Calculation Method for Likelihood Ratios Dictates Interpretation

Recently, likelihood ratios were published for use as an aid in the clinical interpretation of test results obtained from a commercially available enzyme-linked immunosorbent assay (ELISA) for the detection of antibodies against Mycobacterium avium subsp. paratuberculosis in cattle (2). As described by Dr. M. T. Collins, likelihood ratios can provide diagnostic information for multiple levels of a diagnostic test result when results are reported on a continuous scale rather than as a dichotomous (positive and negative) outcome. Unfortunately, the author did not take advantage of this characteristic of likelihood ratios. Because the formula used to calculate likelihood ratios presented in this article incorporates sensitivity and specificity estimates for the ELISA at several arbitrary cutoff points, the resulting comparisons remain dichotomous in nature. Further, the interpretation of these likelihood ratios as calculated is incorrect. For example, the likelihood ratio calculated at the 0.10 level indicates that cows with S/P ratios of ≥0.10 are five times more likely to be infected than noninfected. With this approach, all cows with ELISA S/P ratios of ≥0.10 are included in the comparison. Multiple likelihood ratios that allow for comparisons between different levels of S/P ratios were not calculated. Because the ELISA S/P ratios were not stratified into multiple categories, the likelihood ratios presented in Table ​Table11 of Collins's article (2) are overestimates resulting from heterogeneity within the defined groups of interest. TABLE 1. Calculation of likelihood ratios using a multilevel approach Table ​Table11 provides likelihood ratios based on the multiple-level approach proposed by Sackett et al. (3) and calculated from the data presented by Dr. Collins in his Table 1 (2). The likelihood ratios calculated in this manner differ considerably from those presented by Dr. Collins, and differences in their subsequent interpretations may have significant clinical and economic consequences. For example, cows with ELISA S/P ratios of 0.10 to <0.25 are 0.5 times as likely (i.e., half as likely) to be infected than noninfected, not “5 to 15 times” as likely to be infected, as Dr. Collins indicated in his Table 3 (2). Likelihood ratios demonstrating less-than-eightfold differences between comparison groups have been suggested to provide weak statistical evidence that a test result is indicative of a defined outcome (1). Additionally, the exclusion of ELISA S/P ratios of <0.00 from this analysis is a matter for concern. ELISA results from 1,097 animals, over one-third of the available results, were not considered. As this report indicates, ELISA S/P ratios of <0.00 may constitute a significant proportion of the results obtained during herd screening. These results could have been incorporated into the analysis had the multiple-level approach for likelihood ratio calculations been utilized. Likelihood ratios can provide additional diagnostic information for use in the clinical interpretation of the ELISA for M. avium subsp. paratuberculosis in cattle. However, care must be taken in order to interpret these values correctly and to make correct management recommendations based on them. These data do not support the interpretation of ELISA S/P ratios presented by Dr. Collins.