## 3 Results
### Statistical Analysis, Detailed Sample Ratings  
Many patients in the emergency department have multiple suspected FBs in open wounds. For this reason, the probability of accurately finding FBs in each sample was analyzed. Figure 4 shows the probability distribution of finding FBs in each sample as a function of deviation from the true number of FBs. Thus, zero represents an accurate rating of the sample, i.e., the number of FBs found is equal to the true number of FBs. The results for POCUS and MFXI are shown. Additionally, the POCUS -results, excluding Rater 5 are shown. The distribution for MFXI is relatively symmetric around the maximum at zero. The distribution for POCUS demonstrates a large number of false negatives. The extension of the distribution into the range of false positives is primarily caused by Rater 5 as evidenced by the difference between the distributions for \"POCUS, all raters\" and \"POCUS, raters 1-4\". The deviating performance of Rater 5 was already apparent in Table 1. Because this rater appears to be an outlier for POCUS, he/she was excluded from the summary data in Table 4 but remained in Table 3. Given the sensitivity of POCUS for finding a glass particle, the sensitivity for finding multiple particles (5.3 on average) in a sample is, of course, very low; here only 7.8%. MFXI's sensitivity for a sample is 40%. In summary, across physicians and samples, EM clinicians correctly identified 97.6% of the glass FBs using MFXI with 96.5% interrater reliability and 62.3% of the glass FBs using POCUS with 70.8% interrater reliability. In addition, clinicians were significantly more likely to correctly identify or overestimate the number of glass FBs using MFXI and significantly more likely to underestimate the number of glass FBs using POCUS (\(p<0.01\)). The difference in the proportion of the samples for which glass FBs were underestimated using POCUS as opposed to MFXI was 0.52 with 95% confidence intervals of 0.37-0.66. \begin{table}
\begin{tabular}{l c c} \hline \multicolumn{3}{c}{**Summary of Rated FBs (Rater 1–4)**} \\ \hline  & **Rates, R** & **Absolute Numbers** \\ \hline True Positive, TP (Sensitivity) & 49.2\% & 151 \\ True Negative, TN (Specificity) & 10.0\% & 0.2 \\ Accuracy (TP + TN)/(P + N) & 48.9\% & \\ False Positive, FP & & 5.5 \\ False Negative, FN & & 150.5 \\ Pos. Predictive Value, PPV (Precision) & 96.49\% & \\ Neg. Predictive Value, NPV & 0.13\% & \\ Number of positive FBs, P & & 307 \\ Number of negative FBs, N & & 2 \\ Total number of FBs, P + N & & 309 \\ \hline \multicolumn{3}{c}{**Summary of Rated Samples (Rater 1–4)**} \\ \hline  & **Rates, R** & **Absolute Numbers** \\ \hline True Positiv, TP (Sensitivity) & 7.8\% & 4.5 \\ True Negative, TN (Specificity) & 10.0\% & 0.2 \\ Accuracy (TP + TN)/(P + N) & 7.8\% & \\ False Positive, FP & & 3.25 \\ False Negative, FN & & 52.25 \\ Pos. Predictive Value, PPV (Precision) & 58.06\% & \\ Neg. Predictive Value, NPV & 0.38\% & \\ Average number of FBs/pos. sample & & 5.3 \\ Number of positive samples, P & & 58 \\ Number of negative samples, N & & 2 \\ Total number of samples, P + N & & 60 \\ \hline \end{tabular}
\end{table} 
Table 4: Summaries of performance data for POCUS; all absolute numbers are reported as per rater. Rater 5 was excluded from this table (see text). Although most [8] glass FBs are found with X-ray imaging up to 50% of FBs are still missed [3] after physical examination and radiographs. This is approximately consistent with our findings. Table 3 shows that MXFI using only one X-ray projection has an 82.4% probability of finding glass objects. Given an average number of 5.3 FBs per sample, the accuracy for finding all glass pieces in a sample should be approximately 82.4% to the power of 5.3, which is about 36%, and is in good agreement with our statistical sensitivity of 40%. We note that acquiring several sample projections would likely improve the accuracy as artifacts can be better identified and FBs imperceptible in a particular projection might be visible in another.