Purpose: Decision models often make use of independent distributions for sensitivity and specificity. By doing this, the inverse relationship between sensitivity and specificity is not taken into account and model uncertainty is overestimated. The purpose was to model the inverse relationship between sensitivity and specificity using the diagnostic odds ratio.
Method: According to Haberl et al (2001), the sensitivity and specificity for the diagnosis of coronary artery disease using the CT coronary calcium score is 99.5% and 29.6%, respectively. Using the absolute numbers of true positives (TP), false negatives (FN), true negatives (TN) and false positives (FP), beta distributions were constructed in Data TreeAge Pro 2009 and subsequently used to calculate the 95% CIs (confidence intervals) of sensitivity and specificity. The diagnostic odds ratio (DOR) was calculated using Equation 1. Assuming a normal distribution of the log transformed DOR, we calculated the standard error (SE) with the absolute numbers of TP, FN, TN and FP using Equation 2. The resulting log-normal distribution of the diagnostic odds ratio combined with the distribution of the specificity were used in a simple decision tree. Next, the sensitivity was calculated in the model using Equation 3. A probabilistic sensitivity analysis was performed to simulate the resulting distribution of sensitivity.
Result: The beta distributions for sensitivity and specificity ranged from 98.9 - 99.8% and 26.5 – 32.8%, respectively. According to Equation 1 the diagnostic odds ratio was 78.7 using the mean values of sensitivity and specificity. The natural log transformation of the DOR was 4.37. Using the absolute numbers reported in Haberl for TP (935), FN (5), TN (244) and FP (580), the standard error of the ln (DOR) was 0.45 (Equation 2). The resulting 95% confidence interval for the ln (DOR) ranged from 3.47 – 5.26. Subsequently, back transforming to DOR, the range was 32.3 – 192. The resulting 95% CI of sensitivity modeled by the distributions of specificity and DOR ranged from 98.7% - 99.8%, which closely resembles the distribution for sensitivity as calculated from the absolute numbers.
Conclusion: When modeling the diagnostic accuracy of a test, the inverse relationship between sensitivity and specificity can be taken into account by using the distribution of the diagnostic odds ratio and the distribution of specificity.
Candidate for the Lee B. Lusted Student Prize Competition