| dc.description.abstract | Two solutions are proposed for the estimation of odds ratios (OR) when one or the two elements of the principal (A, D) or secondary (B, C) diagonals of a 2 x 2 matrix (A, B, C, D) are 0. The OR estimate is AD/BC. If A or D are 0, OR = 0; if B or C are 0, the OR is undefined. Analytical solution. This solution conserves the marginal totals. If B = 0 and C = 0, the OR cannot be less than AD/1 (the minimal acceptable value), then the equation (A-X) (D-X)/X2 = KAD/1 searches for that X which subtracted to A and B and added to B (0) and C (0) yields an OR K times AD; if B = 0 and C > 0 then (A-X) (D-X)/X (C+X) = AD/C; if B > 0 and C = 0, then B replaces C in the latter equation. If A and D are 0, X2/(B-X) (C-X) = 1/KBC; if A = 0 and D > 0, X (D+X)/(B-X) (C-X) = D/KBC; if A > 0 and D = 0, A replaces D in the latter equation. K can be taken at the maximum Chi squared value. Probabilistic solution. Zeros are replaced by ones and the elements of the diagonal without zeros are increased proporti | |
