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Brain growth in early childhood is reflected in the evolution of proportional cerebrospinal fluid volumes (pCSF), grey matter (pGM), and white matter (pWM). We study brain development as reflected in the relative fractions of these three tissues for a cohort of 388 children that were longitudinally followed between the ages of 18 and 96 months. We introduce statistical methodology (Riemannian Principal Analysis through Conditional Expectation, RPACE) that addresses major challenges that are of general interest for the analysis of longitudinal neuroimaging data, including the sparsity of the longitudinal observations over time and the compositional structure of the relative brain volumes. Applying the RPACE methodology, we find that longitudinal growth as reflected by tissue composition differs significantly for children of mothers with higher and lower maternal education levels.

Testing the homogeneity between two samples of functional data is an important task. While this is feasible for intensely measured functional data, we explain why it is challenging for sparsely measured functional data and show what can be done for such data. In particular, we show that testing the marginal homogeneity based on point-wise distributions is feasible under some constraints and propose a new two sample statistic that works well with both intensively and sparsely measured functional data. The proposed test statistic is formulated upon Energy distance, and the critical value is obtained via the permutation test. The convergence rate of the test statistic to its population version is derived along with the consistency of the associated permutation test. To the best of our knowledge, this is the first paper that provides guaranteed consistency for testing the homogeneity for sparse functional data. The aptness of our method is demonstrated on both synthetic and real data sets.

Deep learning has enjoyed tremendous success in a variety of applications but its application to quantile regressions remains scarce. A major advantage of the deep learning approach is its flexibility to model complex data in a more parsimonious way than nonparametric smoothing methods. However, while deep learning brought breakthroughs in prediction, it often lacks interpretability due to the black-box nature of multilayer structure with millions of parameters, hence it is not well suited for statistical inference. In this paper, we leverage the advantages of deep learning to apply it to quantile regression where the goal to produce interpretable results and perform statistical inference. We achieve this by adopting a semiparametric approach based on the partially linear quantile regression model, where covariates of primary interest for statistical inference are modelled linearly and all other covariates are modelled nonparametrically by means of a deep neural network. In addition to the new methodology, we provide theoretical justification for the proposed model by establishing the root-$n$ consistency and asymptotically normality of the parametric coefficient estimator and the minimax optimal convergence rate of the neural nonparametric function estimator. Across several simulated and real data examples, our proposed model empirically produces superior estimates and more accurate predictions than various alternative approaches., Comment: 29 pages, 1 figure

This paper is devoted to the R package JSM which performs joint statistical modeling of survival and longitudinal data. In biomedical studies it has been increasingly common to collect both baseline and longitudinal covariates along with a possibly censored survival time. Instead of analyzing the survival and longitudinal outcomes separately, joint modeling approaches have attracted substantive attention in the recent literature and have been shown to correct biases from separate modeling approaches and enhance information. Most existing approaches adopt a linear mixed effects model for the longitudinal component and the Cox proportional hazards model for the survival component. We extend the Cox model to a more general class of transformation models for the survival process, where the baseline hazard function is completely unspecified leading to semiparametric survival models. We also offer a non-parametric multiplicative random effects model for the longitudinal process in JSM in addition to the linear mixed effects model. In this paper, we present the joint modeling framework that is implemented in JSM, as well as the standard error estimation methods, and illustrate the package with two real data examples: a liver cirrhosis data and a Mayo Clinic primary biliary cirrhosis data.

Early childhood is a period marked by rapid brain growth accompanied by cognitive and motor development. However, it remains unclear how early developmental skills relate to neuroanatomical growth across time with no growth quantile trajectories of typical brain development currently available to place and compare individual neuroanatomical development. Even though longitudinal neuroimaging data have become more common, they are often sparse, making dynamic analyses at subject level a challenging task. Using the Principal Analysis through Conditional Expectation (PACE) approach geared towards sparse longitudinal data, we investigate the evolution of gray matter, white matter and cerebrospinal fluid volumes in a cohort of 446 children between the ages of 1 and 120 months. For each child, we calculate their dynamic age-varying association between the growing brain and scores that assess cognitive functioning, applying the functional varying coefficient model. Using local Fréchet regression, we construct age-varying growth percentiles to reveal the evolution of brain development across the population. To further demonstrate its utility, we apply PACE to predict individual trajectories of brain development.

We apply tools from functional data analysis to model cumulative trajectories of COVID-19 cases across countries, establishing a framework for quantifying and comparing cases and deaths across countries longitudinally. It emerges that a country’s trajectory during an initial first month “priming period” largely determines how the situation unfolds subsequently. We also propose a method for forecasting case counts, which takes advantage of the common, latent information in the entire sample of curves, instead of just the history of a single country. Our framework facilitates to quantify the effects of demographic covariates and social mobility on doubling rates and case fatality rates through a time-varying regression model. Decreased workplace mobility is associated with lower doubling rates with a roughly 2 week delay, and case fatality rates exhibit a positive feedback pattern.

Malnutrition remains a leading contributor to the morbidity and mortality of children under the age of 5 years and can weaken the immune system and increase the severity of concurrent infections. Livestock milk with the protective properties of human milk is a potential therapeutic to modulate intestinal microbiota and improve outcomes. The aim of this study was to develop an infection model of childhood malnutrition in the pig to investigate the clinical, intestinal and microbiota changes associated with malnutrition and enterotoxigenic Escherichia coli (ETEC) infection and to test the ability of goat milk and milk from genetically engineered goats expressing the antimicrobial human lysozyme (hLZ) milk to mitigate these effects. Pigs were weaned onto a protein–energy-restricted diet and after 3 weeks were supplemented daily with goat, hLZ or no milk for a further 2 weeks and then challenged with ETEC. The restricted diet enriched faecal microbiota in Proteobacteria as seen in stunted children. Before infection, hLZ milk supplementation improved barrier function and villous height to a greater extent than goat milk. Both goat and hLZ milk enriched for taxa (Ruminococcaceae) associated with weight gain. Post-ETEC infection, pigs supplemented with hLZ milk weighed more, had improved Z-scores, longer villi and showed more stable bacterial populations during ETEC challenge than both the goat and no milk groups. This model of childhood disease was developed to test the confounding effects of malnutrition and infection and demonstrated the potential use of hLZ goat milk to mitigate the impacts of malnutrition and infection.

The maturation of the myelinated white matter throughout childhood is a critical developmental process that underlies emerging connectivity and brain function. In response to genetic influences and neuronal activities, myelination helps establish the mature neural networks that support cognitive and behavioral skills. The emergence and refinement of brain networks, traditionally investigated using functional imaging data, can also be interrogated using longitudinal structural imaging data. However, few studies of structural network development throughout infancy and early childhood have been presented, likely owing to the sparse and irregular nature of most longitudinal neuroimaging data, which complicates dynamic analysis. Here, we overcome this limitation and investigate through concurrent correlation the co-development of white matter myelination and volume, and structural network development of white matter myelination between brain regions as a function of age, using statistically well-supported methods. We show that the concurrent correlation of white matter myelination and volume is overall positive and reaches a peak at 580days. Brain regions are found to differ in overall magnitudes and patterns of time-varying association throughout early childhood. We introduce time-dynamic developmental networks based on temporal similarity of association patterns in the levels of myelination across brain regions. These networks reflect groups of brain regions that share similar patterns of evolving intra-regional connectivity, as evidenced by levels of myelination, are biologically interpretable and provide novel visualizations of brain development. Comparing the constructed networks between different maternal education groups, we found that children with higher and lower maternal education differ significantly in the overall magnitude of the time-dynamic correlations.

We propose optimal weighting schemes for both mean and covariance estimations for functional data based on local linear smoothing such that the L 2 rate of convergence is minimized. These schemes can self-adjust to the sampling plan and lead to practical improvements.

Background: Diarrheal diseases in infancy and childhood are responsible for substantial morbidity and mortality in developing nations. Lysozyme, an antimicrobial component of human milk, is thought to play a role in establishing a healthy intestinal microbiota and immune system. Consumption of breast milk has been shown to prevent intestinal infections and is a recommended treatment for infants with diarrhea.Objective: This study aimed to examine the ability of lysozyme-rich goat milk to prevent intestinal infection.Methods: Six-week-old Hampshire-Yorkshire pigs were assigned to treatment groups balanced for weight, sex, and litter and were fed milk from nontransgenic control goats (GM group) or human lysozyme transgenic goats (hLZM group) for 2 wk before they were challenged with porcine-specific enterotoxigenic Escherichia coli (ETEC). Fecal consistency, complete blood counts, intestinal histology, and microbial populations were evaluated.Results: Pigs in the hLZM group had less severe diarrhea than did GM pigs at 24 and 48 h after ETEC infection (P = 0.01 and 0.05, respectively), indicating a less severe clinical disease state. Relative to baseline, postmilk hLZM pigs had 19.9% and 137% enrichment in fecal Bacteroidetes (P = 0.028) and Paraprevotellaceae (P = 0.003), respectively, and a 93.8% reduction in Enterobacteriaceae (P = 0.007), whereas GM pigs had a 60.9% decrease in Lactobacillales (P = 0.003) and an 83.3% enrichment in Burkholderiales (P = 0.010). After ETEC infection, hLZM pigs tended to have lower amounts (68.7% less) of fecal Enterobacteriaceae than did GM pigs (P = 0.058). There were 83.1% fewer bacteria translocated into the mesenteric lymph nodes of hLZM pigs than into those of GM pigs (P = 0.039), and hLZM pigs had 34% lower mucin 1 and 61% higher tumor necrosis factor-α expression in the ileum than did GM pigs (P = 0.046 and 0.034, respectively).Conclusion: Results of this study indicate that human lysozyme milk consumption before and during ETEC infection has a positive effect on clinical disease, intestinal mucosa, and gut microbiota in young pigs.

Mount Everest is an extreme environment for humans. Nevertheless, hundreds of mountaineers attempt to summit Everest each year. In a previous study we analyzed interview data for all climbers (2,211) making their first attempt on Everest during 1990-2005. Probabilities of summiting were similar for men and women, declined progressively for climbers about 40 and older, but were elevated for climbers with experience climbing in Nepal. Probabilities of dying were also similar for men and women, increased for climbers about 60 and older (especially for the few that had summited), and were independent of experience. Since 2005, many more climbers (3,620) have attempted Everest. Here our primary goal is to quantify recent patterns of success and death and to evaluate changes over time. Also, we investigate whether patterns relate to key socio-demographic covariates (age, sex, host country, prior experience). Recent climbers were more diverse both in gender (women = 14.6% vs. 9.1% for 1990-2005) and in age (climbers ≥ 40 = 54.1% vs. 38.7%). Strikingly, recent climbers of both sexes were almost twice as likely to summit-and slightly less likely to die-than were comparable climbers in the previous survey. Temporal shifts may reflect improved weather forecasting, installation of fixed ropes on much of the route, and accumulative logistic equipment and experience. We add two new analyses. The probability of dying from illness or non-traumas (e.g., high-altitude illness, hypothermia), relative to dying from falling or from 'objective hazards' (avalanche, rock or ice fall), increased marginally with age. Recent crowding during summit bids was four-fold greater than in the prior sample, but surprisingly crowding has no evident effect on success or death during summit bids. Our results inform prospective climbers as to their current odds of success and of death, as well as inform governments of Nepal and China of the safety consequences and economic impacts of periodically debated restrictions based on climber age and experience.

We consider estimation of mean and covariance functions of functional snippets, which are short segments of functions possibly observed irregularly on an individual specific subinterval that is much shorter than the entire study interval. Estimation of the covariance function for functional snippets is challenging since information for the far off-diagonal regions of the covariance structure is completely missing. We address this difficulty by decomposing the covariance function into a variance function component and a correlation function component. The variance function can be effectively estimated nonparametrically, while the correlation part is modeled parametrically, possibly with an increasing number of parameters, to handle the missing information in the far off-diagonal regions. Both theoretical analysis and numerical simulations suggest that this hybrid strategy % divide-and-conquer strategy is effective. In addition, we propose a new estimator for the variance of measurement errors and analyze its asymptotic properties. This estimator is required for the estimation of the variance function from noisy measurements., Comment: 54 pages, 4 figures; to appear in Journal of the American Statistical Association

Convolutional neural networks (CNNs) are widely used to recognize the user's state through electroencephalography (EEG) signals. In the previous studies, the EEG signals are usually fed into the CNNs in the form of high-dimensional raw data. However, this approach makes it difficult to exploit the brain connectivity information that can be effective in describing the functional brain network and estimating the perceptual state of the user. We introduce a new classification system that utilizes brain connectivity with a CNN and validate its effectiveness via the emotional video classification by using three different types of connectivity measures. Furthermore, two data-driven methods to construct the connectivity matrix are proposed to maximize classification performance. Further analysis reveals that the level of concentration of the brain connectivity related to the emotional property of the target video is correlated with classification performance.

Deep neural networks obtain state-of-the-art performance on a series of tasks. However, they are easily fooled by adding a small adversarial perturbation to the input. The perturbation is often imperceptible to humans on image data. We observe a significant difference in feature attributions between adversarially crafted examples and original examples. Based on this observation, we introduce a new framework to detect adversarial examples through thresholding a scale estimate of feature attribution scores. Furthermore, we extend our method to include multi-layer feature attributions in order to tackle attacks that have mixed confidence levels. As demonstrated in extensive experiments, our method achieves superior performances in distinguishing adversarial examples from popular attack methods on a variety of real data sets compared to state-of-the-art detection methods. In particular, our method is able to detect adversarial examples of mixed confidence levels, and transfer between different attacking methods. We also show that our method achieves competitive performance even when the attacker has complete access to the detector.

Longitudinal genomics data and survival outcome are common in biomedical studies, where the genomics data are often of high dimension. It is of great interest to select informative longitudinal biomarkers (e.g. genes) related to the survival outcome. In this paper, we develop a computationally efficient tool, LCox, for selecting informative biomarkers related to the survival outcome using the longitudinal genomics data. LCox is powerful to detect different forms of dependence between the longitudinal biomarkers and the survival outcome. We show that LCox has improved performance compared to existing methods through extensive simulation studies. In addition, by applying LCox to a dataset of patients with idiopathic pulmonary fibrosis, we are able to identify biologically meaningful genes while all other methods fail to make any discovery. An R package to perform LCox is freely available at https://CRAN.R-project.org/package=LCox.

Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. In this paper, we investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly (and often much) shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed approach allows one to consistently estimate an infinite-rank covariance function from functional snippets. We establish the convergence rates for the proposed estimators and illustrate their finite-sample performance via simulation studies and two data applications., Comment: 51 pages, 10 figures

The aim of this paper is to conduct a systematic and theoretical analysis of estimation and inference for a class of functional mixed effects models (FMEM). Such FMEMs consist of fixed effects that characterize the association between longitudinal functional responses and covariates of interest and random effects that capture the spatial-temporal correlations of longitudinal functional responses. We propose local linear estimates of refined fixed effect functions and establish their weak convergence along with a simultaneous confidence band for each fixed-effect function. We propose a global test for the linear hypotheses of varying coefficient functions and derive the associated asymptotic distribution under the null hypothesis and the asymptotic power under the alternative hypothesis are derived. We also establish the convergence rates of the estimated spatial-temporal covariance operators and their associated eigenvalues and eigenfunctions. We conduct extensive simulations and apply our method to a white-matter fiber data set from a national database for autism research to examine the finite-sample performance of the proposed estimation and inference procedures.

From birth to 5 years of age, brain structure matures and evolves alongside emerging cognitive and behavioral abilities. In relating concurrent cognitive functioning and measures of brain structure, a major challenge that has impeded prior investigation of their time‐dynamic relationships is the sparse and irregular nature of most longitudinal neuroimaging data. We demonstrate how this problem can be addressed by applying functional concurrent regression models (FCRMs) to longitudinal cognitive and neuroimaging data. The application of FCRM in neuroimaging is illustrated with longitudinal neuroimaging and cognitive data acquired from a large cohort (n = 210) of healthy children, 2–48 months of age. Quantifying white matter myelination by using myelin water fraction (MWF) as imaging metric derived from MRI scans, application of this methodology reveals an early period (200–500 days) during which whole brain and regional white matter structure, as quantified by MWF, is positively associated with cognitive ability, while we found no such association for whole brain white matter volume. Adjusting for baseline covariates including socioeconomic status as measured by maternal education (SES‐ME), infant feeding practice, gender, and birth weight further reveals an increasing association between SES‐ME and cognitive development with child age. These results shed new light on the emerging patterns of brain and cognitive development, indicating that FCRM provides a useful tool for investigating these evolving relationships.

In this paper, we investigate frailty models for clustered survival data that are subject to both left- and right-censoring, termed “doubly-censored data”. This model extends current survival literature by broadening the application of frailty models from right-censoring to a more complicated situation with additional left-censoring. ¶ Our approach is motivated by a recent Hepatitis B study where the sample consists of families. We adopt a likelihood approach that aims at the nonparametric maximum likelihood estimators (NPMLE). A new algorithm is proposed, which not only works well for clustered data but also improve over existing algorithm for independent and doubly-censored data, a special case when the frailty variable is a constant equal to one. This special case is well known to be a computational challenge due to the left-censoring feature of the data. The new algorithm not only resolves this challenge but also accommodates the additional frailty variable effectively. ¶ Asymptotic properties of the NPMLE are established along with semi-parametric efficiency of the NPMLE for the finite-dimensional parameters. The consistency of Bootstrap estimators for the standard errors of the NPMLE is also discussed. We conducted some simulations to illustrate the numerical performance and robustness of the proposed algorithm, which is also applied to the Hepatitis B data.

In this article, we present a novel method to obtain both improved estimates and reliable stopping rules for stochastic optimization algorithms such as the Monte Carlo EM (MCEM) algorithm. By characterizing a stationary point, θ*, of the algorithm as the solution to a fixed point equation, we provide a parameter estimation procedure by solving for the fixed point of the update mapping. We investigate various ways to model the update mapping, including the use of a local linear (regression) smoother. This simple approach allows increased stability in estimating the value of θ* as well as providing a natural quantification of the estimation uncertainty. These uncertainty measures can then also be used to construct convergence criteria that reflect the inherent randomness in the algorithm. We establish convergence properties of our modified estimator. In contrast to existing literature, our convergence results do not require the Monte Carlo sample size to go to infinity. Simulation studies are provided to il...

There is a surge in medical follow-up studies that include longitudinal covariates in the modeling of survival data. So far, the focus has been largely on right-censored survival data. We consider survival data that are subject to both left truncation and right censoring. Left truncation is well known to produce biased sample. The sampling bias issue has been resolved in the literature for the case which involves baseline or time-varying covariates that are observable. The problem remains open, however, for the important case where longitudinal covariates are present in survival models. A joint likelihood approach has been shown in the literature to provide an effective way to overcome those difficulties for right-censored data, but this approach faces substantial additional challenges in the presence of left truncation. Here we thus propose an alternative likelihood to overcome these difficulties and show that the regression coefficient in the survival component can be estimated unbiasedly and efficiently. Issues about the bias for the longitudinal component are discussed. The new approach is illustrated numerically through simulations and data from a multi-center AIDS cohort study., Comment: Published in at http://dx.doi.org/10.1214/12-AOS996 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Hypotheses exploring the influence of dietary conditions on the life-history trade-off between survival and reproductive success are extensively tested in female insects but only rarely explored in males. The present study examines the impact of dietary quality and female access on age-specific reproduction and survival of the male Mexican fruit fly Anastrepha ludens Loew (Diptera: Tephritidae). There is a clear cost of female access for males with access to dietary protein, measurable as a decrease in life expectancy, which is further influenced by the age when females are introduced. A protein deficient diet reduces the lifespan benefit of virginity and masks the detrimental effect of female access on male life expectancy. Dietary protein is not necessary for reproductive success, although access to protein at eclosion improves the lifetime reproductive success of males compared to when it is delayed. Overall, reproductive success diminishes as the male flies age, regardless of the dietary conditions, providing evidence for reproductive senescence in males. Delaying the males' access to a protein source fails to influence the negative effect of age on reproductive ability. Because age-specific reproductive rates decline with age, regardless of diet, male fitness does not benefit from lifespan extension. Therefore, males can be expected to allocate available resources towards reproductive effort in favour of an extended lifespan, regardless of mate and protein availability.