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**11 - 18**of**18**### Case-control studies for rare diseases: improved estimation of

"... Abstract. To capture the dependencesof a diseaseon severalrisk factors, a challengeis to combinemodel-basedestimation with evidence-basedarguments. Standardcase-control methods allow estimation of the dependences of a rare disease on several regressors via logistic regressions. For case-control stud ..."

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Abstract. To capture the dependencesof a diseaseon severalrisk factors, a challengeis to combinemodel-basedestimation with evidence-basedarguments. Standardcase-control methods allow estimation of the dependences of a rare disease on several regressors via logistic regressions. For case-control studies, the sampling design leads to samples from two different populations and for the set of regressors in every logistic regression, these samples are then mixed and taken as given observations. But, it is the differences in independence structures of regressors for cases and for controls that can improve logistic regression estimates and guide us to the important feature dependences that are specific to the diseased. A case-control study on laryngeal cancer is used as illustration.

### MULTIVARIATE STATISTICAL ANALYSIS

"... Classical multivariate statistical methods concern models, distributions and inference based on the Gaussian distribution. These are the topics in the first textbook for mathematical statisticians by T.W. Anderson that was published in 1958 and that appeared as a slightly expanded 3rd edition in 200 ..."

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Classical multivariate statistical methods concern models, distributions and inference based on the Gaussian distribution. These are the topics in the first textbook for mathematical statisticians by T.W. Anderson that was published in 1958 and that appeared as a slightly expanded 3rd edition in 2003. Matrix theory and notation is used there extensively to efficiently derive properties of the multivariate Gaussian or the Wishart distribution, of principal components, of canonical correlation and discriminant analysis and of the general multivariate linear model in which a Gaussian response vector variable Ya has linear least-squares regression on all components of an explanatory vector variable Yb. In contrast, many methods for analysing sets of observed variables have been developed first within special substantive fields and some or all of the models in a given class were justified in terms of probabilistic and statistical theory much later. Among them are factor analysis, path analysis, structural equation models, and models for which partial-least squares estimation have been proposed. Other multivariate techniques such as cluster analysis and multidimensional scaling have

### Log-mean linear models for binary data Alberto

, 2012

"... This paper introduces a novel class of models for binary data, which we call log-mean linear models. The characterizing feature of these models is that they are specified by linear constraints on the log-mean linear parameter, defined as a log-linear expansion of the mean parameter of the multivaria ..."

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This paper introduces a novel class of models for binary data, which we call log-mean linear models. The characterizing feature of these models is that they are specified by linear constraints on the log-mean linear parameter, defined as a log-linear expansion of the mean parameter of the multivariate Bernoulli distribution. We show that marginal independence relationships between variables can be specified by setting certain log-mean linear interactions to zero and, more specifically, that graphical models of marginal inde-pendence are log-mean linear models. Our approach overcomes some drawbacks of the existing parameterizations of graphical models of marginal independence.

### Multiple Hidden Markov Models for Categorical Time Series

, 2014

"... We introduce multiple hidden Markov models (MHMMs) where an observed multivariate categorical time series depends on an unobservable multivariate Mar-kov chain. MHMMs provide an elegant framework for specifying various indepen-dence relationships between multiple discrete time processes. These indep ..."

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We introduce multiple hidden Markov models (MHMMs) where an observed multivariate categorical time series depends on an unobservable multivariate Mar-kov chain. MHMMs provide an elegant framework for specifying various indepen-dence relationships between multiple discrete time processes. These independen-cies are interpreted as Markov properties of a mixed graph and a chain graph associated to the latent and observable components of the MHMM, respectively. These Markov properties are also translated into zero restrictions on the parame-ters of marginal models for the transition probabilities and the distributions of the observable variables given the latent states.