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Diagnostic tests usually need to operate at a high sensitivity or specificity level in practice. Accordingly, specificity at the controlled sensitivity, or vice versa, is a clinically sensible performance metric for evaluating continuous biomarkers. Meanwhile, the performance of a biomarker may vary across sub-populations as defined by covariates, and covariate-specific evaluation can be informative. In this article, we develop a novel modeling and estimation method for covariate-specific specificity at a controlled sensitivity level. Unlike existing methods which typically adopt elaborate models of covariate effects over the entire biomarker distribution, our approach models covariate effects locally at a specific sensitivity level of interest. We also extend our proposed model to handle the whole continuum of sensitivities via dynamic regression and derive covariate-specific ROC curves. We provide the variance estimation through bootstrapping. The asymptotic properties are established. We conduct extensive simulation studies to evaluate the performance of our proposed methods in comparison with existing methods, and further illustrate the applications in two clinical studies for aggressive prostate cancer.

Additional file 7. Proportions of variance component estimates for feeding behavior traits at three timepoints. The plot depicts the proportions of total phenotypic variance explained by pen and sire in Null model and pen, sire, and gut microbiota in MBLUP model for Duroc (DR), Landrace (LR), and Large White (LW) at 73 days (T1), 123 days (T2),and 158 days (T3). P = the proportion of variance explained by pen effect; S =the proportion of variance explained by sire effect; M = the proportion of variance explained by the gut microbial composition; R = residual.

Additional file 4. Contrasts of estimates for feeding behavior traits among rooms during three time periods.Data are presented as least squares mean with the confidence interval. Colors represent different rooms (n = 8).

Additional file 6. Comparisons of least squares means of microbiability across breeds, time points, andfeeding behavior traits. DR = Duroc (n = 205); LR = Landrace (n = 226); LW =Large White (n = 220). T1 = 73 days of age; T2 = 123 days of age; T3 = 158 daysof age. ADFI = average amount of feed consumed (g) daily; AOTD = average daily feeder occupation time (s); ADFR = average daily feeding rate (g/min); ANVD = average daily number of visits to feeder; AFIV = average amount of feed consumed (g) per visit; AOTV = average feeder occupation time (s) per visit; AFRV = average feeding rate (g/min) per visit. Different letters a, b, and c denote P

Additional file 5. Summary of F values and P-values from ANOVA of fixed effects on feeding behavior traits. F values are calculated as the Mean Square Model divided by the Mean Square Residual in the ANOVA test from SAS. ADFI = average daily amount of feed consumed (g); AOTD = average daily feeder occupation time (s); ADFR = average daily feeding rate (g/min); ANVD = average daily number of visits to feeder; AFIV = average amount of feed consumed (g) per visit; AOTV = average feeder occupation time (s) per visit; AFRV = average feeding rate (g/min) per visit. * P

Additional file 2. Distribution of animals for three breeds kept in each room. The y-axis represents the number of animals from each breed group kept in each room. The x-axis represents the room (n=8). Colors represent three breeds: Duroc (green), Landrace (orange), and Large White (purple).

Additional file 3. Ingredient composition for the standard diet for pigs during the present study period. The diet ingredients listed in the table were used to feed all the animals in the present study throughout the experimental period (73 to 163 days of age). This diet was provided as of 70 days of age until pigs reached the final body weight (127 kg).