Mathematical verification of summary formula in retinal vessel diameter measurement

Our previous study found the retinal vessel diameter measurement using summary formula has no significant difference for the multiple retinal images of the same person, while the individual vessel measures show the significant difference. It was speculated that the revised formula summarizing the individual measures and therefore against variation. This paper uses the mathematical models to verify this speculation. The impacts of the sample size, branching coefficients, different graders and grader/systemic errors are analyzed and discussed. Our results confirmed the revised formula is robust against the variation which exists on the individual measures. However, the results also demonstrate 1) the revised formula is not able to remove the systemic errors and the variations caused by the different graders. 2) the measures summarized by the revised formula may not be suitable for monitoring the changes on the individual retinal vessels.