Table 1 Performance of remedying procedures for all possible situations of phs000634.

From: Precise diagnosis of three top cancers using dbGaP data

Instance no.	True status	\({\texttt {NBC}_{\texttt {634}}^{\texttt {(1)}}}\)	\({\texttt {NBC}_{\texttt {634}}^{\texttt {(2)}}}\)	Conclusion	Instance no.	True status	\({\texttt {NBC}_{\texttt {634}}^{\texttt {(2)}}}\)	\({\texttt {NBC}_{\texttt {634}}^{\texttt {(1)}}}\)	Conclusion
(A)					(B)
118	Case	0.5132	0.6442	Improved	29	Case	0.4896	0.6215	Corrected
811	Case	0.5005	0.9954	Improved	39	Case	0.5495	0.9332	Improved
1024	Case	0.5225	0.9034	Improved	375	Case	0.5290	0.9450	Improved
1077	Control	0.4590	0.2712	Improved	435	Control	0.4726	0.0838	Improved
1126	Case	0.5140	0.9823	Improved	1026	Case	0.5352	0.8606	Improved
1128	Control	0.4987	0.0508	Improved	1086	Control	0.4549	0.1960	Improved
1365	Control	0.4525	0.3326	Improved	1495	Case	0.5015	0.7915	Improved
1482	Case	0.5277	0.6845	Improved	1597	Case	0.5398	0.8696	Improved
1655	Control	0.4545	0.0392	Improved

(A) Results of using \({\texttt {NBC}_{\texttt {634}}^{\texttt {(2)}}}\) to remedy \({\texttt {NBC}_{\texttt {634}}^{\texttt {(1)}}}\). (B) Results of using \({\texttt {NBC}_{\texttt {634}}^{\texttt {(1)}}}\) to remedy \({\texttt {NBC}_{\texttt {634}}^{\texttt {(2)}}}\). The 3rd and 3th columns are posterior probabilities of diagnosing instances as “positive” using the main model (i.e., \({\texttt {NBC}_{\texttt {634}}^{\texttt {(1)}}}\) for (A) and \({\texttt {NBC}_{\texttt {634}}^{\texttt {(2)}}}\) for (B)) and the remedying model (i.e., \({\texttt {NBC}_{\texttt {634}}^{\texttt {(2)}}}\) for (A) and \({\texttt {NBC}_{\texttt {634}}^{\texttt {(1)}}}\) for (B)). Only an instance with posterior probability of being diagnosed as “positive” equaling from 0.45 to 0.55 is considered by remedying procedures. Taking the 29th instance (case) for example, \({\texttt {NBC}_{\texttt {634}}^{\texttt {(2)}}}\) accepts “negative” because the posterior probability of diagnosing it as “positive” equals 0.4896 \((<0.5)\); \({\texttt {NBC}_{\texttt {634}}^{\texttt {(1)}}}\) corrects the diagnosis with posterior probability of making correct diagnosis, 0.6215 \((>0.5)\). In this situation, we label the conclusion as corrected. For the 1655th instance (control), \({\texttt {NBC}_{\texttt {634}}^{\texttt {(2)}}}\) remedies \({\texttt {NBC}_{\texttt {634}}^{\texttt {(1)}}}\) by improving the posterior probability of making correct diagnosis from 0.5455 \((=1-0.4545>0.5)\) to 0.9608 \((=1-0.0392>0.5455)\). In this situation, the conclusion is labeled as improved. Other results can be explained similarly.

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Table 1 Performance of remedying procedures for all possible situations of phs000634.

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