Quantifying Infinite-Dimensional Data: Functional Data Analysis in Action

Dynamic prediction of survival using multivariate functional principal component analysis: A strict landmarking approach

Dynamically predicting patient survival probabilities using longitudinal measurements has become of great importance with routine data collection becoming more common. Many existing models utilize a multi-step landmarking approach for this problem, mostly due to its ease of use and versatility but unfortunately most fail to do so appropriately. In this article we make use of multivariate functional principal component analysis to summarize the available longitudinal information, and employ a Cox proportional hazards model for prediction. Additionally, we consider a centred functional principal component analysis procedure in an attempt to remove the natural variation incurred by the difference in age of the considered subjects. We formalize the difference between a 'relaxed' landmarking approach where only validation data is landmarked and a 'strict' landmarking approach where both the training and validation data are landmarked. We show that a relaxed landmarking approach fails to effectively use the information contained in the longitudinal outcomes, thereby producing substantially worse prediction accuracy than a strict landmarking approach.

Oxytocin is not associated with postpartum hemorrhage in labor augmentation in a retrospective cohort study in the United States

BACKGROUND

Previous studies reported conflicting results on the relationship between oxytocin use for labor augmentation and the risk of postpartum hemorrhage, probably because it is rather challenging to disentangle oxytocin use from labor dystocia.

OBJECTIVE

This study aimed to investigate the independent association between oxytocin use for augmentation and the risk of postpartum hemorrhage by using advanced statistical modeling to control for labor patterns and other covariates.

STUDY DESIGN

We used data from 20,899 term, cephalic, singleton pregnancies of patients with spontaneous onset of labor and no previous cesarean delivery from Intermountain Healthcare in Utah in the Consortium on Safe Labor. Presence of postpartum hemorrhage was identified on the basis of a clinical diagnosis. Propensity scores were calculated using a generalized linear mixed model for oxytocin use for augmentation, and covariate balancing generalized propensity score was applied to obtain propensity scores for the duration and total dosage of oxytocin augmentation. A weighted generalized additive mixed model was used to depict dose-response curves between the duration and total dosage of oxytocin augmentation and the outcomes. The average treatment effects of oxytocin use for augmentation on postpartum hemorrhage and estimated blood loss (mL) were assessed by inverse probability weighting of propensity scores.

RESULTS

The odds of both postpartum hemorrhage and estimated blood loss increased modestly when the duration and/or total dosage of oxytocin used for augmentation increased. However, in comparison with women for whom oxytocin was not used, oxytocin augmentation was not clinically or statistically significantly associated with estimated blood loss (6.5 mL; 95% confidence interval, 2.5-10.3) or postpartum hemorrhage (adjusted odds ratio, 1.02; 95% confidence interval, 0.82-1.24) when rigorously controlling for labor pattern and potential confounders. The results remained consistent regardless of inclusion of women with an intrapartum cesarean delivery.

CONCLUSION

The odds of postpartum hemorrhage and estimated blood loss increased modestly with increasing duration and total dosage of oxytocin augmentation. However, in comparison with women for whom oxytocin was not used and after controlling for potential confounders, there was no clinically significant association between oxytocin use for augmentation and estimated blood loss or the risk of postpartum hemorrhage.

FTO variation and early frontostriatal brain development in children

OBJECTIVE

Common obesity-associated genetic variants at the fat mass and obesity-associated (FTO) locus have been associated with appetitive behaviors and altered structure and function of frontostriatal brain regions. The authors aimed to investigate the influence of FTO variation on frontostriatal appetite circuits in early life.

METHODS

Data were drawn from RESONANCE, a longitudinal study of early brain development. Growth trajectories of nucleus accumbens and frontal lobe volumes, as well as total gray matter and white matter volume, by risk allele (AA) carrier status on FTO single-nucleotide polymorphism rs9939609 were examined in 228 children (102 female, 126 male) using magnetic resonance imaging assessments obtained from infancy through middle childhood. The authors fit functional concurrent regression models with brain volume outcomes over age as functional responses, and FTO genotype, sex, BMI z score, and maternal education were included as predictors.

RESULTS

Bootstrap pointwise 95% CI for regression coefficient functions in the functional concurrent regression models showed that the AA group versus the group with no risk allele (TT) had greater nucleus accumbens volume (adjusted for total brain volume) in the interval of 750 to 2250 days (2-6 years).

CONCLUSIONS

These findings suggest that common genetic risk for obesity is associated with differences in early development of brain reward circuitry and argue for investigating dynamic relationships among genotype, brain, behavior, and weight throughout development.

Human milk oligosaccharide composition and associations with growth: results from an observational study in the US

Background

Breast milk is the recommended source of nutrients for newborns and infants. Human milk oligosaccharides (HMO) are the third most abundant solid component in human milk and their composition varies during lactation.

Objectives

Our objective was to investigate longitudinal and cross-sectional changes in HMO composition and whether these changes were associated with infant growth up to 24 months of age. Associations with maternal characteristics were also investigated.

Methods

24 HMOs were quantified in samples taken at 2 weeks (n = 107), 6 weeks (n = 97) and 3 months (n = 76), using high performance liquid chromatography. Body length, weight, and head circumference were measured at 8 timepoints, until 24 months. Clusters of breast milk samples, reflecting different HMO profiles, were found through a data-driven approach. Longitudinal associations were investigated using functional principal component analysis (FPCA) and used to characterize patterns in the growth trajectories.

Results

Four clusters of samples with similar HMO composition were derived. Two patterns of growth were identified for length, body weight and head circumference via the FPCA approach, explaining more than 90% of the variance. The first pattern measured general growth while the second corresponded to an initial reduced velocity followed by an increased velocity ("higher velocity"). Higher velocity for weight and height was significantly associated with negative Lewis status. Concentrations of 3'GL, 3FL, 6'GL, DSNLT, LNFP-II, LNFP-III, LNT, LSTb were negatively associated with higher velocity for length.

Conclusion

We introduced novel statistical approaches to establish longitudinal associations between HMOs evolution and growth. Based on our approach we propose that HMOs may act synergistically on children growth. A possible causal relationship should be further tested in pre-clinical and clinical setting.

Associations between daily step count trajectories and clinical outcomes among adults with comorbid obesity and depression

Purpose

To examine the relationship between features of daily measured step count trajectories and clinical outcomes among people with comorbid obesity and depression in the ENGAGE-2 Trial.

Methods

This post hoc analysis used data from the ENGAGE-2 trial where adults (n=106) with comorbid obesity (BMI ≥30.0 or 27.0 if Asian) and depressive symptoms (Patient Health Questionnaire-9 score ≥10) were randomized (2:1) to receive the experimental intervention or usual care. Daily step count trajectories over the first 60 days (Fitbit Alta HR) were characterized using functional principal component analyses. 7-day and 30-day trajectories were also explored. Functional principal component scores that described features of step count trajectories were entered into linear mixed models to predict weight (kg), depression (Symptom Checklist-20), and anxiety (Generalized Anxiety Disorder Questionnaire-7) at 2-months (2M) and 6-months (6M).

Results

Features of 60-day step count trajectories were interpreted as overall sustained high, continuous decline, and disrupted decline. Overall sustained high step count was associated with low anxiety (2M, β=-0.78, p<.05; 6M, β=-0.80, p<.05) and low depressive symptoms (6M, β=-0.15, p<.05). Continuous decline in step count was associated with high weight (2M, β=0.58, p<.05). Disrupted decline was not associated with clinical outcomes at 2M or 6M. Features of 30-day step count trajectories were also associated with weight (2M, 6M), depression (6M), and anxiety (2M, 6M); Features of 7-day step count trajectories were not associated with weight, depression, or anxiety at 2M or 6M.

Conclusions

Features of step count trajectories identified using functional principal component analysis were associated with depression, anxiety, and weight outcomes among adults with comorbid obesity and depression. Functional principal component analysis may be a useful analytic method that leverages daily measured physical activity levels to allow for precise tailoring of future behavioral interventions.

Analysis of Exosomal MicroRNA Dynamics in Response to Rhinovirus Challenge in a Longitudinal Case-Control Study of Asthma

Asthma symptoms are often exacerbated by the common-cold-causing rhinovirus (RV). In this study, we characterized the temporal behavior of circulating exosomal microRNAs (ExoMiRNAs) in a longitudinal bi-phasic case-control study of mild asthmatics (n = 12) and matched non-atopic healthy controls (n = 12) inoculated with rhinovirus. We aimed to define clinical and immunologic characteristics associated with differentially expressed (DE) miRNAs. In total, 26 DE ExoMiRNAs, including hsa-let-7f-5p, hsa-let-7a-5p, hsa-miR-122-5p, hsa-miR-101-3p, and hsa-miR-126-3p, were identified between asthmatic and healthy subjects after inoculation with RV. Time series clustering identified a unique Cluster of Upregulated DE ExoMiRNAs with augmenting mean expression and a distinct Cluster of Downregulated DE ExoMiRNAs with mean expression decline in asthmatic subjects upon RV challenge. Notably, the Upregulated Cluster correlated with Th1 and interferon-induced cytokines/chemokines (IFN-γ and IFN-γ-inducible protein-10) and interleukin-10 (IL-10). Conversely, the Downregulated Cluster correlated with IL-13, a Th2 cytokine, pulmonary function measurements (FVC%, FEV1%, and PEF%), and inflammatory biomarkers (FeNO, eosinophil%, and neutrophil%). Key ExoMiRNA-target gene and anti-viral defense mechanisms of the Upregulated and Downregulated Clusters were identified by network and gene enrichment analyses. Our findings provide insight into the regulatory role of ExoMiRNAs in RV-induced asthma.

The dynamics of ideology drift among U.S. Supreme Court justices: A functional data analysis

We study the U.S. Supreme Court dynamics by analyzing the temporal evolution of the underlying policy positions of the Supreme Court Justices as reflected by their actual voting data, using functional data analysis methods. The proposed fully flexible nonparametric method makes it possible to dissect the time-dynamics of policy positions at the level of individual Justices, as well as providing a comprehensive view of the ideology evolution over the history of Supreme Court since its establishment. In addition to quantifying individual Justice’s policy positions, we uncover average changes over time and also the major patterns of change over time. Additionally, our approach allows for representing highly complex dynamic trajectories by a few principal components which complements other models of analyzing and predicting court behavior.

Classifying pollutant flush signals in stormwater using functional data analysis on TSS MV curves

Pollution levels in stormwater vary significantly during rain events, with pollutant flushes carrying a major fraction of an event pollutant load in a short period. Understanding these flushes is thus essential for stormwater management. However, current studies mainly focus on describing the first flush or are limited by predetermined flush categories. This study provides a new perspective on the topic by applying data-driven approaches to categorise Mass Volume (MV) curves for TSS into distinct classes of flush tailored to specific monitoring location. Functional Data Analysis (FDA) was used to investigate the dynamics of MV curves in two large data sets, consisting of 343 measured events and 915 modelled events, respectively. Potential links between classes of MV curves and combinations of rain characteristics were explored through a priori clustering. This yielded correct class assignments for 23-63% of the events using different combinations of MV curve clustering and rainfall characteristics. This suggests that while global rainfall characteristics influence flush, they are not sufficient as sole explanatory variables of different flush phenomena, and additional explanatory variables are needed to assign MV curves into classes with a predictive power that is suitable for e.g. design of stormwater control measures. Our results highlight the great potential of the FDA methodology as a new approach for classifying, describing, and understanding pollutant flush signals in stormwater.

Quantifying cancer risk from exposures to medical imaging in the Risk of Pediatric and Adolescent Cancer Associated with Medical Imaging (RIC) Study: research methods and cohort profile

PURPOSE

The Risk of Pediatric and Adolescent Cancer Associated with Medical Imaging (RIC) Study is quantifying the association between cumulative radiation exposure from fetal and/or childhood medical imaging and subsequent cancer risk. This manuscript describes the study cohorts and research methods.

METHODS

The RIC Study is a longitudinal study of children in two retrospective cohorts from 6 U.S. healthcare systems and from Ontario, Canada over the period 1995-2017. The fetal-exposure cohort includes children whose mothers were enrolled in the healthcare system during their entire pregnancy and followed to age 20. The childhood-exposure cohort includes children born into the system and followed while continuously enrolled. Imaging utilization was determined using administrative data. Computed tomography (CT) parameters were collected to estimate individualized patient organ dosimetry. Organ dose libraries for average exposures were constructed for radiography, fluoroscopy, and angiography, while diagnostic radiopharmaceutical biokinetic models were applied to estimate organ doses received in nuclear medicine procedures. Cancers were ascertained from local and state/provincial cancer registry linkages.

RESULTS

The fetal-exposure cohort includes 3,474,000 children among whom 6,606 cancers (2394 leukemias) were diagnosed over 37,659,582 person-years; 0.5% had in utero exposure to CT, 4.0% radiography, 0.5% fluoroscopy, 0.04% angiography, 0.2% nuclear medicine. The childhood-exposure cohort includes 3,724,632 children in whom 6,358 cancers (2,372 leukemias) were diagnosed over 36,190,027 person-years; 5.9% were exposed to CT, 61.1% radiography, 6.0% fluoroscopy, 0.4% angiography, 1.5% nuclear medicine.

CONCLUSION

The RIC Study is poised to be the largest study addressing risk of childhood and adolescent cancer associated with ionizing radiation from medical imaging, estimated with individualized patient organ dosimetry.

Computational methods for characterizing and learning from heterogeneous cell signaling data

Heterogeneity in cell signaling pathways is increasingly appreciated as a fundamental feature of cell biology and a driver of clinically relevant disease phenotypes. Understanding the causes of heterogeneity, the cellular mechanisms used to control heterogeneity, and the downstream effects of heterogeneity in single cells are all key obstacles for manipulating cellular populations and treating disease. Recent advances in genetic engineering, including multiplexed fluorescent reporters, have provided unprecedented measurements of signaling heterogeneity, but these vast data sets are often difficult to interpret, necessitating the use of computational techniques to extract meaning from the data. Here, we review recent advances in computational methods for extracting meaning from these novel data streams. In particular, we evaluate how machine learning methods related to dimensionality reduction and classification can identify structure in complex, dynamic datasets, simplifying interpretation. We also discuss how mechanistic models can be merged with heterogeneous data to understand the underlying differences between cells in a population. These methods are still being developed, but the work reviewed here offers useful applications of specific analysis techniques that could enable the translation of single-cell signaling data to actionable biological understanding.

Interpoint-ranking sign covariance for the test of independence

We generalize the sign covariance introduced by Bergsma & Dassios (2014) to multivariate random variables and beyond. The new interpoint-ranking sign covariance is applicable to general types of random objects as long as a meaningful similarity measure can be defined, and it is shown to be zero if and only if the two random variables are independent. The test statistic is a $U$-statistic, whose large-sample behaviour guarantees that the proposed test is consistent against general types of alternatives. Numerical experiments and data analyses demonstrate the superior empirical performance of the proposed method.

Variable selection with P-splines in functional linear regression: Application in graft-versus-host disease

This paper focuses on the problems of estimation and variable selection in the functional linear regression model (FLM) with functional response and scalar covariates. To this end, two different types of regularization (L₁ and L₂ ) are considered in this paper. On the one hand, a sample approach for functional LASSO in terms of basis representation of the sample values of the response variable is proposed. On the other hand, we propose a penalized version of the FLM by introducing a P-spline penalty in the least squares fitting criterion. But our aim is to propose P-splines as a powerful tool simultaneously for variable selection and functional parameters estimation. In that sense, the importance of smoothing the response variable before fitting the model is also studied. In summary, penalized (L₁ and L₂ ) and nonpenalized regression are combined with a presmoothing of the response variable sample curves, based on regression splines or P-splines, providing a total of six approaches to be compared in two simulation schemes. Finally, the most competitive approach is applied to a real data set based on the graft-versus-host disease, which is one of the most frequent complications (30% -50%) in allogeneic hematopoietic stem-cell transplantation.

Longitudinal associations between white matter maturation and cognitive development across early childhood

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.

Quantifying and Visualizing Intraregional Connectivity in Resting-State Functional Magnetic Resonance Imaging with Correlation Densities

The use of correlation densities is introduced to quantify and provide visual interpretation for intraregional functional connectivity in the brain. For each brain region, pairwise correlations are computed between a seed voxel and other gray matter voxels within the region, and the distribution of the ensemble of these correlation values is represented as a probability density, the correlation density. The correlation density can be estimated by kernel smoothing. It provides an intuitive and comprehensive representation of subject-specific functional connectivity strength at the local level for each region. To address the challenge of interpreting and utilizing this rich connectivity information when multiple regions are considered, methods from functional data analysis are implemented, including a recently developed method of dimensionality reduction specifically tailored to the analysis of probability distributions. To illustrate the utility of these methods in neuroimaging, experiments were carried out to identify the associations between local functional connectivity and a battery of neurocognitive scores. These experiments demonstrate that correlation densities facilitate the discovery and interpretation of specific region-score associations.