Samuele E. Locatelli
33 lines
3.7 KiB
Plaintext
33 lines
3.7 KiB
Plaintext
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<h2>METHODOLOGICAL SPECIFICATION</h2>
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<p>All methodological details can be found in Marizzoni, Ferrari et al. 2019 Neurobiology of Aging <a href="https://doi.org/10.1016/j.neurobiolaging.2019.12.019" target="_blank">https://doi.org/10.1016/j.neurobiolaging.2019.12.019</a>. In brief finite (one dimension) mixture model<sup>1,2</sup>, was applied to the distribution of biomarker in order to detect any subgroup (component). Formally, a mixture model is defined as a weighted sum of random variables (components) belonging to the same family of probability distribution. Each component identifies a cluster and the mixture model procedure allows to produce a probabilistic clustering that quantifies the uncertainty of observations belonging to components of the mixture. In our case, each component belongs to the Gaussian distribution family defined by corresponding parameters mean and standard deviation (SD). The estimation procedure was carried out by Expectation-Maximization algorithm<sup>3</sup>, whereas the number of component and the parametrization of each component (i.e. the ‘best-fit’ model) was chosen by the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) indexes): lower indexes values indicate best model<sup>4</sup>. The cut-off values for distinguishing the subgroups were defined as the biomarker values for which the Gaussian mixture model assigned equal probability of belonging to two consecutive components.</p>
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<p>In order to investigate the effect of covariates in the identifications of subgroups and, thus, cut-offs, an extension of finite mixture model applied to generalized linear model was adopted <sup>5</sup>. With this extension, the components can follow a simple parametric distribution (as for the simple finite mixture model if no risk factors -covariates- are added ) or can be defined by a more complex model as a generalized linear model (if covariates are added). The effect of the covariates on each mixture component were carried out in terms of beta (regression) coefficients (and corresponding pvalues), as well as in terms of the estimated parameters of the component (mean and SD) obtained by taking into account the effect of the covariate. Significant effects of covariates lead to an alteration of the component shape and to the subgroups mixing.</p>
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References:
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<li>
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McLAchlan and Peel 2000, “Finite Mixture Models” Wiley&Son, ISBN:9780471006268.
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<li>Fraley and Raftery, 2007, “Model-based Methods of Classification: Using the mclust software in Chemometrics”, Journal of Statistical Software, vol. 18 issue 6.</li>
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<li>Dempster, Laird, Rubin, 1977, "Maximum Likelihood from Incomplete Data via the EM Algorithm"; Journal of the Royal Statistical Society, Series B. 39 (1): 1–38.</li>
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<li>Schwarz G, 1978, “Estimating the Dimension of a Model”; The Annals of Statistics, 6, 461–464.</li>
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<li>Leisch F, 2004; FlexMix: A general framework for finite mixture models and latent class regression in R; Journal of Statistical Software, vol 11, issue 8.</li>
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