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CPS1848 J.A. Roldán-Nofuentes et al.
is made by solving the individual tests and applying Bonferroni’s method or
Holm’s method to an error  .

3. Example
The results obtained were applied to the study by Matovu et al (2010) on
the diagnosis of Human African trypanosomiasis (HAT) in Uganda. HAT, also
known as sleeping sickness, is a parasitic disease caused by protozoa
belonging to the genus Trypanosoma, and it is transmitted to human beings
by a bite from the tsetse fly (genus Glossina) infected by other people or
animals that host human pathogenic parasites. In some rural areas of Africa,
the disease prevalence may reach 50% in periods of epidemics, and is a
significant cause of death. Matovu et al (2010) applied two diagnostic tests to
a sample of 75 cases and another sample of 65 controls. For a prevalence value
ˆ
ˆ
equal to 10%, the estimations of the PVs are PPV  0.540 , PPV  0.858 ,
2
1
ˆ
ˆ
NPV  0.978 and NPV  0.982, and the estimated variance and covariance
1 2
matrix of the estimators of the PVs is
 0.01158 0.00562 0.00015 0.00005
 0.00562 0.01456 0.00006 0.00006 
 ˆ ˆ ω    0.00015 0.00006 0.00003 0.00001 
 
 0.00005 0.00006 0.00001 0.00002 
The value of the test statistic for the test
H 0  : PPV  1 PPV 2 and NPV  1 NPV 2  vs :at least one equality is not true,
H
1
is Q  6.954 P value  0.031  and therefore null hypothesis of the global

2
test is rejected. Solving the individual hypothesis tests it is found that the value
of the test statistic for the H 0 : PPV  PPV 2 is equal to 2.606
1


two sided p-value 0.009 , and that the value of the test statistic for the test


H 0 : NPV  NPV is equal to 0.886 two sided p-value 0.375 . Applying
1
2
Bonferroni’s (Holm’s) method the equality hypothesis of the negative
predictive values is not rejected and the equality hypothesis of the two positive
predictive values is rejected. The positive predictive value of the NASBA-OC
test is significantly greater than that of the PCR-OC test (95% CI: 0.079 to
0.558).

Acknowledgements
This research was supported by the Spanish Ministry of Economy, Grant
Number MTM2016-76938-P.

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