Bayesian penalized model for classification and selection of functional predictors using longitudinal MRI data from ADNI

Figures & data

Figure 1. Plots based on Example 1.

Table 1. Classification and selection performance table.

	Bayesian classification with
	Bayesian Group Lasso
	Sensitivity	Specificity	TPR	FPR	−2 Log likelihood
$\begin{array}{c}\mathrm{E}\mathrm{x}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}1\\ n=200\\ p=20\\ t=50\end{array}$	0.97 (0.01)	0.93 (0.01)	1 (0)	0 (0)	3.65
$\begin{array}{c}\mathrm{E}\mathrm{x}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}2\\ n=200\\ p=50\\ t=50\end{array}$	0.97 (0.01)	0.95 (0.01)	1 (0)	0.0073 (0.05)	0.219
$\begin{array}{c}\mathrm{E}\mathrm{x}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}3\\ n=500\\ p=100\\ t=20\end{array}$	0.98 (0.001)	0.97 (0.01)	1 (0)	0 (0)	6.87
	Logistic regression
	with frequentist group lasso
	Sensitivity	Specificity	TPR	FPR	$-2$ Log likelihood
$\begin{array}{c}\mathrm{E}\mathrm{x}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}1\\ n=200\\ p=20\\ t=50\end{array}$	0.92 (0.01)	0.86 (0.01)	1 (0)	0.114 (0.04)	69.23
$\begin{array}{c}\mathrm{E}\mathrm{x}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}2\\ n=200\\ p=50\\ t=50\end{array}$	0.81 (0.01)	0.88 (0.01)	1 (0)	0.34 (0.05)	53.66
$\begin{array}{c}\mathrm{E}\mathrm{x}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}3\\ n=500\\ p=100\\ t=20\end{array}$	0.91 (0.001)	0.94 (0.001)	1 (0)	0.05 (0.02)	190.23

Note: Simulation result comparisons between Bayesian and Frequentist methods.

Table 2. Patients baseline characteristics.

	AD	CN	p-value
n	174	122
Age (Mean ± sd)	$74.76\pm 7.23$	$75.61\pm 5.45$	0.25
Gender (F/M)	69/105	55/67	0.35
MMSE (Mean ± sd)	$25.43\pm 2.40$	$28.96\pm 1.17$	<.0001
ADAS11 (Mean ± sd)	$14.78\pm 5.44$	$5.95\pm 2.94$	<.0001
APOE $(+/-)$	119/55	30/90	<.0001

Note: Comparison of Baseline Age, Gender ratio, MMSE score, ADAS11 score and APOE ratio between AD and CN groups.

Figure 2. Brain volume changes of Left Hippocampus, Left Lateral Orbitofrontal cortex, and Left Posterior Cingulate over time for Normal and Dementia patients.

Figure 3. Acceptance probability of MCMC sample for Left Hippocampus and Left-Lateral Orbitofrontal brain regions.

Figure 4. Pictorial representation of selected brain ROI's discriminating diseased group from normal control. (a) Left Hippocampus^a. (b) Posterior Singulate^a. (c) Middle Temporal Gyrus^a and (d) Left lateral orbitofrontal cortex^a.

^a Plot obtained from on-line resources.