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Sex differences in the human brain emerge as early as mid-gestation and have been linked to sex hormones, particularly testosterone. Here, we analyzed the influence of markers of early sex hormone exposure (polygenic risk score (PRS) for testosterone, salivary testosterone, number of CAG repeats, digit ratios, and PRS for estradiol) on the growth pattern of cortical surface area in a longitudinal cohort of 722 infants. We found PRS for testosterone and right-hand digit ratio to be significantly associated with surface area, but only in females. PRS for testosterone at the most stringent P value threshold was positively associated with surface area development over time. Higher right-hand digit ratio, which is indicative of low prenatal testosterone levels, was negatively related to surface area in females. The current work suggests that variation in testosterone levels during both the prenatal and postnatal period may contribute to cortical surface area development in female infants.

The white matter (WM) connectome is important for cognitive development and intelligence and is altered in neuropsychiatric illnesses. Little is known about how the WM connectome develops or its relationship to IQ in early childhood.The development of node centrality in the WM connectome was studied in a longitudinal cohort of 226 (123 female) children from the University of North Carolina (UNC) Early Brain Development Study. Structural and diffusion weighted images were acquired after birth and at 1, 2, 4 and 6 years and IQ was assessed at 6 years. Eigenvector centrality, betweenness centrality, and the global graph metrics of global efficiency, small worldness and modularity were determined at each age.The greatest developmental change in eigenvector centrality and betweenness centrality occurred in the first year of life with relative stability between ages 1 and 6 years. Most of the high centrality hubs at age 6 were also high centrality hubs at 1 year, and many were already high centrality hubs at birth. There were generally small but significant changes in global efficiency and modularity from birth to 6 years, while small worldness increased between 2 and 4 years. Individual node centrality was not significantly correlated with IQ at 6 years.Node centrality in the WM connectome is established very early in childhood and is relatively stable from age 1 to 6 years. Many high centrality hubs are established before birth and most are present by age 1.

Background Increased volume of extra-axial cerebrospinal fluid (EA-CSF) is associated with autism spectrum disorder diagnosis in young children. However, little is known about EA-CSF development in typically developing (TD) children or in children at risk for schizophrenia (SCZHR). Methods 3T magnetic resonance imaging scans were obtained in TD children (n = 105) and in SCZHR children (n = 38) at 1 and 2 years of age. EA-CSF volume and several measures of brain structure were generated, including global tissue volumes, cortical thickness, and surface area. Cognitive and motor abilities at 1 and 2 years of age were assessed using the Mullen Scales of Early Learning. Results In the TD children, EA-CSF volume was positively associated with total brain volume, gray and white matter volumes, and total surface area at 1 and 2 years of age. In contrast, EA-CSF volume was negatively associated with average cortical thickness. Lower motor ability was associated with increased EA-CSF volume at 1 year of age. EA-CSF was not significantly increased in SCZHR children compared with TD children. Conclusions EA-CSF volume is positively associated with overall brain size and cortical surface area but negatively associated with cortical thickness. Increased EA-CSF is associated with delayed motor development at 1 year of age, similar to studies of children at risk for autism, suggesting that increased EA-CSF may be an early biomarker of abnormal brain development in infancy. Infants in the SCZHR group did not exhibit significantly increased EA-CSF, suggesting that increased EA-CSF could be specific to neurodevelopmental disorders with an earlier onset, such as autism.

Genetic influences on cortical thickness (CT) and surface area (SA) are known to vary across the life span. Little is known about the extent to which genetic factors influence CT and SA in infancy and toddlerhood. We performed the first longitudinal assessment of genetic influences on variation in CT and SA in 501 twins who were aged 0–2 years. We observed substantial additive genetic influences on both average CT (0.48 in neonates, 0.37 in 1-year-olds, and 0.44 in 2-year-olds) and total SA (0.59 in neonates, 0.74 in 1-year-olds, and 0.73 in 2-year-olds). In addition, we found strong heritability of the change in average CT (0.49) from neonates to 1-year-olds, but not from 1- to 2–year-olds. Moreover, we found strong genetic correlations for average CT (rG = 0.92) between 1- and 2-year-olds and strong genetic correlations for total SA across all timepoints (rG = 0.96 between neonates and 1-year-olds, rG = 1 between 1- and 2-year-olds). In addition, we found CT and SA are strongly genetic correlated at birth, but weaken over time. Overall, results suggest a dynamic genetic relationship between CT and SA during first 2 years of life and provide novel insights into how genetic influences shape the cortical structure during early brain development.

Functional magnetic resonance imaging has been used to identify complex brain networks by examining the correlation of blood-oxygen-level-dependent signals between brain regions during the resting state. Many of the brain networks identified in adults are detectable at birth, but genetic and environmental influences governing connectivity within and between these networks in early infancy have yet to be explored. We investigated genetic influences on neonatal resting-state connectivity phenotypes by generating intraclass correlations and performing mixed effects modeling to estimate narrow-sense heritability on measures of within network and between-network connectivity in a large cohort of neonate twins. We also used backwards elimination regression and mixed linear modeling to identify specific demographic and medical history variables influencing within and between network connectivity in a large cohort of typically developing twins and singletons. Of the 36 connectivity phenotypes examined, only 6 showed narrow-sense heritability estimates greater than 0.10, with none being statistically significant. Demographic and obstetric history variables contributed to between- and within-network connectivity. Our results suggest that in early infancy, genetic factors minimally influence brain connectivity. However, specific demographic and medical history variables, such as gestational age at birth and maternal psychiatric history, may influence resting-state connectivity measures.

Cortical structure has been consistently related to cognitive abilities in children and adults, yet we know little about how the cortex develops to support emergent cognition in infancy and toddlerhood when cortical thickness (CT) and surface area (SA) are maturing rapidly. In this report, we assessed how regional and global measures of CT and SA in a sample (N = 487) of healthy neonates, 1-year-olds, and 2-year-olds related to motor, language, visual reception, and general cognitive ability. We report novel findings that thicker cortices at ages 1 and 2 and larger SA at birth, age 1, and age 2 confer a cognitive advantage in infancy and toddlerhood. While several expected brain–cognition relationships were observed, overlapping cortical regions were also implicated across cognitive domains, suggesting that infancy marks a period of plasticity and refinement in cortical structure to support burgeoning motor, language, and cognitive abilities. CT may be a particularly important morphological indicator of ability, but its impact on cognition is relatively weak when compared with gestational age and maternal education. Findings suggest that prenatal and early postnatal cortical developments are important for cognition in infants and toddlers but should be considered in relation to other child and demographic factors.

Significance Environmental and genetic risk factors, and the early antecedents of schizophrenia, represent pieces of a puzzle still far from completion. We show that, in infants with a history of prenatal complications, a measure of genomic risk for schizophrenia linked with placental gene expression is associated with early neurodevelopmental trajectories of risk, particularly in male individuals. While the majority of individuals on this altered neurodevelopmental path likely “canalize” back toward normal development, some may not be rescued and instead “decanalize” toward illness. Specific strategies of prevention may benefit from understanding the unique placental effects of schizophrenia genomic risk and from defining which factors contribute to decanalize the neurodevelopmental trajectories of individuals with a history of risk factors who develop schizophrenia., Tracing the early paths leading to developmental disorders is critical for prevention. In previous work, we detected an interaction between genomic risk scores for schizophrenia (GRSs) and early-life complications (ELCs), so that the liability of the disorder explained by genomic risk was higher in the presence of a history of ELCs, compared with its absence. This interaction was specifically driven by loci harboring genes highly expressed in placentae from normal and complicated pregnancies [G. Ursini et al., Nat. Med. 24, 792–801 (2018)]. Here, we analyze whether fractionated genomic risk scores for schizophrenia and other developmental disorders and traits, based on placental gene-expression loci (PlacGRSs), are linked with early neurodevelopmental outcomes in individuals with a history of ELCs. We found that schizophrenia’s PlacGRSs are negatively associated with neonatal brain volume in singletons and offspring of multiple pregnancies and, in singletons, with cognitive development at 1 y and, less strongly, at 2 y, when cognitive scores become more sensitive to other factors. These negative associations are stronger in males, found only with GRSs fractionated by placental gene expression, and not found in PlacGRSs for other developmental disorders and traits. The relationship of PlacGRSs with brain volume persists as an anlage of placenta biology in adults with schizophrenia, again selectively in males. Higher placental genomic risk for schizophrenia, in the presence of ELCs and particularly in males, alters early brain growth and function, defining a potentially reversible neurodevelopmental path of risk that may be unique to schizophrenia.

Highlights • Heatmaps quantify degrees of developmental changes in functional connectivity. • More changes are observed in the first than second postnatal year, driven by girls. • Most change is observed from ages 2–4 compared with any other age span. • Limbic and subcortical areas show more changes than primary sensory regions. • Consistent trajectories of functional connectivity are found across validations., Different functional networks exhibit distinct longitudinal trajectories throughout development, but the timeline of the dynamics of functional connectivity across the whole brain remains to be elucidated. Here we used resting-state fMRI to investigate the development of voxel-level changes in functional connectivity across the first six years of life. Globally, we found that developmental changes in functional connectivity are nonlinear with more changes during the first postnatal year than the second, followed by most significant changes from ages 2–4 and from ages 4–6. However, the overall global difference observed between the first and second year appears to have been driven by girls. Limbic and subcortical areas consistently demonstrated the most substantial changes, whereas primary sensory areas were the most stable. These patterns were consistent in full-term and preterm subgroups. Validation on randomly divided subsamples as well as in an independent cross-sectional sample revealed global patterns consistent with the main results. Overall, the derived developmental heatmaps reveal novel dynamics underlying functional circuit development during the first 6 years of life.

BACKGROUND: Subdural hemorrhage (SDH) is thought to have a benign course in asymptomatic neonates. However, effects on neurodevelopmental outcomes have not been established. PURPOSE: To evaluate neurodevelopmental outcomes, gray matter volumes, and MRI findings in asymptomatic neonates with SDH compared with control neonates. MATERIALS AND METHODS: This retrospective analysis was conducted between 2003 and 2016 and was based on data from the University of North Carolina Early Brain Development Study. Neurodevelopmental outcomes were evaluated at 2 years of age by using the Mullen Scales of Early Learning (MSEL). All infants were imaged with 3.0-T MRI machines and were evaluated for SDH at baseline (neonates) and at ages 1 and 2 years. Volumetric MRI for brain segmentation was performed at ages 1 and 2 years. A secondary analysis was performed in neonates matched 1:1 with control neonates. Differences in categorical variables were measured by using the Fisher exact test, and the t test was used for continuous variables. RESULTS: A total of 311 neonates (mean gestational age ± standard deviation, 39.3 weeks ± 1.5), including 57 with SDH (mean gestational age, 39.5 weeks ± 1.2), were evaluated. The subgroup included 55 neonates with SDH (mean gestational age, 39.6 weeks ± 1.2) and 55 matched control neonates (mean gestational age, 39.7 weeks ± 1.2). Fifty-five of 57 neonates with SDH (97%; 95% CI: 92, 100) were delivered vaginally compared with 157 of 254 control neonates (62%, 95% CI: 56, 68; P < .001). Otherwise, there were no differences in perinatal, maternal, or obstetric parameters. There were no differences in composite MSEL scores (115 ± 15 and 109 ± 16 at 2 years, respectively; P = .05) or gray matter volumes between the neonatal SDH group and control neonates (730 cm(3) ± 85 and 742 cm(3) ± 76 at 2 years, respectively; P = .70). There was no evidence of rebleeding at follow-up MRI. CONCLUSION: Neurodevelopmental scores and gray matter volumes at age 2 years did not differ between asymptomatic neonates with subdural hemorrhage and control neonates. © RSNA, 2020 Online supplemental material is available for this article.

The hippocampus is a key limbic region involved in higher-order cognitive processes including learning and memory. Although both typical and atypical functional connectivity patterns of the hippocampus have been well-studied in adults, the developmental trajectory of hippocampal connectivity during infancy and how it relates to later working memory performance remains to be elucidated. Here we used resting state fMRI (rsfMRI) during natural sleep to examine the longitudinal development of hippocampal functional connectivity using a large cohort (N = 202) of infants at 3 weeks (neonate), 1 year, and 2 years of age. Next, we used multivariate modeling to investigate the relationship between both cross-sectional and longitudinal growth in hippocampal connectivity and 4-year working memory outcome. Results showed robust local functional connectivity of the hippocampus in neonates with nearby limbic and subcortical regions, with dramatic maturation and increasing connectivity with key default mode network (DMN) regions resulting in adult-like topology of the hippocampal functional connectivity by the end of the first year. This pattern was stabilized and further consolidated by 2 years of age. Importantly, cross-sectional and longitudinal measures of hippocampal connectivity in the first year predicted subsequent behavioral measures of working memory at 4 years of age. Taken together, our findings provide insight into the development of hippocampal functional circuits underlying working memory during this early critical period.

The presence of heterogeneity/subgroups in infants and older populations against single-domain brain or behavioral measures has been previously characterized. However, few attempts have been made to explore heterogeneity at the brain–behavior relationship level. Such a hypothesis posits that different subgroups of infants may possess qualitatively different brain–behavior relationships that could ultimately contribute to divergent developmental outcomes even with relatively similar brain phenotypes. In this study, we aimed to explore such relationship-level heterogeneity and delineate the subgrouping structure of newborns with differential brain–behavior associations based on a typically developing sample of 81 infants with 3-week resting-state functional magnetic resonance imaging scans and 4-year intelligence quotient (IQ) measures. Our results not only confirmed the existence of relationship-level heterogeneity in newborns but also revealed divergent developmental outcomes associated with two subgroups showing similar brain functional connectivity but contrasting brain–behavior relationships. Importantly, further analyses unveiled an intriguing pattern that the subgroup with higher 4-year IQ outcomes possessed brain–behavior relationships that were congruent to their functional connectivity pattern in neonates while the subgroup with lower 4-year IQ not, providing potential explanations for the observed IQ differences. The characterization of heterogeneity at the brain–behavior relationship level may not only improve our understanding of the patterned intersubject variability during infancy but could also pave the way for future development of heterogeneity-inspired, personalized, subgroup-specific models for better prediction.

Background Defining reliable brain markers for the prediction of abnormal behavioral outcomes remains an urgent but extremely challenging task in neuroscience research. This is particularly important for infant studies given the most dramatic brain and behavioral growth during infancy. Methods In this study, we proposed a novel prediction scheme through abstracting individual newborn's whole‐brain functional connectivity pattern to three outlier measures (Triple O) and tested the hypothesis that neonates identified as “brain outliers” based on Triple O were more likely to develop as IQ outliers at 4 years of age. Without need for training with behavioral data, Triple O represents a novel proof‐of‐concept approach to predict later IQ outcomes based on neonatal brain data. Results Triple O correctly identified 42.1% true IQ outliers among a mixed cohort of 175 newborns with different term, twin, and maternal disorder statuses. Triple O also reached a high level of specificity (96.2%) and overall accuracy (90.3%). Further incorporating a demographic information indicator, the enhanced Triple O+ could further differentiate between high and low 4YR IQ outliers. Validation tests against seven independent reference samples revealed highly consistent results and a minimum sample size of ~50 for robust performance. Conclusions Considering that postnatal brain growth and various environmental factors likely also contribute to 4YR IQ, the fact that Triple O, based purely on neonatal functional connectivity data, could identify >40% of 4YR IQ outliers is striking. Together with the very high level of specificity, each outlier predicted by Triple O represents a meaningful risk but future efforts are needed to explore ways to identify the rest of outliers. Overall, with no need for training, a high level of robustness, and a minimal requirement on sample size, the proposed Triple O approach demonstrates great potential to predict later outlying IQ performances using neonatal functional connectivity data., One of the most desired goals of developmental research is to be able to predict childhood behavioral outcomes based on brain biomarkers as early as possible to facilitate in‐time intervention. However, this problem is notoriously challenging, partly due to the complex nature of brain function and reportedly weak brain–behavioral relationships. In this study, we derived a simple, training‐free prediction scheme to abstract the neonatal whole‐brain functional connectivity pattern to three outlier measures (Triple O) and showed that it could identify over forty percent of 4‐year IQ performance outliers with a high level of robustness against different reference samples. Results in this study represent a first step in this novel direction of brain outlier‐based prediction of later behavioral outcomes.

OBJECTIVE To examine the early cognitive, temperament, and adaptive functioning of infants and toddlers with Turner syndrome (TS). METHODS Cognitive abilities were measured using the Mullen Scales of Early Learning at 1 year of age for 31 girls with TS and compared with neurotypical female (N = 53) and male (N = 54) control groups. Temperament (Carey Toddler Temperament Scales) and adaptive functioning (Vineland Adaptive Behavior Scales-Second Edition) were measured at 1 year of age and compared with normative data. An exploratory analysis of cognitive/developmental trajectories was also conducted comparing age 12-month to 24-month time points for 22 TS subjects. RESULTS Infants with TS performed largely within the average range for adaptive behavior, temperament, and early cognitive development with some increased risk for delays in language and significant increased risk for delays in motor skills (p < 0.001). Although exploratory, there was some suggestion of slower rates of progression in fine-motor and visual reception skills from 12 to 24 months of age. CONCLUSIONS Infants and toddlers with TS exhibit a relatively positive neurodevelopmental profile overall, with some indication of an increasing gap in function in fine-motor and visual perceptual abilities as compared to neurotypical peers. It is unclear whether these apparent differences represent normal variability in this very young population or, perhaps, are early precursors of later phenotypic characteristics of TS in the school-age and young adult years.

Background Individual differences in cortical gray matter (GM) structure are associated with cognitive function and psychiatric disorders with developmental origins. Identifying when individual differences in cortical structure are established in childhood is critical for understanding the timing of abnormal cortical development associated with neuropsychiatric disorders. Methods We studied the development of cortical GM and white matter volume, cortical thickness, and surface area using structural magnetic resonance imaging in two unique cohorts of singleton (121 male and 131 female) and twin (99 male and 83 female) children imaged longitudinally from birth to 6 years. Results Cortical GM volume increases rapidly in the first year of life, with more gradual growth thereafter. Between ages 1 and 6 years, total surface area expands 29%, while average cortical thickness decreases about 3.5%. In both cohorts, a large portion of individual variation in cortical GM volume (81%–87%) and total surface area (73%–83%) at age 6 years is present by age 1 year. Regional heterogeneity of cortical thickness observed at age 6 is largely in place at age 1. Conclusions These findings indicate that individual differences in cortical GM structure are largely established by the end of the first year of life, following a period of rapid postnatal GM growth. This suggests that alterations in GM structure associated with psychiatric disorders with developmental origins may largely arise in the first year of life and that interventions to normalize or mitigate abnormal GM development may need to be targeted to very early childhood.

White matter (WM) integrity has been related to cognitive ability in adults and children, but it remains largely unknown how WM maturation in early life supports emergent cognition. The associations between tract-based measures of fractional anisotropy (FA) and axial and radial diffusivity (AD, RD) shortly after birth, at age 1, and at age 2 and cognitive measures at 1 and 2 years were investigated in 447 healthy infants. We found that generally higher FA and lower AD and RD across many WM tracts in the first year of life were associated with better performance on measures of general cognitive ability, motor, language, and visual reception skills at ages 1 and 2, suggesting an important role for the overall organization, myelination, and microstructural properties of fiber pathways in emergent cognition. RD in particular was consistently related to ability, and protracted development of RD from ages 1 to 2 years in several tracts was associated with higher cognitive scores and better language performance, suggesting prolonged plasticity may confer cognitive benefits during the second year of life. However, we also found that cognition at age 2 was weakly associated with WM properties across infancy in comparison to child and demographic factors including gestational age and maternal education. Our findings suggest that early postnatal WM integrity across the brain is important for infant cognition, though its role in cognitive development should be considered alongside child and demographic factors.

Intelligence is an important individual difference factor related to mental health, academic achievement, and life success, yet there is a lack of research into its early cognitive predictors. This study investigated the predictive value of infant developmental assessment scores for school-age intelligence in a large, heterogeneous sample of single- and twin-born subjects (N = 521). We found that Early Learning Composite (ELC) scores from the Mullen Scales of Early Learning have similar predictive power to that of other infant tests. ELC scores at age 2 were predictive of Stanford-Binet abbreviated intelligence (ABIQ) scores at age 6 (r = 0.46) even after controlling for sex, gestation number, and parental education. ELC scores at age 1 were less predictive of 6-year ABIQ scores (r = 0.17). When the sample was split to test robustness of findings, we found that results from the full sample replicated in a subset of children born at ≥32 weeks gestation without birth complications (n = 405), though infant cognitive scores did not predict IQ in a subset born very prematurely or with birth complications (n = 116). Scores at age 2 in twins and singletons showed similar predictive ability for scores at age 6, though twins had particularly high correlations between ELC at age 1 and ABIQ at age 6.

Turner syndrome (TS) is a genetic disorder affecting approximately 1:2000 live-born females. It results from partial or complete X monosomy and is associated with a range of clinical issues including a unique cognitive profile and increased risk for certain behavioral problems. Structural neuroimaging studies in adolescents, adults, and older children with TS have revealed altered neuroanatomy but are unable to identify when in development differences arise. In addition, older children and adults have often been exposed to years of growth hormone and/or exogenous estrogen therapy with potential implications for neurodevelopment. The study presented here is the first to test whether brain structure is altered in infants with TS. Twenty-six infants with TS received high-resolution structural MRI scans of the brain at 1 year of age and were compared to 47 typically developing female and 39 typically developing male infants. Results indicate that the typical neuroanatomical profile seen in older individuals with TS, characterized by decreased gray matter volumes in premotor, somatosensory, and parietal-occipital cortex, is already present at 1 year of age, suggesting a stable phenotype with origins in the prenatal or early postnatal period.

BACKGROUND: Schizophrenia is considered a neurodevelopmental disorder with a pathophysiology that likely begins long before the onset of clinical symptoms. White matter abnormalities have been observed in schizophrenia and we hypothesized that the first 2 years of life is a period in which white matter abnormalities associated with schizophrenia risk may emerge. METHODS: 38 infants at high risk for schizophrenia and 202 healthy controls underwent diffusion tensor MRIs after birth and at 1 and 2 years of age. Quantitative tractography was used to determine diffusion properties (fractional anisotropy(FA), axial diffusivity(AD), and radial diffusivity(RD)) of 18 white matter tracts and a general linear model was used to analyze group differences at each age. RESULTS: Adjusting gestational age at birth, postnatal age at MRI, gender, MRI scanner type, and maternal education, neonates at high risk had significantly lower FA (p=0.02) and AD (p=0.03) in the superior segment of the left cingulate, and higher RD in the hippocampal segment of the left cingulate (p=0.04). High risk one year olds had significantly lower FA (p

The aim of this propensity-matched cohort study was to evaluate the impact of prenatal SSRI exposure and a history of maternal depression on neonatal brain volumes and white matter microstructure. SSRI-exposed neonates (n = 27) were matched to children of mothers with no history of depression or SSRI use (n=54). Additionally, neonates of mothers with a history of depression, but no prenatal SSRI exposure (n=41), were matched to children of mothers with no history of depression or SSRI use (n=82). Structural magnetic resonance imaging and diffusion weighted imaging scans were acquired with a 3T Siemens Allegra scanner. Global tissue volumes were characterized using an automatic, atlas-moderated expectation maximization segmentation tool. Local differences in gray matter volumes were examined using deformation-based morphometry. Quantitative tractography was performed using an adaptation of the UNC-Utah NA-MIC DTI framework. SSRI-exposed neonates exhibited widespread changes in white matter microstructure compared to matched controls. Children exposed to a history of maternal depression but no SSRIs showed no significant differences in brain development compared to matched controls. No significant differences were found in global or regional tissue volumes. Additional research is needed to clarify whether SSRIs directly alter white matter development or whether this relationship is mediated by depressive symptoms during pregnancy.

In oncology clinical trials, progression-free survival (PFS), generally defined as the time from randomization until disease progression or death, has been a key endpoint to support licensing approval. In the U.S. Food and Drug Administration guidance for industry, May 2007, concerning the PFS as the primary or co-primary clinical trial endpoint, it is recommended to have tumor assessments verified by an independent review committee blinded to study treatments, especially in open-label studies. It is considered reassuring about the lack of reader-evaluation bias if treatment effect estimates from the investigators' and independent review committees' evaluations agree. The agreement between these evaluations may vary for subjects with short or long PFS, while there exist no such statistical quantities that can completely account for this temporal pattern of agreements. Therefore, in this paper, we propose a new method to assess temporal agreement between two time-to-event endpoints, while the two event times are assumed to have a positive probability of being identical. This method measures agreement in terms of the two event times being identical at a given time or both being greater than a given time. Overall scores of agreement over a period of time are also proposed. We propose a maximum likelihood estimation to infer the proposed agreement measures using empirical data, accounting for different censoring mechanisms, including reader's censoring (event from one reader dependently censored by event from the other reader). The proposed method is demonstrated to perform well in small samples via extensive simulation studies and is illustrated through a head and neck cancer trial.

Background Currently, most attempts at early identification and intervention for individuals at risk for schizophrenia focus on the prodromal phase of the illness during adolescence. However, cognitive and other deficits likely arise well before the prodromal phase. Many risk genes for schizophrenia play a role in early brain development, and recent studies indicate that the basic structural and functional networks of the brain are in place by the second year of life. This suggests that schizophrenia likely has origins in prenatal and early childhood brain development, and that early identification and intervention may need to be shifted to this developmental period to have a real impact on the incidence and severity of schizophrenia. Methods We studied early childhood brain development 25 children of mothers with schizophrenia and 178 control children. Children had a 3T MRI after birth and at 1 and 2 years of age, and global tissue volumes (gray matter, white matter, CSF), ventricle volumes, and cortical thickness and surface area were determined. Children were also assessed with the Mullen Scales of Early Learning at 1 and 2 years. Results Children at risk for schizophrenia had significantly lower Mullen Composite scores at both age 1 (p=0.0078) and 2 years (p=0.0001) compared to control children. Reductions were present in fine motor, expressive and receptive language scales at both ages. Overall, high-risk children did not differ from controls in global tissue volumes, though there was evidence of a gender effect. Female high-risk children tended to have reduced gray matter volumes after birth and at age 1 year (significant reduction after birth, p =0.018), while males tended have increased gray matter volumes at age 1 and 2 years (significant at 1 year, p = 0.037). Cortical thickness and surface area results tended to reflect the gray matter volume findings. Females had regions of significant cortical surface area reduction after birth, while males had several regions of significant of cortical surface area expansion at 1 year. Males had a few regions of significant changes of cortical thickness after birth. Discussion In the context of its limitations, this study confirms previous studies that find alterations of very early childhood development in children at risk for schizophrenia. It also indicates that alterations of cortical gray matter are evident in very early childhood, and that there is a gender difference in these alterations, with females having reduced gray matter volumes and males having increased gray matter volumes. Brain structure and cognitive abnormalities associated with risk for schizophrenia are present shortly after birth; future studies may be able to identify very early biomarkers of risk that will not only improve our understanding of how brain abnormalities associated with schizophrenia develop, but also define periods of childhood development that can be targeted with early intervention.

Summary The paper develops a general regression framework for the analysis of manifold-valued response in a Riemannian symmetric space (RSS) and its association with multiple covariates of interest, such as age or gender, in Euclidean space. Such RSS-valued data arise frequently in medical imaging, surface modelling and computer vision, among many other fields. We develop an intrinsic regression model solely based on an intrinsic conditional moment assumption, avoiding specifying any parametric distribution in RSS. We propose various link functions to map from the Euclidean space of multiple covariates to the RSS of responses. We develop a two-stage procedure to calculate the parameter estimates and determine their asymptotic distributions. We construct the Wald and geodesic test statistics to test hypotheses of unknown parameters. We systematically investigate the geometric invariant property of these estimates and test statistics. Simulation studies and a real data analysis are used to evaluate the finite sample properties of our methods.

We propose a new concept of very weak solutions to Euler's equations. We show global existence of such solutions.

In oncology clinical trials, progression-free survival (PFS), generally defined as the time from randomization until disease progression or death, has been a key endpoint to support licensing approval. In the U.S. Food and Drug Administration guidance for industry, May 2007, concerning the PFS as the primary or co-primary clinical trial endpoint, it is recommended to have tumor assessments verified by an independent review committee blinded to study treatments, especially in open-label studies. It is considered reassuring about the lack of reader-evaluation bias if treatment effect estimates from the investigators' and independent review committees' evaluations agree. The agreement between these evaluations may vary for subjects with short or long PFS, while there exist no such statistical quantities that can completely account for this temporal pattern of agreements. Therefore, in this paper, we propose a new method to assess temporal agreement between two time-to-event endpoints, while the two event times are assumed to have a positive probability of being identical. This method measures agreement in terms of the two event times being identical at a given time or both being greater than a given time. Overall scores of agreement over a period of time are also proposed. We propose a maximum likelihood estimation to infer the proposed agreement measures using empirical data, accounting for different censoring mechanisms, including reader's censoring (event from one reader dependently censored by event from the other reader). The proposed method is demonstrated to perform well in small samples via extensive simulation studies and is illustrated through a head and neck cancer trial.

A detailed study of solutions to the first-order partial differential equation $H(x,y,z_x,z_y)=0$, with special emphasis on the eikonal equation $z_x^2+z_y^2=h(x,y)$, is made near points where the equation becomes singular in the sense that $dH=0$, in which case the method of characteristics does not apply. The main results are that there is a strong lack of uniqueness of solutions near such points and that solutions can be less regular than both the function $H$ and the initial data of the problem, but that this loss of regularity only occurs along a pair of curves through the singular point. The main tools are symplectic geometry and the Sternberg normal form for Hamiltonian vector fields.

A detailed study of solutions to the rst order partial dier- ential equation H(x;y;zx;zy) = 0, with special emphasis on the eikonal equation z 2 + z 2 y = h(x;y), is made near points where the equation be- comes singular in the sense that dH = 0, in which case the method of characteristics does not apply. The main results are that there is a strong lack of uniqueness of solutions near such points and that solutions can be less regular than both the function H and the initial data of the problem, but that this loss of regularity only occurs along a pair of curves through the singular point. The main tools are symplectic geometry and the Sternberg normal form for Hamiltonian vector elds.