Comparison of discriminant analysis procedures in laboratory differentiation of hypercalcemia

Logistic, linear, and quadratic discriminant analyses were compared in their ability to differentiate hypercalcemic patients with primary hyperparathyroidism from those with malignancy. Linear and quadratic discriminant analyses were performed by use of both untransformed and logarithmically transformed data. Application of principal components analysis with varimax rotation was helpful in revealing the underlying relationships between variables. All discriminant methods identified serum albumin as the best single discriminating test, with the log-quadratic discriminant analysis classifying 81% of patients correctly. The combination of albumin, carboxy-terminal parathyroid hormone, and chloride improved classification accuracy (92% by use of log-quadratic discriminant analysis). Logistic discriminant analysis, using all 20 variables, gave a classification accuracy of 100%. Quadratic discriminant analysis gave better classification than linear discriminant analysis, and both methods performed better when log-transformed data were used. Logistic discriminant analysis followed by discrimination procedures using log-transformed data yielded the highest classification accuracy and reliability of the methods used.