Pelvic disease group | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Menopause | Pre | Post | Post | Pre/post | Pre | Post | ||||||

Stage | III/IV | III/IV | I/II | I/II/III/IV | Benign | Benign | ||||||

Histology | Nonmucinous | Nonmucinous | Nonmucinous | Mucinous | Endometriosis | Ovarian serous | ||||||

Z value CA 125 | 6.8 | 11.0 | 7.2 | 3.4 | 2.6 | 4.0 | ||||||

Marker pair | Square-root Mahalanobis distance | |||||||||||

CA 125 and CA 15.3 | 8.0 | 11.9 | 7.3 | 3.4 | 2.6 | 4.0 | ||||||

CA 125 and CA 19.9 | 6.8 | 11.0 | 7.6 | 5.4 | 2.6 | 4.0 | ||||||

CA 125 and CEA | 6.8 | 11.0 | 7.2 | 4.2 | 2.6 | 4.0 | ||||||

CA 125 and SMRP | 8.4 | 11.8 | 7.2 | 3.4 | 2.6 | 4.0 |

NOTE: Calculation of Mahalanobis distances: denote by

*x*_{1}= CA 125 value in pool, by*x*_{2}= CA 19.9/CA 15.3/CEA value in pool, and let*X*= [*x*_{1}*x*_{2}]. Denote by*y*_{1}= vector of CA 125 values from appropriate control group, and*y*_{2}= vector of CA 19.9/CA 15.3/CEA values from appropriate control group, and bivariately by*Y*= [*y*_{1}*y*_{2}]. Then, the mean on the logarithmic scale is given by*m*_{1}= mean(log(*y*_{1})) and*m*_{2}= mean(log(*y*_{2})), bivariately denoted by*M*= [*m*_{1}*m*_{2}]. The difference between the measurement in the pooled sample and the mean of the individual samples, on the logarithmic scale, is*D*= log(*X*) −*M*. The variance-covariance matrix is calculated from the individual observations for each biomarker,*Σ*= variance-covariance matrix of log(*Y*). The variance-covariance matrix controls for any correlation between the biomarkers; thus, for example, when two biomarkers are elevated in the presence of ovarian cancer, a negative correlation induces greater complementarity than either a zero or positive correlation, the latter inducing a degree of redundancy. The Mahalanobis distance is given by*D*^{T}*Σ*^{−1}*D*, and the square root of the Mahalanobis distance is analogous to the*z*value in one dimension.