Reference intervals and regions are widely used to identify the measurement range expected
from a reference population. Such regions capture the central part of the population,
and have potential applications in the field of laboratory medicine. Furthermore, the
uncertainty in an estimated reference region can be assessed using a central tolerance region,
namely, a region that will contain the population reference region, with a specified
confidence level. The construction of a central tolerance region is investigated in this article
for a multivariate normal population, and also for a multivariate normal linear regression
model. A theoretical framework is developed that will facilitate the numerical computation
of the tolerance factor. The performance of a prediction region is also evaluated, in terms
of capturing the central part of the population, and the prediction region is found to be unsatisfactory.
Some examples from laboratory medicine are used to illustrate the results.
Reference intervals and regions are widely used to identify the measurement range expectedfrom a reference population. Such regions capture the central part of the population,and have potential applications in the field of laboratory medicine. Furthermore, theuncertainty in an estimated reference region can be assessed using a central tolerance region,namely, a region that will contain the population reference region, with a specifiedconfidence level. The construction of a central tolerance region is investigated in this articlefor a multivariate normal population, and also for a multivariate normal linear regressionmodel. A theoretical framework is developed that will facilitate the numerical computationof the tolerance factor. The performance of a prediction region is also evaluated, in termsof capturing the central part of the population, and the prediction region is found to be unsatisfactory.Some examples from laboratory medicine are used to illustrate the results.
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