The FIRM Tool (Febrile Infant Rural Model): bivariate meta-analysis of published decision rules with individual-level prediction modelling

Background: Published febrile infant decision rules assume access to procalcitonin (PCT), point-of-care urinalysis, and automated differentials -- investigations frequently unavailable in rural and regional emergency departments. No existing tool quantifies how missing inputs degrade risk estimation or whether safe clinical decisions remain possible with incomplete data. Methods: We conducted a bivariate hierarchical summary receiver operating characteristic (HSROC) meta-analysis of seven published febrile infant decision rules (Rochester, Philadelphia, Step-by-Step, PECARN, Aronson, AAP 2021, BSAC/NICE) using 2x2 data from 6 studies (11 cohort-rule combinations). We then developed the FIRM tool (Febrile Infant Rural Model), a pooled logistic regression model for individual-level invasive bacterial infection (IBI) probability estimation using the PECARN Biosignatures public-use dataset (n=4,434 complete cases; 88 IBI events). The model was internally validated with bootstrap resampling (200 iterations) and assessed across simulated missing-input scenarios. CRP-for-PCT substitution was evaluated on 88 patients with both biomarkers available. Reporting followed PRISMA-DTA and TRIPOD+AI guidelines. Results: In the meta-analysis, the PECARN rule had pooled sensitivity 95.5% (95% CI 83.8-98.9) and specificity 61.0% (59.1-62.9); the Aronson rule had pooled sensitivity 91.5% (84.2-95.6) and specificity 28.0% (25.1-31.0). The individual-level prediction model achieved optimism-corrected AUC 0.780 (bootstrap 95% CI 0.705-0.853), calibration slope 0.937, and Brier score 0.0189. A four-tier risk stratification classified 14.6% of infants as very low risk (predicted IBI probability <0.5%, observed IBI rate 0.00%) and 51.8% as low risk (0.5-1.5%, observed rate 0.87%). In the simulated rural scenario (no PCT available), predicted IBI probability was 0.87% -- within the low-risk tier and comparable to the full-input estimate. CRP-for-PCT substitution showed 97.7% agreement (86/88 patients). Decision curve analysis demonstrated positive net benefit over treat-all at all clinically relevant thresholds. Conclusions: The FIRM tool (Febrile Infant Rural Model), a continuous prediction model using routinely available clinical and laboratory data, identifies a larger proportion of febrile infants as low risk than binary decision rules, while maintaining comparable safety. The model quantifies the cost of missing inputs rather than treating them as binary exclusions. Prospective validation in Australian rural emergency departments is required before clinical deployment.