Page 130 - Contributed Paper Session (CPS) - Volume 6

CPS1848 J.A. Roldán-Nofuentes et al.
PVs quantify the clinical value of the BDT, since both the individual and the
clinician are more interested in knowing how probable it is to have the disease
given a BDT result.
The comparison of the performance of two binary diagnostic tests is a
topic of special importance in the study of statistical methods for the diagnosis
of diseases. This comparison is made through a paired-design or through a
case-control design. Paired design consists of applying the two BDTs and the
gold standard to all of the individuals in a single sample. Case-control design
consists of applying the two BDTs to all of the individuals in two samples, one
made up of individuals who have the disease (case sample) and another made
up of individuals who do not have the disease (control sample). In this
research, we study the comparison of the PVs of two BDTs subject to a case-
control design. Subject to this type of design, the two BDTs are applied to all
of the individual in two samples, one of n individuals who have the disease
1
(case sample) and another with n individuals who do not have the disease
2
(control sample). In a case-control design, the sample sizes n and n are set
1 0
by the researcher. The sample of individuals that have the disease is extracted
from a population of individuals that have the disease (e.g. registers of
diseases), and the control sample is extracted from a population of individuals
who are known not to have the disease. As the PVs depend on the disease
prevalence and subject to a case-control design the quotient n  n 2  is
n
1
1
not an estimator of the prevalence, in order to estimate and compare the PVs
subject to this design it is necessary to have an estimation of the disease
prevalence. This estimation can be obtained from health surveys or from
previous studies. In Section 2, we study hypothesis tests to jointly and
individually compare the PVs of two BDTs subject to case-control study. In
Section 3 the results are applied to a real example of the diagnosis of Human
African Trypanosomiasis.

2. The model
Let us consider two BDTs, Test 1 and Test 2, which are applied to all of the
individuals in two samples, one of n individuals who have the disease (case
1
sample) and another of n individuals who do not have it (control sample).
2
Let T and T be two binary variables that model the results of each BDT, in
1 2
such a way that T  when the result of the corresponding BDT is positive
1
i
and T  0 when it is negative. In Table 1, we can see the probabilities
i
associated to the application of both BDTs to both types of individuals (cases
and controls), as well as the frequencies observed.

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