Follow-up radiographs are usually used as the reference standard for the diagnosis of suspected scaphoid fractures. However, these are prone to errors in interpretation. We performed a meta-analysis of 30 clinical studies on the diagnosis of suspected scaphoid fractures, in which agreement data between any of follow-up radiographs, bone scintigraphy, magnetic resonance (MR) imaging, or CT could be obtained, and combined this with latent class analysis to infer the accuracy of these tests on the diagnosis of suspected scaphoid fractures in the absence of an established standard. The estimated sensitivity and specificity were respectively 91.1% and 99.8% for follow-up radiographs, 97.8% and 93.5% for bone scintigraphy, 97.7% and 99.8% for MRI, and 85.2% and 99.5% for CT. The results were generally robust in multiple sensitivity analyses. There was large between-study heterogeneity for the sensitivity of follow-up radiographs and CT, and imprecision about their sensitivity estimates. If we acknowledge the lack of a reference standard for diagnosing suspected scaphoid fractures, MRI is the most accurate test; follow-up radiographs and CT may be less sensitive, and bone scintigraphy less specific.
The stability n umber (G) for a given graph G is the size of a maximum stable set in G. T h e L o v asz theta number provides an upper bound on (G) and can be computed in polynomial time as the optimal value of the Lov asz semide nite program. In this paper, we s h o w that restricting the matrix variable in the Lov asz semide nite program to be rank-one and rank-two, respectively, yields a pair of continuous, nonlinear optimization problems each h a ving the global optimal value (G). We propose heuristics for obtaining large stable sets in G based on these new formulations and present computational results indicating the e ectiveness of the heuristics.
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