Related Experiment Video
Updated: Aug 13, 2026

Diagonal Method to Measure Synergy Among Any Number of Drugs
Published on: June 21, 2018
An alternative analysis for crossover studies that accounts for between-group disparities in drug response
1Department of Medicine, Merwede Hospital Dordrecht, Sliedrecht, The Netherlands.
Background:
In crossover clinical trials comparing completely different treatments, patients tend to fall into different populations: those who respond better to treatment 1 and those who respond better to treatment 2. The correlation between treatment response in such trials is negative. The current ANCOVA analysis for crossover studies does not allow for correlations being negative, and is therefore not adequate for testing in this kind of trials.
Objective Of Study:
To study whether matrix algebra provides a more appropriate approach for this purpose.
Results And Conclusions:
Using a mathematical model as well as hypothesized examples, it is demonstrated that matrix algebra of 2 pairs of cells of the same order not only allows for negative correlations in a crossover design but also provides enough power to test both the treatment and carryover effect.
Related Concept Videos
Crossover Experiments
Crossover designs are performed even with smaller sample sizes since the samples can act as their controls. These are better than simple randomized trials since patients are exposed to all the treatments.
Analysis of Population Pharmacokinetic Data
Types of Biopharmaceutical Studies: Controlled and Non-Controlled Approaches
Non-controlled studies, commonly employed for initial exploration, lack a control group, rendering them susceptible to biases and external influences. In contrast, controlled...
Bioequivalence Experimental Study Designs: Repeated Measures, Cross-Over, Carry-Over, and Latin Square Designs
Bioequivalence Data: Statistical Interpretation
Comparing the Survival Analysis of Two or More Groups

