. Author manuscript; available in PMC: 2014 Dec 26.

Published in final edited form as: Stat Methods Med Res. 2013 Jun 26;25(4):1596–1619. doi: 10.1177/0962280213492588

Table 3.

2 by 2 table when the reference test is not a gold standard

		Reference test		Total
		+	−	Total
Diagnostic test	+	n_i₁₁	n_i₀₁
	+	p_i ₁₁ =π_iSe_AiSe_Bi + (1−π_i)(1−Sp_Ai)(1−Sp_Bi)	p_i ₀₁ = π_iSe_Ai (1−Se_Bi) + (1−π_i)(1−Sp_Ai)Sp_Bi
	−	n_i₁₀	n_i₀₀
	−	p_i ₁₀ =π_i (1− Se_Ai)Se_Bi + (1−π_i)Sp_Ai (1−Sp_Bi)	p_i ₀₀ = π_i (1− Se_Ai)(1 − Se_Bi) + (1 − π_i)Sp_Ai Sp_Bi

Total		n_i₁₊	n_i₀₊	n_i₊₊
Total		p_i_{1+ =} π_iSe_Bi + (1 −π_i)(1 − Sp_Bi)	p_i ₀₊ = π_i (1 − Se_Bi) + (1−π_i)Sp_Bi	1

Se_Ai, Sp_Ai are the sensitivity and specificity for the diagnostic test; Se_Bi, Sp_Bi are sensitivity and specificity for the reference test. π_i is the disease prevalence in the i^th study