TITLE:
On the Index of Repeatability: Estimation and Sample Size Requirements
AUTHORS:
Maha Al-Eid, Mohamed M. Shoukri
KEYWORDS:
Measurements Errors, Functions of Variance Components, Delta Method, Lagrange Multiplier, Bootstrap Technique
JOURNAL NAME:
Open Journal of Statistics,
Vol.9 No.4,
August
20,
2019
ABSTRACT: Background: Repeatability is a statement on the magnitude of measurement error.
When biomarkers are used for disease diagnoses, they should be measured
accurately. Objectives: We derive an index of repeatability based on the
ratio of two variance components. Estimation of the index is derived from the
one-way Analysis of Variance table based on the one-way random effects model.
We estimate the large sample variance of the estimator and assess its adequacy
using bootstrap methods. An important requirement for valid estimation of
repeatability is the availability of multiple observations on each subject taken
by the same rater and under the same conditions. Methods: We use the
delta method to derive the large sample variance of the estimate of
repeatability index. The question related to the number of required repeats per
subjects is answered by two methods. In first methods we estimate the number of
repeats that minimizes the variance of the estimated repeatability index, and
the second determine the number of repeats needed under cost-constraints. Results
and Novel Contribution: The situation when the measurements do not follow
Gaussian distribution will be dealt with. It is shown that the required sample
size is quite sensitive to the relative cost. We illustrate the methodologies
on the Serum Alanine-aminotransferase (ALT) available from hospital registry
data for samples of males and females. Repeatability is higher among females in
comparison to males.