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International Biometric Society
LOG-MEAN LINEAR REGRESSION MODELS FOR ASSESSING THE EFFECT OF HIV-INFECTION ON
MULTIMORBIDITY IN A CASE-CONTROL STUDY
Monia Lupparelli and Alberto Roverato
Department of Statistical Sciences, University of Bologna
Multimorbidity is defined as the co-occurrence of two or more chronic medical conditions in
one person. It is well-known that multimorbidity correlates with age and, furthermore, that
HIV-infected patients experience an increased prevalence of noninfectious comorbidities,
compared with the general population.
Guaraldi et al. (2011) investigated the effect of HIV-infection on the prevalence of five
noninfectious chronic medical conditions from an Italian dataset obtained from a crosssectional retrospective case-control study. The dataset includes five binary variables
representing the presence/absence of each comorbidity and some covariates in a sample of
patients with 25% of them affected by HIV. More specifically, Guaraldi et al. (2011) analysed
the effect of the infection by means of univariate logistic regressions on the presence of
every single comorbidity. Nevertheless, multimorbidity is characterized by complex
interactions of co-existing diseases so, the role of HIV-infection is better explored through a
multivariate, rather than an univariate, regression approach. In particular, our interest is in
modelling the infection effect on the marginal association of subsets of comorbidities.
Lang (1996) investigated the statistical properties of a broad family of multivariate
regression models using several link functions for categorical responses based on suitable
parameterizations. Special cases of these link functions include the multivariate logistic
transform, the dependence ratios, the logarithm of the mean parameterization. These link
functions have already been used in a context of marginal regression modelling. See
Bergsma et al. (2009) for a comprehensive review.
We propose a link function for multivariate regression models based on the log-mean linear
(LML) parameterization recently developed by Roverato et al., (2013). The resulting LML
regression model belongs to the Lang’s family of models, therefore it preserves the main
properties of this well-established approach and the appealing features of the LML
parameterization at the same time. In particular, the LML link function allows the selection of
regression models of interest which could not be easily tested otherwise. We discuss the
statistical properties and the maximum likelihood estimation of LML regression models for
the analysis of this case-control study.
Assessing the effect of covariates, and in particular of HIV-infection, on interactions of coexisting diseases is the principal aim of this application. Unlike the standard regression
approach, our interest is focused on the covariate effect on response interactions rather
than on the effect of covariate interactions on single responses. From this perspective, the
link function choice becomes crucial as it defines the association measures to regress on
the covariates with substantive differences in terms of model selection. We discuss some
issues on testing hypothesis for LML regression coefficients which have a straightforward
interpretation in terms of relative risks for assessing the HIV effect on multimorbidity.
References
[1] Bergsma, W. P., M. A. Croon, and J. A. Hagenaars (2009). Marginal Models. Springer.
[2] Guaraldi, G., G. Orlando, S. Zona, M. Menozzi, F. Carli, E. Garlassi, A. Berti, E. Rossi,
A. Roverato, and F. Palella (2011). Premature age-related comorbidities among HIV-infected
persons compared with the general population. Clinical Infectious Diseases, 53, 1120-1126.
[3] Lang, J. B. (1996). Maximum likelihood methods for a generalized class of log-linear
models. The Annals of Statistics, 24 (2), 726-752.
[4] Roverato, A., M. Lupparelli, and L. La Rocca (2013). Log-mean linear models for binary
data. Biometrika, 100 (2), 485-494.
International Biometric Conference, Florence, ITALY, 6 – 11 July 2014