Supplementary Table 1. Demographic characteristics of the included ADNI subjects. rfmri. MMSE tics (n=907; (n=1092; n long =107.

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1 Supplementary Fig. 1. Assumed disease state (DS) vs aging relationships. In a) the DS increases linearly with age, while in b) it follows a sigmoid relationship with age (as suggested by 1 ). In both cases, the assumed DS values ranged from 1 to 4, with DS=1 (for HC), DS=2 (for EMCI), DS=3 (for LMCI) and DS=4 (for LOAD). Supplementary Fig. 2. Multi-factorial temporal ordering in disease progression, based on the factors-specific abnormality trajectories (temporal abnormalities averaged across all brain regions) and memory deficit. All results were calculated for the HC to LOAD clinical transition, using a sigmoid (rather than linear) relationship between age and disease state. In general, these results are similar to those obtained following a linear relation. However, there are two relevant differences that, in the context of our model (Equation 3), support the preferential use 1

2 of a linear over a sigmoid relationship. First, notice a decrease in vascular, Aβ, metabolic and functional alteration levels around the final period of disease progression. The use of a sigmoid function for DS vs age introduces a strong non-linearity effect on the interaction term (age*ds) of Equation 3, and eventually, for high values of age and DS, a visual degeneration effect on the estimated abnormality trajectories. Notice also that structural abnormalities are now earlier/stronger than functional alterations. In Fig. 3b, we observed that at advanced disease states (around the end of the LMCI phase) the changes in structural biomarkers exceed the functional alterations. The alternative use of a sigmoid function, implying considerably faster changes in disease state with aging, seems to reinforce the previous effect starting from the early ages of the pathologic process. Supplementary Table 1. Demographic characteristics of the included ADNI subjects. Characteris Aβ PET FDG PET ASL rfmri T1 Plasma CSF MMSE tics (n=907; (n=1070; (n=324; (n=164; (n=1092; (n=1063) (n=326) (n=1092; n long =107 n long =168 n long =114 n long =62 n long =494 n long =512 9) 0) 5) 1) 3) 9) Women 396( ( ( ( ( ( ( (44.5 Age (years) 73.2(7.3) 73.4(7.3) 72.8 (7.3) 72.6(7.1 ) 73.4(7.3) 75.1(7.3) 74.9(6.9) 73.4(7.3) APOE e4 (1 copy) 323( ( ( ( ( ( ( (35.4 APOE e4 (2 copies) 85( (9.6 37( ( ( ( ( (9.7) Education (years) 16.2(2.7) 16.0(2.7) 16.2(2.7 1) 16.1(2.6 ) 16.1(2.7) 15.6(3.0) 15.6(3.0) 16.1(2.7) MMSE, mini-mental state examination; Data are number ( or mean (std); N long, samples sizes considering longitudinal measures. 2

3 Supplementary Table 2. LOAD-abnormality indices obtained for the PLASMA proteins. Order Plasma Proteins 1 Interferon gamma Induced Protein 10 (IP-10) Pregnancy-Associated Plasma Protein A Proinsulin-Total (pm) Proinsulin-Intact (pm) Tamm-Horsfall Urinary Glycoprotein (THP) Trefoil Factor 3 (TFF3) CD 40 antigen (CD40) Glutathione S-Transferase alpha (GST-alp) Insulin-like Growth Factor-Binding Insulin (uiu/ml) Thrombomodulin (TM) Resistin Matrix Metalloproteinase-1 (MMP-1) Osteopontin Leptin Vitronectin Neutrophil Gelatinase-Associated Lipocal Apolipoprotein B (Apo B) Receptor for advanced glycosylation end Sex Hormone-Binding Globulin (SHBG) (nmol/l) Eotaxin Tenascin-C (TN-C) Apolipoprotein(a) (Lp(a)) von Willebrand Factor (vwf) Apolipoprotein A-II (Apo A-II) Vascular Endothelial Growth Factor (VEGF) Interleukin-3 (IL-3) Immunoglobulin A (IgA) Chemokine CC-4 (HCC-4) Cancer Antigen 19-9 (CA-19-9) Macrophage Inflammatory Protein-1 alpha Tissue Inhibitor of Metalloproteinases Clusterin (CLU) Intercellular Adhesion Molecule 1 (ICAM Angiotensin-Converting Enzyme (ACE) Brain Natriuretic Peptide (BNP) FASLG Receptor (FAS) Apolipoprotein A-IV (Apo A-IV) Alpha-2-Macroglobulin (A2Macro) Apolipoprotein C-III (Apo C-III) Vascular Cell Adhesion Molecule-1 (VCAM

4 42 AXL Receptor Tyrosine Kinase (AXL) T Lymphocyte-Secreted Protein I-309 (I-3) Carcinoembryonic Antigen (CEA) Angiopoietin-2 (ANG-2) Platelet-Derived Growth Factor BB (PDGF-BB) Kidney Injury Molecule-1 (KIM-1) Immunoglobulin M (IGM) E-Selectin Apolipoprotein E (Apo E) Apolipoprotein H (Apo H) Matrix Metalloproteinase-9- total (MMP-9) C-Reactive Protein (CRP) Stem Cell Factor (SCF) Adiponectin Interleukin-18 (IL-18) Serum Amyloid P-Component (SAP) Epidermal Growth Factor (EGF) Monocyte Chemotactic Protein 4 (MCP-4) Cystatin-C TNF-Related Apoptosis-Inducing Ligand Complement Factor H Fetuin-A Bone Morphogenetic Protein 6 (BMP-6) Pancreatic Polypeptide (PPP) CD40 Ligand (CD40-L) C-peptide Alpha-1-Microglobulin (A1Micro) Ferritin (FRTN) Fatty Acid-Binding Protein- heart (FABP Alpha-1-Antitrypsin (AAT) Fibroblast Growth Factor 4 (FGF-4) Beta-2-Microglobulin (B2M) Macrophage Colony-Stimulating Factor Matrix Metalloproteinase-2 (MMP-2) Interleukin-8 (IL-8) Immunoglobulin E (IgE) Serotransferrin (Transferrin) Apolipoprotein C-I (Apo C-I) Hepatocyte Growth Factor (HGF) Ciliary Neurotrophic Factor (CNTF) Growth-Regulated alpha protein (GRO-alph Tumor Necrosis Factor Receptor-Like Complement C3 (C3) Neuronal Cell Adhesion Molecule (Nr-CAM) Tumor Necrosis Factor alpha (TNF-alpha) Pulmonary and Activation-Regulated Chemo

5 88 Epidermal Growth Factor Receptor (EGFR) Epithelial-Derived Neutrophil-Activating CD5 (CD5L) Prostatic Acid Phosphatase (PAP) Thyroxine-Binding Globulin (TBG) Testosterone- Total Thrombopoietin Monocyte Chemotactic Protein 3 (MCP-3) Interleukin-16 (IL-16) Monokine Induced by Gamma Interferon Angiotensinogen Sortilin Peptide YY (PYY) Transthyretin (TTR) Growth Hormone (GH) Vitamin K-Dependent Protein S (VKDPS) Monocyte Chemotactic Protein 2 (MCP-2) Factor VII Brain-Derived Neurotrophic Factor (BDNF) Macrophage Inflammatory Protein-1 beta Myeloid Progenitor Inhibitory Factor Fibrinogen Plasminogen Activator Inhibitor Matrix Metalloproteinase-9 (MMP-9) Interleukin-6 receptor (IL-6r) Macrophage Migration Inhibitory Factor Apolipoprotein A-I (Apo A-I) Agouti-Related Protein (AGRP) Eotaxin Alpha-Fetoprotein (AFP) Haptoglobin Apolipoprotein D (Apo D) Myeloperoxidase (MPO) B Lymphocyte Chemoattractant (BLC) Macrophage-Derived Chemokine (MDC) Thyroid-Stimulating Hormone (TSH) Chromogranin-A (CgA) Alpha-1-Antichymotrypsin (AACT) Prolactin (PRL) Creatine Kinase-MB (CK-MB) Superoxide Dismutase 1- Soluble (SOD-1) T-Cell-Specific Protein RANTES (RANTES) Myoglobin Matrix Metalloproteinase-10 (MMP-10) Thrombospondin Cortisol

6 134 Thymus-Expressed Chemokine (TECK) Follicle-Stimulating Hormone (FSH) Matrix Metalloproteinase-7 (MMP-7) Placenta Growth Factor (PLGF) Monocyte Chemotactic Protein 1 (MCP-1) Calcitonin Fas Ligand (FasL) Heparin-Binding EGF-Like Growth Factor Macrophage Inflammatory Protein-3 alpha Luteinizing Hormone (LH) Interleukin-13 (IL-13) Betacellulin (BTC) Serum Glutamic Oxaloacetic Transaminase Proteins were sorted according to their total LOAD-abnormality levels ( ). Supplementary Table 3. LOAD-abnormality indices obtained for the CSF proteins. Order CSF Proteins 1 Fatty Acid-Binding Protein, heart (FABP) Cortisol Apolipoprotein(a) (Lp(a)) Tau Prolactin (PRL) ptau TNF-Related Apoptosis-Inducing Ligand Re Chemokine CC-4 (HCC-4) Macrophage Migration Inhibitory Factor Ferritin (FRTN) Serum Glutamic Oxaloacetic Transaminase Follicle-Stimulating Hormone Amyloid-Beta Sortilin Heparin-Binding EGF-Like Growth Factor Alpha-1-Antitrypsin (AAT) CD 40 antigen (CD40) Resistin Angiotensin-Converting Enzyme (ACE) S100 calcium-binding protein B (S100-B) Alpha-2-Macroglobulin (A2Macro) Monokine Induced by Gamma Interferon (MI Vascular Endothelial Growth Factor (VEGF) Tumor Necrosis Factor Receptor 2 (TNFR2) Cancer Antigen 19-9 (CA-19-9) (U/mL)

7 26 Sex Hormone-Binding Globulin (SHBG) Macrophage Colony-Stimulating Factor Neutrophil Gelatinase-Associated Lipocal Placenta Growth Factor (PLGF) Interleukin-6 receptor (IL-6r) N-terminal prohormone of brain natriuret Matrix Metalloproteinase-3 (MMP-3) Interleukin-25 (IL-25) Hepatocyte Growth Factor (HGF) Pregnancy-Associated Plasma Protein A (P (miu/ml) Intercellular Adhesion Molecule 1 (ICAM-1) Chromogranin-A (CgA) Apolipoprotein C-III (Apo C-III) C-Reactive Protein (CRP) Macrophage Inflammatory Protein-1 beta Clusterin (CLU) Stem Cell Factor (SCF) Adiponectin Beta-2-Microglobulin (B2M) Alpha-1-Microglobulin (A1Micro) Tissue Inhibitor of Metalloproteinases Agouti-Related Protein (AGRP) Apolipoprotein A-I (Apo A-I) AXL Receptor Tyrosine Kinase (AXL) Complement C3 (C3) Fibrinogen Pancreatic Polypeptide (PPP) Immunoglobulin A (IgA) Monocyte Chemotactic Protein 2 (MCP-2) Endothelin-1 (ET-1) Trefoil Factor 3 (TFF3) Myoglobin Leptin Osteopontin Tissue Factor (TF) Apolipoprotein H (Apo H) Calcitonin Apolipoprotein E (Apo E) Prostatic Acid Phosphatase (PAP) Interleukin-16 (IL-16) Thyroxine-Binding Globulin (TBG) Thrombomodulin (TM) Lectin-Like Oxidized LDL Receptor Cystatin-C Plasminogen Activator Inhibitor 1 (PAI-1) Fibroblast Growth Factor 4 (FGF-4)

8 72 Angiopoietin-2 (ANG-2) Interferon gamma Induced Protein Vascular Cell Adhesion Molecule-1 (VCAM-1) Interleukin-3 (IL-3) von Willebrand Factor (vwf) Transforming Growth Factor alpha (TGF-al) Serum Amyloid P-Component (SAP) Matrix Metalloproteinase-2 (MMP-2) T Lymphocyte-Secreted Protein I Interleukin-8 (IL-8) Insulin-like Growth Factor-Binding Prote Apolipoprotein D (Apo D) Monocyte Chemotactic Protein 1 (MCP-1) Fas Ligand (FasL) Alpha-Synuclein T-Cell-Specific Protein RANTES (RANTES) Proteins were sorted according to their total LOAD-abnormality levels ( ). Supplementary Note 1. Algorithmic details for model evaluation. Algorithm: 1. Cognitive homogenization of clinical groups: 1.1. For all clinical groups, removal of subjects that presented clinical conversions For each clinical group, removal of subjects that presented a low likelihood (under 10 th percentile) of belonging (cognitively) to the given group. Individual likelihoods were calculated using as reference a multivariate normal distribution defined by the data from the corresponding clinical group. Cognitive evaluations were based on five specific scores known to be sensitive to LOAD progression 2 : the Mini Mental State Examination (MMSE), the Alzheimer s Disease Assessment Scale-cognitive subscales (ADAS11 and ADAS13), the Clinical Dementia Rating Sum of Boxes (CDRSB), and the Rey Auditory Verbal Learning Test (RAVLT30). 2. For each biomarker i (i=1..n bios ), with subjects indexed by j (j=1..n i ): 2.1. Outlier detection, with a significant squared Mahalanobis distance (P < 0.05) meaning an outlier 3. For spatial (neuroimaging) biomarkers, the detection of ourliers was performed only once, based on the multivariate Mahalanobis distances obtained for the corresponding imaging modality, with brain regions defining the multivariate space. 8

9 2.2. Bootstrapping replication r (r=1..n boots ; here N boots =500): Creation of a different data set, considering replacements across subjects. The selected subjects keep their original longitudinal points For each created data set, standardizing the biomarker levels (i.e. centering to have mean 0 and scaling to have standard deviation 1) Models fitting (Equation 3) and model selection (i.e. using the Bayesian Information Criterion to select between the purely fixed effects model, the mixed effects model with different intercepts and fixed slopes, or the mixed effects model with different time intercepts and different slopes) For the fitted fixed effects parameters (Equation 3), averaging the obtained analytic expression by gender, educational level and apoe-e4, from their minimum to their maximum values: ( ) ( ) ( )( )( ). Note that as gender and apoe-e4 are categorical variables, the integration over these factors is equivalent to the sum over all their possible values Generation of multiple characteristic trajectories for each possible aging and clinical transition. For each transition, age and DS changes linearly (or following a sigmoid function; see Supplementary Fig. 1) from their minimum/baseline (age = 40, and DS = 1) to their maximum values (age = 70, and DS = 1, 2, 3 or 4 for a HC to HC, HC to EMCI, HC to LMCI or HC to LOAD transitions, respectively). Each trajectory consists of multiple time points (here 1560 increasing values, i.e. one point for every week) Calculation of the temporal ( ( ) ) and total (,, ) abnormality indexes, using expressions (4) and (5) respectively Calculation of mean and 95 % confidence intervals (CI) for each aging/disease trajectory and their associated abnormality indexes, based on all the bootstrap outcomes. 9

10 3. For spatial (neuroimaging) biomarkers, creation of an average abnormality trajectory across brain regions, weighting each region according to its total (multi-factorial) abnormality level (see Figs. 3b and 4). References 1. Jack, C. R. et al. Tracking pathophysiological processes in Alzheimer s disease: an updated hypothetical model of dynamic biomarkers. Lancet Neurol. 12, (2013). 2. Jedynak, B. M. et al. A computational neurodegenerative disease progression score: Method and results with the Alzheimer s disease neuroimaging initiative cohort. Neuroimage (2012). doi: /j.neuroimage Trujillo-Ortiz, A., Hernandez-Walls, R., Castro-Perez, A. & Barba-Rojo., K. MOUTLIER1:Detection of Outlier in Multivariate Samples Test. A MATLAB file [WWW Doc. (2006). at < 10

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