Objective: To describe the use of second order discriminant analysis as a classification methodology along with the underlying assumptions and sampling requirements, with special emphasis on the use of this analysis in chemopreventive efficacy studies.
Study design: The discriminant function score distributions derived in an analysis of 2 diagnostic groups may show such overlap that a statistically significant difference in mean values cannot be shown and, more important, that a useful case-based classification cannot be attained. By using the discriminant function score distributions from each case, it is frequently possible to derive a second order discriminant function based on case-specific characteristics, rather than characteristics of nuclei, thereby attaining improved case classification.
Results: Second order discriminant analysis has proven very useful in the documentation of case-level efficacy in chemopreventive trials. In a study of orally administered vitamin A, a first order discriminant analysis did not achieve a statistically significant difference in the score distributions for nuclei, but a second order discriminant analysis allowed a correct recognition of intervention effects in 85% of submitted cases. In a chemopreventive study of triamcinolone, a similarly inadequate discrimination based on discriminant function scores for nuclei resulted. After a second order discriminant analysis, a reduction in solar-actinic damage could be shown in 14/15, or 93%, of treated cases.
Conclusion: Second order discriminant analysis can be highly effective when the discriminating information offered at the nuclear level is inadequate due to high dispersion and small differences in mean values of discriminant function scores for the diagnostic groups. Second order analysis utilizes case-specific characteristics of the discriminant function score distributions to document diagnostic group separation and/or efficacy of chemopreventive intervention by a reduction in case discriminant function scores.