A two-step log-linear procedure for graphical representation and inference of associations in cross-classified data for disease diagnosis
Metadata
Show full item recordEditorial
Wiley
Materia
Binary diagnostic tests Cross-classified data Distance associations Hypothesis testing Log-linear models
Date
2023-08-24Referencia bibliográfica
Vera, J. F., & Roldán‐Nofuentes, J. A. (2023). A two‐step log‐linear procedure for graphical representation and inference of associations in cross‐classified data for disease diagnosis. Statistics in Medicine.[https://doi.org/10.1002/sim.9854]
Sponsorship
ERDF/Ministry of Economic Transformation, Industry, knowledge and Universities of Andalucía, Grant/Award Number: B-CTS-184-UGR20; MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”,; Grant/Award Number: PID2021-126095NB-100; Ministry of Science and Innovation-State Research Agency/10.13039/501100011033/Spain; ERDF A way of making Europe”, Grant/Award Number: RTI2018-099723-B-I00Abstract
Biometrical sciences and disease diagnosis in particular, are often concerned
with the analysis of associations for cross-classified data, for which distance
association models give us a graphical interpretation for non-sparse matrices
with a low number of categories. In this framework, usually binary exploratory
and response variables are present, with analysis based on individual profiles
being of great interest. For saturated models, we show the usual linear relationship
for log-linear models is preserved in full dimension for the distance
association parameterization. This enables a two-step procedure to facilitate the
analysis and the interpretation of associations in terms of unfolding after the
overall and main effects are removed. The proposed procedure can deal with
cross-classified data for profiles by binary variables, and it is easy to implement
using traditional statistical software. For disease diagnosis, the problems of a
degenerate solution in the unfolding representation, and that of determining significant
differences between the profile locations are addressed. A hypothesis
test of independence based on odds ratio is considered. Furthermore, a procedure
is proposed to determine the causes of the significance of the test, avoiding
the problem of error propagation. The equivalence between a test for equality
of odds ratio pairs and the test for equality of location for two profiles in the
unfolding representation in the disease diagnosis is shown. The results have
been applied to a real example on the diagnosis of coronary disease, relating the
odds ratios with performance parameters of the diagnostic test