Page 129 - Contributed Paper Session (CPS) - Volume 6

CPS1848 J.A. Roldán-Nofuentes et al.

Global hypothesis test to compare the predictive
values of two diagnostic tests subject to a case-
control study
1
2
José Antonio Roldán-Nofuentes , Saad Bouh Sidaty-Regad
1 Biostatistics, School of Medicine, University of Granada, Spain.
2 Public Health and Epidemiology, School of Medicine, University of Nouakchott, Mauritania.

Abstract
The accuracy of a binary diagnostic test (BDT) is measured in terms of two
fundamental parameters: sensitivity and specificity. The sensitivity is the
probability of the result of the BDT being positive when the individual has the
disease and the specificity is the probability of the result of the BDT being
negative when the individual does not have the disease. Other fundamental
parameters of a binary diagnostic test are the positive predictive value and the
negative predictive value. The predictive values represent the clinical accuracy
of the test, and they depend on the sensitivity and specificity of the diagnostic
test and on the disease prevalence. The comparison of the predictive values
of two binary diagnostic tests is a topic that has been the subject of different
studies in the field of Statistics. In this work, we propose a global hypothesis
test to compare the predictive values of two binary diagnostic tests subject to
a case-control design, assuming for this purpose that there is an estimation of
the disease prevalence. This global hypothesis test is based on the chi-squared
distribution. The method proposed was applied to a real example.

Keywords
Chi-square distribution; Positive and negative predictive values; Type I
binomial bivariate distribution

1. Introduction
The positive predictive value (PPV) is the probability of an individual having
the disease when the result of the BDT is positive, and the negative predictive
value (NPV) is the probability of an individual not having the disease when the
result of the BDT is negative. The predictive values (PVs) represent the accuracy
of the diagnostic test when it is applied to a cohort of individuals, and they are
measures of the clinical accuracy of the BDT. The PVs depend on the sensitivity
(Se) and the specificity (Sp) of the BDT and on the disease prevalence (p), i.e.
p Se 1 p  Sp
PPV  and NPV  .
p Se  1 p  1 Sp   p 1 Se  1 p   Sp

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