Stability of singular spectrum analysis and causality in time series

The concept of causality has been widely studied in econometrics and statistics since 1969, when C. J. Granger published his paper "Investigating causal relations by econometric models and cross-spectral methods". The intuitive basis for his definition of causality is the following: time series Y is causing time series X if the use of the additional information provided by Y improves the forecast of series X. In the present thesis we focus on combining Granger's causality concept with the Singular Spectrum Analysis (SSA) technique. SSA is founded on the idea of transforming the time series into a multidimensional trajectory form (Hankel matrices), Singular Value Decomposition with subsequent projection to a lower-dimensional subspace and diagonal averaging. The main aim of the present thesis is to study the causality concept through SSA prism in details and suggest a novel causality measure, which can be used outside the stationary autoregressive class, which is the framework for Granger's original causality concept. We first apply standard statistical tests directly to simulated data to assess the improvement of forecast quality of bivariate multidimensional SSA (MSSA) of time series X and Y compared with SSA of time series X only. Although the results of performance of these tests are reasonably conclusive, the simulation method is time consuming and, thus, more theoretical understanding is desirable. We solve a fundamental scaling problem of the MSSA approach by introducing so-called linearized MSSA. The linearized MSSA approach shows a way towards a causality measure, calculated from the forecast linear recurrence formula (LRF) coefficients. We finally analyze SSA and (non-linear) bivariate MSSA approach in terms of first order stability analysis under perturbations leading to the construction of a valid suitable measure of causality. The construction of the measure requires some simplifying assumptions in the stability analysis whose validity we verify for both simulated and real data

Rare coding variants in PLCG2, ABI3, and TREM2 implicate microglial-mediated innate immunity in Alzheimer's disease

We identified rare coding variants associated with Alzheimer’s disease (AD) in a 3-stage case-control study of 85,133 subjects. In stage 1, 34,174 samples were genotyped using a whole-exome microarray. In stage 2, we tested associated variants (P<1×10-4) in 35,962 independent samples using de novo genotyping and imputed genotypes. In stage 3, an additional 14,997 samples were used to test the most significant stage 2 associations (P<5×10-8) using imputed genotypes. We observed 3 novel genome-wide significant (GWS) AD associated non-synonymous variants; a protective variant in PLCG2 (rs72824905/p.P522R, P=5.38×10-10, OR=0.68, MAFcases=0.0059, MAFcontrols=0.0093), a risk variant in ABI3 (rs616338/p.S209F, P=4.56×10-10, OR=1.43, MAFcases=0.011, MAFcontrols=0.008), and a novel GWS variant in TREM2 (rs143332484/p.R62H, P=1.55×10-14, OR=1.67, MAFcases=0.0143, MAFcontrols=0.0089), a known AD susceptibility gene. These protein-coding changes are in genes highly expressed in microglia and highlight an immune-related protein-protein interaction network enriched for previously identified AD risk genes. These genetic findings provide additional evidence that the microglia-mediated innate immune response contributes directly to AD development

Rare Functional Variant in TM2D3 is Associated with Late-Onset Alzheimer's Disease

We performed an exome-wide association analysis in 1393 late-onset Alzheimer's disease (LOAD) cases and 8141 controls from the CHARGE consortium. We found that a rare variant (P155L) in TM2D3 was enriched in Icelanders (similar to 0.5% versus <0.05% in other European populations). In 433 LOAD cases and 3903 controls from the Icelandic AGES substudy, P155L was associated with increased risk and earlier onset of LOAD [odds ratio (95% CI) = 7.5 (3.5-15.9), p = 6.6x10(-9)]. Mutation in the Drosophila TM2D3 homolog, almondex, causes a phenotype similar to loss of Notch/Presenilin signaling. Human TM2D3 is capable of rescuing these phenotypes, but this activity is abolished by P155L, establishing it as a functionally damaging allele. Our results establish a rare TM2D3 variant in association with LOAD susceptibility, and together with prior work suggests possible links to the beta-amyloid cascade.Peer reviewe

A novel Alzheimer disease locus located near the gene encoding tau protein

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordAPOE ε4, the most significant genetic risk factor for Alzheimer disease (AD), may mask effects of other loci. We re-analyzed genome-wide association study (GWAS) data from the International Genomics of Alzheimer's Project (IGAP) Consortium in APOE ε4+ (10 352 cases and 9207 controls) and APOE ε4- (7184 cases and 26 968 controls) subgroups as well as in the total sample testing for interaction between a single-nucleotide polymorphism (SNP) and APOE ε4 status. Suggestive associations (P<1 × 10-4) in stage 1 were evaluated in an independent sample (stage 2) containing 4203 subjects (APOE ε4+: 1250 cases and 536 controls; APOE ε4-: 718 cases and 1699 controls). Among APOE ε4- subjects, novel genome-wide significant (GWS) association was observed with 17 SNPs (all between KANSL1 and LRRC37A on chromosome 17 near MAPT) in a meta-analysis of the stage 1 and stage 2 data sets (best SNP, rs2732703, P=5·8 × 10-9). Conditional analysis revealed that rs2732703 accounted for association signals in the entire 100-kilobase region that includes MAPT. Except for previously identified AD loci showing stronger association in APOE ε4+ subjects (CR1 and CLU) or APOE ε4- subjects (MS4A6A/MS4A4A/MS4A6E), no other SNPs were significantly associated with AD in a specific APOE genotype subgroup. In addition, the finding in the stage 1 sample that AD risk is significantly influenced by the interaction of APOE with rs1595014 in TMEM106B (P=1·6 × 10-7) is noteworthy, because TMEM106B variants have previously been associated with risk of frontotemporal dementia. Expression quantitative trait locus analysis revealed that rs113986870, one of the GWS SNPs near rs2732703, is significantly associated with four KANSL1 probes that target transcription of the first translated exon and an untranslated exon in hippocampus (P≤1.3 × 10-8), frontal cortex (P≤1.3 × 10-9) and temporal cortex (P≤1.2 × 10-11). Rs113986870 is also strongly associated with a MAPT probe that targets transcription of alternatively spliced exon 3 in frontal cortex (P=9.2 × 10-6) and temporal cortex (P=2.6 × 10-6). Our APOE-stratified GWAS is the first to show GWS association for AD with SNPs in the chromosome 17q21.31 region. Replication of this finding in independent samples is needed to verify that SNPs in this region have significantly stronger effects on AD risk in persons lacking APOE ε4 compared with persons carrying this allele, and if this is found to hold, further examination of this region and studies aimed at deciphering the mechanism(s) are warranted

Common polygenic variation enhances risk prediction for Alzheimer's disease.

Background: The identification of subjects at high risk for Alzheimer’s disease is important for prognosis and early intervention. We investigated the polygenic architecture of Alzheimer’s disease (AD) and the accuracy of AD prediction models, including and excluding the polygenic component in the model. Methods: This study used genotype data from the powerful dataset comprising 17,008 cases and 37,154 controls obtained from the International Genomics of Alzheimer’s Project (IGAP). Polygenic score analysis tested whether the alleles identified to associate with disease in one sample set were significantly enriched in the cases relative to the controls in an independent sample. The disease prediction accuracy was investigated by means of sensitivity, specificity, Area Under the receiver operating characteristic Curve (AUC) and positive predictive value (PPV). Results: We observed significant evidence for a polygenic component enriched in Alzheimer’s disease (p=4.9x10-26). This enrichment remained significant after APOE and other genome-wide associated regions were excluded (p=3.4x10 19). The best prediction accuracy AUC=78% was achieved by a logistic regression model with APOE, the polygenic score as predictors and age. When looking at the genetic component only, the PPV was 81%, increasing to 82% when age was added as a predictor. Setting the total normalised polygenic score of greater than 0.91, the positive predictive value has reached 90%. Conclusion: Polygenic score has strong predictive utility of Alzheimer’s disease risk and is a valuable research tool in experimental designs, e.g. for selecting Alzheimer’s disease patients into clinical trials