Article

# Graphical modeling of binary data using the LASSO: a simulation study.

Institute for Medical Informatics, Biometrics and Epidemiology, Ludwig-Maximilians-Universität München, Munich, Germany.
BMC Medical Research Methodology (impact factor: 2.67). 02/2012; 12:16. DOI:10.1186/1471-2288-12-16 pp.16
Source: PubMed

ABSTRACT Graphical models were identified as a promising new approach to modeling high-dimensional clinical data. They provided a probabilistic tool to display, analyze and visualize the net-like dependence structures by drawing a graph describing the conditional dependencies between the variables. Until now, the main focus of research was on building Gaussian graphical models for continuous multivariate data following a multivariate normal distribution. Satisfactory solutions for binary data were missing. We adapted the method of Meinshausen and Bühlmann to binary data and used the LASSO for logistic regression. Objective of this paper was to examine the performance of the Bolasso to the development of graphical models for high dimensional binary data. We hypothesized that the performance of Bolasso is superior to competing LASSO methods to identify graphical models.
We analyzed the Bolasso to derive graphical models in comparison with other LASSO based method. Model performance was assessed in a simulation study with random data generated via symmetric local logistic regression models and Gibbs sampling. Main outcome variables were the Structural Hamming Distance and the Youden Index.We applied the results of the simulation study to a real-life data with functioning data of patients having head and neck cancer.
Bootstrap aggregating as incorporated in the Bolasso algorithm greatly improved the performance in higher sample sizes. The number of bootstraps did have minimal impact on performance. Bolasso performed reasonable well with a cutpoint of 0.90 and a small penalty term. Optimal prediction for Bolasso leads to very conservative models in comparison with AIC, BIC or cross-validated optimal penalty terms.
Bootstrap aggregating may improve variable selection if the underlying selection process is not too unstable due to small sample size and if one is mainly interested in reducing the false discovery rate. We propose using the Bolasso for graphical modeling in large sample sizes.

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Available from
25 Jan 2013

### Keywords

binary data

Bootstrap aggregating

building Gaussian graphical models

conservative models

continuous multivariate data

derive graphical models

dimensional binary data

Graphical models

modeling high-dimensional clinical data

multivariate normal distribution

promising new approach

random data

real-life data

Satisfactory solutions

simulation study

small penalty term

small sample size

symmetric local logistic regression models

variable selection

Youden Index.We