Identification of novel cortical surface biomarkers for predicting cognitive outcomes based on group-level `2,1 norm

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1 Identification of novel cortical surface biomarkers for predicting cognitive outcomes based on group-level `2,1 norm Jingwen Yan 1,2, Taiyong Li 1,3, Hua Wang 4, Heng Huang 4,?, Jing Wan 1,5, Kwangsik Nho 1, Sungeun Kim 1, Shannon L. Risacher 1, Andrew J. Saykin 1, and Li Shen 1,2,5,?, for the Alzheimer s Disease Neuroimaging Initiative?? 1 Radiology and Imaging Sciences, Indiana University School of Medicine, IN, USA 2 School of Informatics, Indiana University Indianapolis, IN, USA 3 Economic Info. Eng., Southwestern Univ. of Finance & Economics, Chengdu, China 4 Computer Science and Engineering, University of Texas at Arlington, TX, USA 5 Computer and Information Science, Purdue University Indianapolis, IN, USA Abstract. Regression models have been widely studied to investigate whether neuroimaging measures can be used as predictive biomarkers for inferring cognitive outcomes in the study of Alzheimer s Disease (AD). Most of these models ignore the interrelated structures either within neuroimaging measures or between cognitive outcomes, and thus may have limited power to yield optimal solutions. To address this issue, we propose to employ a new sparse multi-task learning model called G-SMuRFS, and demonstrate its e ectiveness by examining the predictive power of detailed cortical thickness measures towards the TRAILS cognitive scores in a large cohort. G-SMuRFS proposes a group-level `2,1 norm strategy to achieve two goals: (1) group relevant surface features together in an anatomically meaningful manner and use this prior knowledge to guide the learning process; and (2) take into account the correlation among cognitive outcomes for building a more appropriate predictive model. In our empirical study, compared with linear, ridge and multi-task `2,1 norm regression, G-SMuRFS not only demonstrates a superior and more stable predictive performance, but also identifies a small set of surface markers that are biologically meaningful. Applications of G-SMuRFS to other biomarker studies in AD would be promising future directions.? Correspondence to Li Shen (shenli@iupui.edu) or Heng Huang (heng@uta.edu).?? Data used in preparation of this article were obtained from the Alzheimer s Disease Neuroimaging Initiative (ADNI) database (adni.loni.ucla.edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at: to apply/adni Acknowledgement List.pdf. L. Wang, P. Yushkevich and S. Ourselin (Eds.): MICCAI 212 Workshop on Novel Imaging Biomarkers for Alzheimer s Disease and Related Disorders (NIBAD 12), p. 27, 212. Copyright held by author/owner(s).

2 28 Yan et al. 1 Introduction The large-scale imaging and biomarker data of the Alzhiemer s Disease Neuroimaging Initiative (ADNI) cohort has been publicly available and has provided great opportunities for people to develop advanced computational methods for better understanding of the underlying neurodegenerative mechanism in relation to cognitive decline in AD. For example, using the ADNI data, many regression models have been employed to investigate the relationships between multi-modal imaging measures and cognitive scores [7, 9, 12]. Most of these models have used summary statistics (e.g., average intensity) of each region of interest (ROI) as input features. While voxel-based measures may provide more information than ROI summary statistics, standard voxel-based methods often do not make use of (1) the ROI information and (2) the spatial correlation between voxels. To address this issue, we propose to employ a new sparse multi-task learning model called G-SMuRFS [8] for identifying surface biomarkers that can predict cognitive outcomes. We demonstrate its e ectiveness by examining the predictive power of detailed cortical thickness measures towards the TRAILS cognitive scores in the ADNI cohort. G-SMuRFS proposes a group-level `2,1 norm strategy to achieve three goals: (1) group relevant surface features together in an anatomically meaningful manner (i.e., ROI information is incorporated) and use this prior knowledge to guide the learning process (i.e., spatial correlation within each ROI is addressed); (2) take into account the correlation among cognitive outcomes for building a more appropriate predictive model (i.e., multiple correlated cognitive scores are predicted together); and (3) optimize the selection of cognition-relevant surface biomarkers while maintaining high prediction accuracy. Our overarching goal is to examine and validate the predictive power of cortical thickness measures towards cognitive outcomes while considering the group structures defined by anatomically meaningful ROIs. The results may provide important information about potential surrogate biomarkers for early detection and/or therapeutic trials in AD. 2 Materials and Methods 2.1 Neuroimaging and Cognition Data All the data used in the preparation of this article were obtained from the Alzheimer s Disease Neuroimaging Initiative (ADNI) database (adni.loni.ucla.edu) [1]. One goal of ADNI has been to test whether serial magnetic resonance imaging (MRI), positron emission tomography (PET), other biological markers, and clinical and neuropsychological assessment can be combined to measure the progression of mild cognitive impairment (MCI) and early Alzheimer s disease (AD). For up-to-date information, we refer interested readers to We downloaded the baseline 1.5 T magnetic resonance imaging (MRI) scans, demographic information, baseline diagnosis and cognitive scores from the Trail making test (TRAILS) for all the ADNI participants. For each participant, FreeSurfer V4, an automatic brain segmentation and cortical parcellation tool,

3 Novel Cortical Surface Biomarkers for Predicting Cognitive Outcomes 29 Table 1. Participant characteristics Category HC MCI AD Number of Subjects Gender (M/F) 17/9 224/125 94/78 Handedness (R/L) 183/14 316/33 16/12 Baseline Age (years, mean±sd) 76.2±5. 75.± ±7.5 Education (years, mean±sd) 16.2± ± ±3.1 was applied to automatically label cortical and subcortical tissue classes [1, 2] and to extract thickness measures of 34 cortical ROIs. Following a previous imaging genetics study [5], in this work, we concentrated our analyses on the Caucasian subjects determined by population stratification analysis using the ADNI genetics data [4]. 719 out of 745 Caucasian participants with no missing MRI morphometric and the TRAILS information were included in the study. The 719 participants were categorized by three baseline diagnostic groups: healthy control (HC, n=197), MCI (n=349), and AD (n=172). Demographics information of these subjects can be found in Table G-SMuRFS Throughout this section, we write matrices as boldface uppercase letters and vectors as boldface lowercase letters. Given a matrix M =(m ij ), its i-th row and j-th column are denoted as m i and m j respectively. The Frobenius norm and `2,1 -norm (also called as `1,2 -norm) of a matrix are defined as M F = pp i mi 2 2 and M 2,1 = P i q P j m2 ij = P i mi 2,respectively. This study is centered on multi-task learning paradigm, where multimodal imaging measures are used to predict one or more cognitive outcomes. Let {x 1,, x n } < d be imaging measures and {y 1,, y n } < c cognitive outcomes, where n is the number of samples, d is the number of predictors (feature dimensionality) and c is the number of response variables (tasks). Let X =[x 1,...,x n ] and Y =[y 1,...,y n ]. To investigate the correlation between imaging measures and cognitive outcomes, linear and ridge regression are two standard methods. While linear regression (least square) can easily get overfitted and therefore cannot achieve the optimal regression, ridge regression have one more regularization term, the Frobenius norm of trained weights, to successfully solve the problem and ascertain the numerical stability simultaneously (Eq. (1)). min W WT X Y 2 F + W 2 F, (1) Yet other drawbacks still greatly limit the application of ridge regression in disease study. While non-sparse regression weight brought by Frobenius norm makes the results hard to interpret, isolation of multi-task training apparently have ignored the interconnection among multiple cognitive outcomes.

4 21 Yan et al. vertex1 vertex2 vertex 3, = vertex 4 vertex 5 =, ( ) vertex n1 vertex n2 vertex n3 W superior frontal superior parietal inferior parietal Fig. 1. Illustration of the G-SMuRFS method. Two regularization terms, group `2,1- norm ( W G2,1 )and`2,1-norm ( W 2,1), were integrated to group surface vertices by ROIs and to jointly select prominent vertices across all cognitive scores. `2,1 norm is one of the advanced techniques that addresses both these two issues, by enforcing an `2-norm across the tasks and an `1-norm across the features (Eq. (2)). While the `2-norm ascertains the similarity pattern across the tasks, the `1 norm ascertains the sparsity across the features. min W WT X Y 2 F + W 2,1. (2) In all the above methods, imaging features were all treated separately, where the underlying brain structures were not taken into account. In many cases, different brain structures may be responsible for di erent brain functions. Therefore it would be much more meaningful to include the structural information in the regression procedure. G-SMuRFS (Group-Sparse Multi-task Regression and Feature Selection) [8], a newly proposed regression model derived from the `2,1 norm, takes into account the group information in the regression procedure and has yielded promising results in a previous imaging genetics study [8]. In this work, we apply this algorithm to group all the vertices within each surface ROI together and incorporate the anatomical boundary information into the regression procedure. As illustrated in Fig. 1, this method can be applied to address this issue by grouping cortical vertices using ROI boundary information (i.e., group `2,1 -norm, or G 2,1 -norm), where cortical measures from the same ROI are hypothesized to have similar predictive powers. On the other hand, the `2,1 -norm can help select imaging features that can predict all or most of the cognitive outcomes. As a result, the learned regression model and the selected cortical biomarkers should be more biologically meaningful and more informative. Mainly motivated by sparse learning, such as Lasso [6] and group Lasso [11], the new regularization term was applied in G-SMuRFS to consider both the

5 Novel Cortical Surface Biomarkers for Predicting Cognitive Outcomes 211 group sparsity through the G 2,1 -norm and the individual biomarker sparsity for joint learning via an `2,1 -norm regularization [3]. In the objective function Eq. (3), while the second term couples all the regression coe cients of a group of features across all the c tasks together, the third term penalizes all c regression coe cient of each individual feature as whole to select features across multiple learning tasks. min W nx W T X Y F + 1 W G2,1 + 2 W 2,1. (3) i=1 Solution of the objective function Eq. (3) can be obtained through an iterative optimization procedure. By setting the derivative with respect to W to zero, W can be solved as in Eq. (4). W =(XX T + 1 D + 2 D) 1 XY T, (4) 1 where D is a block diagonal matrix with the k-th diagonal block as 2kW k k F I k, I k is an identity matrix with size of m k, m k is the total feature numbers included 1 in group k, D is a diagonal matrix with the i-th diagonal element as 2kw i k 2. Detailed optimization procedure and algorithm can be found in [8]. Generally, the advantage of this model is three-fold: (1) It addresses the highly correlated nature of the cortical vertices within each surface ROI. (2) It takes into account the correlation of multiple scores of the same cognitive function test. (3) It achieves both the global biomarker sparsity as well as ROI group sparsity. 3 Experimental Results and Discussion In this study, we examined all the cortical thickness measures across 34 brain surface ROIs regarding their power for predicting the TRAILS cognitive scores. For the e ciency purpose, we down-sampled the raw data generated from Freesurfer to about 63 vertices. Excluding the regions labeled as unknown, totally 66 vertices were included in the experiments. The response variables in our multivariate multiple regression task included the following three cognitive scores: trail making A score (TRAILSA), trail making B score (TRAILSB), and TRAILSB- TRAILSA (TR(B-A)). To provide an unbiased estimate of the prediction performance of each method tested in the experiments, we employed five-fold crossvalidation, where each fold contains the same portion of AD, MCI and HC participants. Root Mean Square Error (RMSE) between the predicted values and actual values of all the test subjects was used to compare the prediction performances across di erent methods. In order to examine the prediction power of the top selected features, we extracted 3 subsets by varying the number of top vertices (from 1 to 15). Prediction performance, measured by RMSE, of these subsets under four di erent regression models is shown in Fig. 2. Obviously no matter how many top features were extracted, the prediction performance using those features selected

6 212 Yan et al. Root Mean Square Error 1 9 x 1 4 Linear Ridge L2,1 norm G SMuRFS Number of Selected Vertices Fig. 2. Performance comparison of linear regression, ridge regression, `2,1 norm, and G- SMuRFS: Cross-validation performance measured by root mean square error (RMSE) is plotted against the number of top vertices used in the regression analysis. by G-SMuRFS is much higher (i.e., lower RMSE) than that of linear, ridge and `2,1 norm regression models. Particularly, as the number of top features increases, performance of all the other three models become much worse. In contrast, the performance of G-SMuRFS shows an improving trend with a decreasing RMSE and finally converges to be flat. This suggests that G-SMuRFS has a potential to include informative biomarkers rather than noisy ones along the process. The RMSEs of G-SMuRFS show a trend to be flat. This demonstrates the global structured sparsity among vertices achieved by G-SMuRFS, where only a limited number of biomarkers are selected to be important. Most surface measures have very low weights and could only result in very limited influences on the final prediction performance. Fig. 3 shows the histogram of regression weights associated with all the cortical measures for each method. While, in ridge and linear regression models, most surface measures share relatively similar impact on the prediction performance, G-SMuRFS and `2,1 norm present a much better sparsity across all the cortical vertices. Despite `2,1 norm yielded the sparsest result, G-SMuRFS outperformed it in the overall prediction performance. Besides the sparsity at the cortical vertex level, we also examined the group sparsity of all four models at the ROI level. Fig. 4 shows the histogram of high impact (i.e., top 1) cortical markers against each of the 34 ROIs for (a) G-SMuRFS, (b) `2,1 -norm, (c) ridge regression and (d) linear regression respectively. Obviously high impact biomarkers identified through `2,1 -norm, ridge regression, and linear regression scattered across a large portion of cortical surface

7 Novel Cortical Surface Biomarkers for Predicting Cognitive Outcomes 213 (a) G SMuRFS 3 (b) L2,1 norm 3 3 (c) Ridge 3 (d) Linear Regression weight.1.1 Regression weight.1.1 Regression weight.1.1 Regression weight Fig. 3. Histogram of regression weights associated with all cortical measures. From left to right: G-SMuRFS, `2,1 norm, ridge regression and linear regression. regions, making the result hard to interpret. Only G-SMuRFS yielded sparse patterns at the ROI level that are potentially more interpretable. Shown in Fig. 5 is the averages of top 1 negative and positive weights within each cortical ROI respectively, and these weights have been generated by applying G-SMuRFS to the study data. The surface biomarkers identified yielded promising patterns that are expected based on prior knowledge on neuroimaging and cognition. TRAILS measures a combination of visual, motor and executive functions; and thus we have identified post central gyri, precentral gyri as the major sensory-motor cortex, superior frontal gyri, supramarginal gyri, precuneus, superior parietal gyri, fusiform gyri and superior temporal gyri. As shown in Fig. 5, there is heterogeneity in each identified region. We observe both strong negative and positive weights in the same ROI, rather than a homogeneous region as we have previously hypothesized. If this pattern is true, the traditional methods by using average thickness measures for biomarker research may be inadequate. Further investigation needs to be done to confirm this finding. To sum up, our empirical results are very encouraging and have demonstrated the promise of the proposed G-SMuRFS method in the application of relating cortical morphology to cognitive outcome: (1) G-SMuRFS regression model outperformed linear regression and ridge regression as well as the multi-task `2,1 norm model in terms of overall RMSE (Fig. 2). (2) The biomarkers identified by the G-SMuRFS method were much sparser at the vertex level than linear regression and ridge regression, and yielded a much more stable performance for predicting cognitive scores. (3) Both G-SMuRFS and `2,1 methods yielded sparse results at the vertex level (Fig. 3), however the G-SMuRFS model presented a much higher prediction performance (Fig. 2) as well as a much sparser pattern at the ROI level (Fig. 4)) than the `2,1 norm model. (4) The average value of top 1 negative weights and that of top 1 positive weights (Fig. 5) indicate that the interior of many ROIs with high predictive power may not be homogenous,

8 214 Yan et al. (a) G SMuRFS 3 1 (b) L2,1 norm 1 (c) Ridge 1 (d) Linear Surface ROIs Surface ROIs Surface ROIs Surface ROIs Fig. 4. Number of high impact (i.e., top 1) cortical markers is plotted against the corresponding ROI (34 ROIs in total). From Left to right: G-SMuRFS, `2,1 norm, ridge regression and linear regression. because most of them demonstrated both strong negative and positive e ects. Refined partition of these cortical regions warrants further investigation. 4 Conclusion We have investigated the power of detailed cortical thickness measurements for predicting TRAILS cognitive scores using the data from the ADNI cohort. We have proposed to employ a newly developed sparse multi-task learning algorithm called G-SMuRFS, and have observed the following strengths of this approach that could greatly improve the prediction performance: (1) seamless integration of anatomical knowledge in the learning process by coupling cortical measures from the same ROI together; (2) sparsity at both vertex level and ROI level; and (3) multitask learning scheme for addressing correlation among response variables. Compared to Linear, ridge and `2,1 norm regression, combining the group `2,1 norm in the regularization term has not only helped select the potential biomarkers in a few ROIs, but also improved overall predictive power. Furthermore, G-SMuRFS has shown a potential capability of inhibiting the noise, resulting in a relatively flat predictive performance while including additional features. Therefore, its application to multi-modal imaging data would be promising future directions for biomarker discovery and better mechanistic understanding in AD research. The heterogeneity of the identified patterns in the same ROI warrants further investigation. Replication in independent large samples will be important

9 Novel Cortical Surface Biomarkers for Predicting Cognitive Outcomes 215 Fig. 5. Average weight of top markers (measured by the absolute weight value) mapped onto the cortical surface. Each ROI is color-mapped by the average weight of top 1 markers. Left: Top 1 positive markers; Right: Top 1 negative markers. to confirm the findings. Spatial restriction may be included in the future development to identify cluster-based biomarkers. Multiple layer groups, similar as in group Lasso, could also become an interesting future direction. Another possible future topic could be to investigate whether nonlinear models can help improve the prediction rates as well as derive biologically meaningful results. Acknowledgement This research was supported by NSF IIS , NIH UL1 RR25761, U1 AG2494, NIA RC2 AG36535, NIA R1 AG19771, and NIA P3 AG S1 at IU; and by NSF CCF-8378, CCF , DMS , and IIS at UTA. Data collection and sharing for this project was funded by the Alzheimer s Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U1 AG2494). ADNI is funded by the National Institute on Aging, the National Institute of Biomedical Imaging and Bioengineering, and through generous contributions from the following: Abbott; Alzheimers Association; Alzheimers Drug Discovery Foundation; Amorfix Life Sciences Ltd.; AstraZeneca; Bayer HealthCare; BioClinica, Inc.; Biogen Idec Inc.; Bristol-Myers Squibb Company; Eisai Inc.; Elan Pharmaceuticals Inc.; Eli Lilly and Company; F. Ho mann-la Roche Ltd and its a liated company Genentech, Inc.; GE Healthcare; Innogenetics, N.V.; IXICO Ltd.; Janssen Alzheimer Immunotherapy Research & Development, LLC.; Johnson & Johnson Pharmaceutical Research & Development LLC.; Medpace, Inc.; Merck & Co., Inc.; Meso Scale Diagnostics, LLC.; Novartis Pharmaceuticals Corporation; Pfizer Inc.; Servier; Synarc Inc.; and Takeda Pharmaceutical Company. The Canadian Institutes of Health Research is providing funds to support ADNI clinical sites in Canada. Private sector contributions are facilitated by the Foundation for the National Institutes of Health

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