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Response to lithium in patients with bipolar disorder is associated with clinical and transdiagnostic genetic factors. The predictive combination of these variables might help clinicians better predict which patients will respond to lithium treatment.
Aims
To use a combination of transdiagnostic genetic and clinical factors to predict lithium response in patients with bipolar disorder.
Method
This study utilised genetic and clinical data (n = 1034) collected as part of the International Consortium on Lithium Genetics (ConLi+Gen) project. Polygenic risk scores (PRS) were computed for schizophrenia and major depressive disorder, and then combined with clinical variables using a cross-validated machine-learning regression approach. Unimodal, multimodal and genetically stratified models were trained and validated using ridge, elastic net and random forest regression on 692 patients with bipolar disorder from ten study sites using leave-site-out cross-validation. All models were then tested on an independent test set of 342 patients. The best performing models were then tested in a classification framework.
Results
The best performing linear model explained 5.1% (P = 0.0001) of variance in lithium response and was composed of clinical variables, PRS variables and interaction terms between them. The best performing non-linear model used only clinical variables and explained 8.1% (P = 0.0001) of variance in lithium response. A priori genomic stratification improved non-linear model performance to 13.7% (P = 0.0001) and improved the binary classification of lithium response. This model stratified patients based on their meta-polygenic loadings for major depressive disorder and schizophrenia and was then trained using clinical data.
Conclusions
Using PRS to first stratify patients genetically and then train machine-learning models with clinical predictors led to large improvements in lithium response prediction. When used with other PRS and biological markers in the future this approach may help inform which patients are most likely to respond to lithium treatment.
Studying phenotypic and genetic characteristics of age at onset (AAO) and polarity at onset (PAO) in bipolar disorder can provide new insights into disease pathology and facilitate the development of screening tools.
Aims
To examine the genetic architecture of AAO and PAO and their association with bipolar disorder disease characteristics.
Method
Genome-wide association studies (GWASs) and polygenic score (PGS) analyses of AAO (n = 12 977) and PAO (n = 6773) were conducted in patients with bipolar disorder from 34 cohorts and a replication sample (n = 2237). The association of onset with disease characteristics was investigated in two of these cohorts.
Results
Earlier AAO was associated with a higher probability of psychotic symptoms, suicidality, lower educational attainment, not living together and fewer episodes. Depressive onset correlated with suicidality and manic onset correlated with delusions and manic episodes. Systematic differences in AAO between cohorts and continents of origin were observed. This was also reflected in single-nucleotide variant-based heritability estimates, with higher heritabilities for stricter onset definitions. Increased PGS for autism spectrum disorder (β = −0.34 years, s.e. = 0.08), major depression (β = −0.34 years, s.e. = 0.08), schizophrenia (β = −0.39 years, s.e. = 0.08), and educational attainment (β = −0.31 years, s.e. = 0.08) were associated with an earlier AAO. The AAO GWAS identified one significant locus, but this finding did not replicate. Neither GWAS nor PGS analyses yielded significant associations with PAO.
Conclusions
AAO and PAO are associated with indicators of bipolar disorder severity. Individuals with an earlier onset show an increased polygenic liability for a broad spectrum of psychiatric traits. Systematic differences in AAO across cohorts, continents and phenotype definitions introduce significant heterogeneity, affecting analyses.
We study relationships between the Nisnevich topology on smooth schemes and certain Grothendieck topologies on proper and not necessarily proper modulus pairs, which were introduced in previous papers. Our results play an important role in the theory of sheaves with transfers on proper modulus pairs.
Serre. In the mean time the fundamental contributions of Grothendieck and Deligne are explained: rationality and the functional equation for L-functions of l-adic sheaves in characteristic p, with essentially complete proofs; the theory of weights; and some theorems of Deligne on the Riemann hypothesis (the last of Weil’s conjectures), this time without proof. Notably, one will find an exposition of functional equations of the L-functions developed by Grothendieck, and a more precise statement and fairly complete parts of the proof of Grothendieck and Deligne’s theorem on the rationality and the functional equation of Hasse–Weil L-functions in characteristic > 0, confirming a conjecture of Serre in this case.
This chapter is dedicated to the Weil conjectures. They are all proven, except the hardest of them: the “Riemann hypothesis”. An overview of Dwork’s p-adic proof of the rationality of zeta functions of varieties over a finite field is given (obtained before the development of Grothendieck’s cohomological methods!).
This last chapter is dedicated to motives and their zeta functions. We consider only an elementary case: that of pure motives of Grothendieck associated to smooth projective varieties over a finite field. One can go much further using the triangulated categories of motives introduced by Voevodsky and developed by Ivorra, Ayoub, and Cisinski–D’eglise, but this would go beyond the scope of the book. Nonetheless, it is explained how this viewpoint considerably clarifies how Weil cohomologies are used to prove rationality and the functional equation, and this theory is applied to prove a somewhat forgotten theorem of Weil: Artin’s conjecture for non-abelian L-functions in positive characteristic.
This chapter returns to more elementary mathematics, introducing Dirichlet, Hecke, and Artin L-functions. A proof of Dirichlet’s theorem on arithmetic progressions is given, by the method expounded by Serre; it would however be a shame to omit Dirichlet’s original method, which gave additional information and anticipated the analytic class number formulae. The two main generalisations of Dirichlet’s L-functions are then introduced: those of Hecke and Artin. Hecke’s main theorem is stated without proof: existence of an analytic continuation and a functional equation, and it is then explained how Artin and Brauer derived the same results for non-abelian L-functions.
This chapter introduces zeta functions of Z-schemes of finite type. It is essentially dedicated to the proof of the Riemann hypothesis for curves over a finite field. An idea of Weil’s proof of the Castelnuovo–Severi inequality is included, and the easy case of curves of genus 1 (due to Hasse) is given. For the general case, the proofs of Mattuck–Tate and Grothendieck, which rely on an a priori weaker inequality, are given; the two inequalities are compared and it is shown that we can recover the first one using the second and the additivity of the numerically trivial divisors.
The amount of mathematics invented for number-theoretic reasons is impressive. It includes much of complex analysis, the re-foundation of algebraic geometry on commutative algebra, group cohomology, homological algebra, and the theory of motives. Zeta and L-functions sit at the meeting point of all these theories and have played a profound role in shaping the evolution of number theory. This book presents a big picture of zeta and L-functions and the complex theories surrounding them, combining standard material with results and perspectives that are not made explicit elsewhere in the literature. Particular attention is paid to the development of the ideas surrounding zeta and L-functions, using quotes from original sources and comments throughout the book, pointing the reader towards the relevant history. Based on an advanced course given at Jussieu in 2013, it is an ideal introduction for graduate students and researchers to this fascinating story.
Longitudinal studies of the relationship between cognition and functioning in bipolar disorder are scarce, although cognition is thought to be a key determinant of functioning. The causal structure between cognition and psychosocial functioning in bipolar disorder is unknown.
Aims
We sought to examine the direction of causality between cognitive performance and functional outcome over 2 years in a large cohort of euthymic patients with bipolar disorder.
Method
The sample consisted of 272 adults diagnosed with bipolar disorder who were euthymic at baseline, 12 and 24 months. All participants were recruited via the FondaMental Advanced Centers of Expertise in Bipolar Disorders. We used a battery of tests, assessing six domains of cognition at baseline and 24 months. Residual depressive symptoms and psychosocial functioning were measured at baseline and 12 and 24 months. The possible causal structure between cognition and psychosocial functioning was investigated with cross-lagged panel models with residual depressive symptoms as a covariate.
Results
The analyses support a causal model in which cognition moderately predicts and is causally primary to functional outcome 1 year later, whereas psychosocial functioning does not predict later cognitive performance. Subthreshold depressive symptoms concurrently affected functioning at each time of measure.
Conclusions
Our results are compatible with an upward causal effect of cognition on functional outcome in euthymic patients with bipolar disorder. Neuropsychological assessment may help specify individual prognoses. Further studies are warranted to confirm this causal link and evaluate cognitive remediation, before or simultaneously with functional remediation, as an intervention to improve functional outcome.