Rethinking navel size thresholds for omphalitis diagnosis in newborn dairy calves using machine learning

Omphalitis in newborn calves is an underreported disease with no gold standard diagnostic test. Comprehensive examination is often impractical on farms, and simplified protocols based on the umbilical stump diameter have been proposed. However, existing thresholds relied on expert opinion or limited clinical evidence. The objectives were to (1) assess the reliability of a technique for measuring umbilical stump diameter by evaluating intra- and interobserver agreement; (2) develop a statistical model describing umbilical stump diameter as a function of disease status in Holstein (HO) and Jersey (JE) heifers aged 3 to 10 d; and (3) propose thresholds to estimate farm-level prevalence (optimum sensitivity Se and specificity Sp) and to identify umbilici with a high probability of omphalitis (maximize Sp). The study enrolled newborn HO and JE heifers from commercial farms in the San Joaquin Valley (California): 157 calves for intraobserver analysis, 44 for interobserver analysis (3 raters), and 667 for threshold estimation. Intra- and interobserver agreement were assessed using the CV and intraclass correlation coefficient (ICC), respectively. Because true disease status was unknown, thresholds were derived using an unsupervised machine-learning approach that inferred healthy and diseased subpopulations from the observed data. Thresholds were estimated separately by breed using 2-component Gaussian mixture models under the biological assumptions that (1) stump diameters arise from a mixture of healthy and diseased subpopulations, (2) diseased umbilici are larger on average, (3) diameters within each subpopulation follow a normal or log-normal distribution, and (4) distributions are stable in calves aged 3 to 10 d across herds. Receiver operating characteristic (ROC) analysis was applied to a simulated sample to estimate diagnostic test performance. Umbilical stump diameter measurements at the external umbilical ring were reliable with good (CV = 5.94% 95% CI: 5.31-6.57) and fair to good (ICC = 0.76 95% CI: 0.65-0.85) agreement for intra- and interobserver agreement, respectively. The breed-specific models accurately described the observed data. Diagnostic tests based on umbilical stump diameter can discriminate between healthy and diseased umbilici (HO area under the curve AUC of 0.56 95% CI: 0.51-0.62; JE AUC of 0.65 95% CI: 0.58-0.72). Thresholds optimizing the Se and Sp trade-off (HO: 16.5 mm; JE: 13.0 mm) achieved high Sp (0.91 and 0.97) but low Se (0.35 and 0.46) for HO and JE. Higher thresholds prioritizing Sp (HO: 19.3 mm; JE: 14.9 mm) yielded Sp ≥0.99, with Se of 0.22 and 0.28. The identified threshold should be interpreted cautiously given the low Se and modest ROC values. Further validation in independent populations and associations with clinical findings are needed.