TN)].
The diagnostic accuracy (inherent validity or predictive validity) is the ability of the smear test to be correctly positive or negative, among the binary results of the culture test, computed as [(TP + TN)/N]. Additionally, this value estimates the accuracy of smear and culture tests together.
The positive likelihood ratio (LR) is the ratio between the TP rate and the FP rate, computed as [sensitivity/(1 − specificity)], when the smear test result was positive.
The negative LR is the ratio between the FN rate and the TN rate, computed as [(1 − sensitivity)/specificity], when the smear test result was negative. In fact, the larger is the positive LR value, the greater the likelihood of infection, and similarly, the lesser is the negative LR value, the lesser the likelihood of infection in a population.
The a posteriori probability is the value from posttest arithmetic computation of the data set for the diagnostic efficiency, and it clarifies the dependability of each test independently, with a numerical probability value in arriving at the truth, i.e., the sought-after conclusions from both tests.
The area under the receiver operating characteristic (ROC) curve, drawn with values of sensitivity and 1 − specificity, gives a graphical analysis for diagnostic efficiency. The graphical method additionally examines the predictive capability as another value of a posteriori probability, independent of the arithmetic computation.
^{} TP = 33 samples were true-positives culture test positive); false-positives (smear test positive, culture test negative); FN = 62 samples were false negatives (smear test negative, culture test positive); and TN = 455 samples were true-negatives (smear test negative, culture test negative); N = population size or total number of samples = 572. Corresponding fraction values are given in parentheses. Prevalence of TB = 0.1669.
^{} ^{a}Alternately, = (sensitivity)(prevalence) + (specificity)(1 − prevalence). For abbreviations, see Table 1; for the detailed formula of a posteriori probability, see text.
^{} CI = confidence interval; FN = false negative; FP = false positive; TN = true negative; TP = true positive.
Smear test results | Culture test results
| Total | |
---|---|---|---|
Infection present | Infection absent | ||
Positive | TP = 33 (0.05769) | FP = 22 (0.03846) | (TP + FP) = 55 (0.09615) |
Negative | FN = 62 (0.10839) | TN = 455 (0.79545) | (FN + TN) = 517 (0.90385) |
Total | (TP + FN) = 95 (0.1669) | (FP + TN) = 477 (0.8339) | N = 572 (1.0, approx.) |
Test statistic | Formula | Value | 95% CI |
---|---|---|---|
Prevalence or a priori probability | (TP + FN)/N | 0.166 | 0.014–0.406 |
Sensitivity (true positive rate) | TP/(TP + FN) | 0.347 | 0.0648–0.5352 |
Specificity (true negative rate) | TN/(FP + TN) | 0.954 | 0.9012–1.0 |
Diagnostic accuracy | (TP + TN)/N^{a} | 0.853 | 0.5944–1.0 |
Positive predictivity | TP/(TP + FP) | 0.6 | 0.248–1.0 |
Negative predictivity | TN/(FN + TN) | 0.88 | 0.6144–1.0 |
False positive rate | FP/(FP + TN) = (1 − specificity) | 0.046 | 0.0008–0.0792 |
False negative rate | FN/(TP + FN) = (1 − sensitivity) | 0.652 | 0.4648–0.9352 |
Positive likelihood ratio | Sensitivity/(1 − specificity) | 7.543 | 0.464–17.556 |
Negative likelihood ratio | (1 − sensitivity)/specificity | 0.685 | 0.524–0.916 |
A posteriori probability | P(E_{1}|E ) | 0.6614 | 0.562–0.758 |
Area under the ROC curve or AUC (a posteriori probability) | 0.62 | 0.473–0.767 |
Population fraction | Prevalence | Sensitivity | Specificity | Posteriori probability |
---|---|---|---|---|
100 | 0.17 | 0.35 | 0.02 | 0.612 |
100 | 0.37 | 0.22 | 0.03 | 0.638 |
100 | 0.33 | 0.12 | 1.0 | 0.6 |
100 | 0.10 | 0.4 | 0.06 | 0.714 |
100 | 0.15 | 0.47 | 0.09 | 0.706 |
72 | 0.111 | 0.25 | 0.03 | 0.692 |
Mean ± SD | 0.23 ± 0.12 | 0.30 ± 0.13 | 0.21 ± 0.39 | 0.66 ± 0.05 |
TP = 33 samples were
CI = confidence interval; FN = false negative; FP = false positive; TN = true negative; TP = true positive.