Computational and Mathematical Methods in Medicine

Research Article

Group Guided Fused Laplacian Sparse Group Lasso for Modeling Alzheimer’s Disease Progression

Table 4

Prediction performance results of ten cognitive scores of six time points based on MRI features.


	Ridge	Lasso	TGL	cFSGL	GFL-SGL

Score: ADAS
nMSE	10.122 ± 1.4156	6.7689 ± 0.7698	6.2740 ± 0.7861	6.3092 ± 0.6991	6.1389 ± 0.6951
wR	0.5638 ± 0.0509	0.6237 ± 0.0541	0.6628 ± 0.0561	0.6560 ± 0.0486	0.6658 ± 0.0469
BL rMSE	7.6553 ± 0.5576	6.8217 ± 0.4238	6.7275 ± 0.4298	6.7151 ± 0.4275	6.6479 ± 0.5045
M6 rMSE	9.1778 ± 1.2467	7.9602 ± 0.8484	7.7637 ± 0.9345	7.6846 ± 0.9493	7.6994 ± 0.9357
M12 rMSE	9.7212 ± 1.0986	8.7050 ± 0.8651	8.3822 ± 0.9401	8.4646 ± 1.0594	8.4076 ± 1.0478
M24 rMSE	11.676 ± 1.6463	10.191 ± 1.2914	9.6773 ± 1.6308	9.7859 ± 1.6170	9.4808 ± 1.6224
M36 rMSE	12.772 ± 2.4262	9.4852 ± 1.3806	8.9110 ± 1.3356	8.9313 ± 1.3762	8.7939 ± 1.2987
M48 rMSE	20.433 ± 2.6163	9.0161 ± 2.3381	8.2041 ± 1.1869	8.6279 ± 2.0852	8.0947 ± 1.6669

Score: MMSE
nMSE	10.447 ± 1.4590	2.5284 ± 0.2230	2.4911 ± 0.1411	2.5048 ± 0.1772	2.3975 ± 0.2140
wR	0.4188 ± 0.0530	0.5720 ± 0.0498	0.5898 ± 0.0431	0.5878 ± 0.0449	0.5975 ± 0.0425
BL rMSE	2.6943 ± 0.1767	2.2001 ± 0.1349	2.2204 ± 0.1367	2.1729 ± 0.1505	2.1478 ± 0.1159
M6 rMSE	3.5136 ± 0.3413	2.8571 ± 0.2697	2.8260 ± 0.2875	2.8069 ± 0.2882	2.7682 ± 0.2470
M12 rMSE	3.9044 ± 0.2313	3.2128 ± 0.3301	3.1438 ± 0.3328	3.1558 ± 0.3650	3.1375 ± 0.3660
M24 rMSE	5.0192 ± 0.6956	3.8663 ± 0.6975	3.8171 ± 0.7064	3.8316 ± 0.6355	3.8371 ± 0.7620
M36 rMSE	5.7022 ± 0.5505	3.2518 ± 0.8592	3.2732 ± 0.8106	3.4828 ± 0.6365	3.1914 ± 0.8230
M48 rMSE	29.958 ± 0.7233	4.0539 ± 0.7097	4.0077 ± 0.8089	3.8018 ± 0.9474	3.5517 ± 0.6933

Score: RAVLT.TOTAL
nMSE	17.139 ± 1.2384	9.7932 ± 0.9119	9.1381 ± 0.8168	8.9621 ± 0.9867	8.7825 ± 0.9241
wR	0.4059 ± 0.0510	0.4989 ± 0.0587	0.5390 ± 0.0603	0.5498 ± 0.0533	0.5512 ± 0.0558
BL rMSE	11.404 ± 0.7043	9.8789 ± 0.9286	9.6628 ± 0.9091	9.6980 ± 0.7418	9.5445 ± 0.6940
M6 rMSE	11.828 ± 1.1623	10.210 ± 1.2512	9.9696 ± 1.1915	10.079 ± 1.1682	9.8337 ± 1.2773
M12 rMSE	13.027 ± 0.9974	11.457 ± 0.9096	10.945 ± 1.1063	10.865 ± 1.3290	10.788 ± 1.2737
M24 rMSE	14.647 ± 1.4006	12.330 ± 1.4231	11.997 ± 1.5765	11.756 ± 1.6851	11.740 ± 1.5374
M36 rMSE	15.899 ± 2.2567	11.512 ± 1.5268	10.640 ± 1.2792	10.331 ± 1.5089	10.306 ± 1.5535
M48 rMSE	41.462 ± 3.4404	12.728 ± 1.5048	13.105 ± 2.8874	11.333 ± 2.0937	11.803 ± 2.5033

Score: RAVLT.TOT6
nMSE	3.9829 ± 0.4397	2.9663 ± 0.1909	2.8853 ± 0.2057	2.8546 ± 0.1867	2.8198 ± 0.1772
wR	0.4528 ± 0.0703	0.5213 ± 0.0803	0.5412 ± 0.0682	0.5458 ± 0.0687	0.5541 ± 0.0730
BL rMSE	3.6885 ± 0.3741	3.2944 ± 0.2617	3.2949 ± 0.2611	3.2756 ± 0.2885	3.2540 ± 0.2390
M6 rMSE	3.4704 ± 0.3949	3.1592 ± 0.3443	3.1628 ± 0.2939	3.1386 ± 0.3116	3.1270 ± 0.2841
M12 rMSE	3.8384 ± 0.2676	3.4284 ± 0.2262	3.4271 ± 0.2632	3.4094 ± 0.2808	3.3763 ± 0.2575
M24 rMSE	4.0656 ± 0.3758	3.6252 ± 0.3469	3.5826 ± 0.3581	3.5894 ± 0.3360	3.5592 ± 0.3293
M36 rMSE	4.3074 ± 0.7174	3.5169 ± 0.3667	3.3890 ± 0.3799	3.3799 ± 0.3926	3.3557 ± 0.3799
M48 rMSE	7.4599 ± 1.0656	4.5834 ± 0.6969	3.7902 ± 0.7846	3.7275 ± 0.7056	3.7694 ± 0.7746

Score: RAVLT.T30
nMSE	3.9392 ± 0.3946	3.0595 ± 0.2012	2.9876 ± 0.1950	2.9706 ± 0.2044	2.9358 ± 0.1919
wR	0.4580 ± 0.0609	0.5255 ± 0.0730	0.5384 ± 0.0679	0.5422 ± 0.0647	0.5474 ± 0.0646
BL rMSE	3.7877 ± 0.3069	3.4076 ± 0.2595	3.4176 ± 0.2485	3.4034 ± 0.2806	3.3806 ± 0.2491
M6 rMSE	3.4750 ± 0.3531	3.1839 ± 0.3380	3.2095 ± 0.2593	3.1991 ± 0.2871	3.1496 ± 0.3013
M12 rMSE	3.9611 ± 0.4480	3.6673 ± 0.3242	3.6343 ± 0.3799	3.6173 ± 0.3800	3.5943 ± 0.3790
M24 rMSE	4.2027 ± 0.5011	3.8070 ± 0.4648	3.7570 ± 0.4051	3.7562 ± 0.4151	3.7389 ± 0.4429
M36 rMSE	4.2142 ± 0.5102	3.5049 ± 0.4595	3.3604 ± 0.4241	3.3473 ± 0.4327	3.3852 ± 0.4545
M48 rMSE	7.1834 ± 0.8145	4.5537 ± 0.6315	4.0102 ± 0.4413	4.0900 ± 0.5064	4.0727 ± 0.5386

Score: RAVLT.RECOG
nMSE	6.2754 ± 1.2306	3.4921 ± 0.3325	3.2186 ± 0.2953	3.2282 ± 0.2992	3.2314 ± 0.2654
wR	0.3496 ± 0.0851	0.4583 ± 0.0793	0.4993 ± 0.0779	0.5075 ± 0.0738	0.5058 ± 0.0799
BL rMSE	4.3887 ± 0.4210	3.6494 ± 0.2993	3.5990 ± 0.3647	3.5721 ± 0.3709	3.5653 ± 0.3386
M6 rMSE	4.4959 ± 0.3686	3.7470 ± 0.2412	3.6722 ± 0.2928	3.6616 ± 0.2995	3.6627 ± 0.2815
M12 rMSE	4.6874 ± 0.3574	3.7850 ± 0.2889	3.7034 ± 0.3521	3.7178 ± 0.2935	3.6942 ± 0.3141
M24 rMSE	4.8253 ± 0.4029	3.9168 ± 0.2251	3.7518 ± 0.2771	3.8103 ± 0.2391	3.8058 ± 0.2488
M36 rMSE	5.4178 ± 0.6548	3.8073 ± 0.2366	3.6448 ± 0.2966	3.6962 ± 0.1616	3.7372 ± 0.1837
M48 rMSE	12.411 ± 0.9035	5.1582 ± 1.0963	3.9023 ± 0.8880	3.7995 ± 0.8998	3.9423 ± 0.7025

Score: FLU.ANIM
nMSE	9.6435 ± 1.1387	5.2513 ± 0.7213	5.1293 ± 0.6597	4.9992 ± 0.6243	4.9478 ± 0.6151
wR	0.2872 ± 0.0942	0.3858 ± 0.0834	0.4212 ± 0.0895	0.4433 ± 0.0839	0.4406 ± 0.0840
BL rMSE	6.3878 ± 0.6423	5.2970 ± 0.5354	5.3535 ± 0.4841	5.1972 ± 0.5149	5.2026 ± 0.4857
M6 rMSE	6.1380 ± 0.5975	5.3040 ± 0.4995	5.3207 ± 0.4732	5.2175 ± 0.4797	5.1951 ± 0.4563
M12 rMSE	6.6219 ± 0.7800	5.7413 ± 0.8672	5.6134 ± 0.7977	5.5704 ± 0.8052	5.5303 ± 0.7929
M24 rMSE	7.2828 ± 0.9366	5.8387 ± 0.7492	5.7844 ± 0.6280	5.7839 ± 0.7570	5.6815 ± 0.7035
M36 rMSE	7.8427 ± 1.4361	5.6450 ± 0.6733	5.3599 ± 0.7423	5.3988 ± 0.8188	5.3655 ± 0.6841
M48 rMSE	20.613 ± 1.8524	6.2549 ± 1.6986	5.7005 ± 1.3167	5.7501 ± 1.5019	5.9240 ± 1.4382

Score: FLU.VEG
nMSE	6.6621 ± 0.8499	3.5364 ± 0.3463	3.4061 ± 0.2879	3.3593 ± 0.3146	3.3575 ± 0.2867
wR	0.3726 ± 0.0730	0.4934 ± 0.0830	0.5257 ± 0.0781	0.5357 ± 0.0746	0.5356 ± 0.0777
BL rMSE	4.4121 ± 0.3082	3.7115 ± 0.2221	3.6980 ± 0.2387	3.6464 ± 0.2179	3.6368 ± 0.2016
M6 rMSE	4.7036 ± 0.1969	3.8593 ± 0.2589	3.8617 ± 0.2075	3.8033 ± 0.2318	3.7892 ± 0.2294
M12 rMSE	5.0566 ± 0.4772	3.9568 ± 0.4941	3.9319 ± 0.4757	3.9226 ± 0.4542	3.9267 ± 0.4761
M24 rMSE	5.2146 ± 0.4402	4.2580 ± 0.4104	4.1408 ± 0.3444	4.1677 ± 0.4192	4.1908 ± 0.4275
M36 rMSE	6.4334 ± 0.7933	4.4230 ± 0.3982	4.2656 ± 0.3702	4.2445 ± 0.4263	4.2392 ± 0.3829
M48 rMSE	13.882 ± 1.4535	4.9607 ± 1.4253	3.9822 ± 1.3527	3.9887 ± 1.4023	4.0292 ± 1.4371

Score: TRAILS.A
nMSE	33.513 ± 3.8491	23.711 ± 1.8805	22.756 ± 1.5155	23.151 ± 1.5754	23.349 ± 1.5768
wR	0.3572 ± 0.0769	0.3740 ± 0.0658	0.4219 ± 0.0682	0.4122 ± 0.0688	0.3965 ± 0.0704
BL rMSE	25.942 ± 3.8665	23.421 ± 4.0061	23.039 ± 3.6598	23.258 ± 3.7233	23.443 ± 3.8347
M6 rMSE	28.290 ± 4.4832	25.328 ± 3.6847	25.021 ± 3.3715	25.198 ± 3.5600	25.634 ± 3.3660
M12 rMSE	27.665 ± 3.8961	25.043 ± 3.4997	24.493 ± 3.3011	24.675 ± 3.3022	24.882 ± 3.2310
M24 rMSE	31.805 ± 4.1087	28.384 ± 3.0384	27.845 ± 3.2106	28.073 ± 3.1074	27.855 ± 3.0427
M36 rMSE	33.414 ± 8.1383	24.980 ± 7.0999	23.996 ± 5.2222	24.162 ± 5.9112	24.247 ± 6.0955
M48 rMSE	53.906 ± 14.730	28.256 ± 16.054	26.493 ± 12.132	26.870 ± 11.598	25.241 ± 11.862

Score: TRAILS.B
nMSE	94.882 ± 9.6015	68.077 ± 6.4277	64.789 ± 5.9269	63.707 ± 6.2629	63.604 ± 5.5813
wR	0.3837 ± 0.0509	0.4383 ± 0.0618	0.4845 ± 0.0565	0.4809 ± 0.0669	0.4858 ± 0.0595
BL rMSE	77.907 ± 6.5622	70.051 ± 4.5144	69.947 ± 4.9343	69.032 ± 3.8304	69.154 ± 4.0030
M6 rMSE	83.326 ± 7.1076	74.327 ± 4.2985	72.514 ± 3.4677	71.401 ± 4.4814	71.756 ± 4.9096
M12 rMSE	81.130 ± 8.9465	72.901 ± 6.0166	70.604 ± 5.8510	70.777 ± 6.4053	70.815 ± 5.7209
M24 rMSE	89.969 ± 13.035	77.722 ± 8.9225	73.456 ± 9.3979	73.950 ± 8.5186	73.460 ± 9.2281
M36 rMSE	100.25 ± 21.732	80.934 ± 26.923	78.130 ± 24.536	78.242 ± 27.867	77.639 ± 23.797
M48 rMSE	134.89 ± 29.881	67.923 ± 29.604	68.356 ± 11.968	65.858 ± 24.964	63.491 ± 18.188

Note that the best results are boldfaced. The superscript symbol “” indicates that GFL-SGL significantly outperformed that method on that score. Paired t-test at a level of 0.05 was used.