Recovering gradients from sparsely observed functional data

Growth dynamics and heritability for plant high-throughput phenotyping studies using hierarchical functional data analysis

In modern high-throughput plant phenotyping, images of plants of different genotypes are repeatedly taken throughout the growing season, and phenotypic traits of plants (e.g., plant height) are extracted through image processing. It is of interest to recover whole trait trajectories and their derivatives at both genotype and plant levels based on observations made at irregular discrete time points. We propose to model trait trajectories using hierarchical functional principal component analysis (HFPCA) and show that the problem of recovering derivatives of the trajectories is reduced to estimating derivatives of eigenfunctions, which is solved by differentiating eigenequations. Based on HFPCA, we also propose a new measure for the broad-sense heritability by allowing it to vary over time during plant growth. Simulation studies show that the proposed procedure performs better than its competitors in terms of recovering both trait trajectories and their derivatives. Interesting characteristics of plant growth and heritability dynamics are revealed in the application to a modern plant phenotyping study.

BAYESIAN ANALYSIS OF INFANT'S GROWTH DYNAMICS WITH IN UTERO EXPOSURE TO ENVIRONMENTAL TOXICANTS

Early infancy from at-birth to 3 years is critical for cognitive, emotional and social development of infants. During this period, infant's developmental tempo and outcomes are potentially impacted by in utero exposure to endocrine disrupting compounds (EDCs), such as bisphenol A (BPA) and phthalates. We investigate effects of ten ubiquitous EDCs on the infant growth dynamics of body mass index (BMI) in a birth cohort study.Modeling growth acceleration is proposed to understand the "force of growth" through a class of semiparametric stochastic velocity models. The great flexibility of such a dynamic model enables us to capture subject-specific dynamics of growth trajectories and to assess effects of the EDCs on potential delay of growth. We adopted a Bayesian method with the Ornstein-Uhlenbeck process as the prior for the growth rate function, in which the World Health Organization global infant's growth curves were integrated into our analysis. We found that BPA and most of phthalates exposed during the first trimester of pregnancy were inversely associated with BMI growth acceleration, resulting in a delayed achievement of infant BMI peak. Such early growth deficiency has been reported as a profound impact on health outcomes in puberty (e.g., timing of sexual maturation) and adulthood.

Derivative estimation for longitudinal data analysis: Examining features of blood pressure measured repeatedly during pregnancy

Estimating velocity and acceleration trajectories allows novel inferences in the field of longitudinal data analysis, such as estimating change regions rather than change points, and testing group effects on nonlinear change in an outcome (ie, a nonlinear interaction). In this article, we develop derivative estimation for 2 standard approaches-polynomial mixed models and spline mixed models. We compare their performance with an established method-principal component analysis through conditional expectation through a simulation study. We then apply the methods to repeated blood pressure (BP) measurements in a UK cohort of pregnant women, where the goals of analysis are to (i) identify and estimate regions of BP change for each individual and (ii) investigate the association between parity and BP change at the population level. The penalized spline mixed model had the lowest bias in our simulation study, and we identified evidence for BP change regions in over 75% of pregnant women. Using mean velocity difference revealed differences in BP change between women in their first pregnancy compared with those who had at least 1 previous pregnancy. We recommend the use of penalized spline mixed models for derivative estimation in longitudinal data analysis.

Autism with intellectual disability related to dynamics of head circumference growth during early infancy

BACKGROUND

It is not yet definitively known whether dynamic features of head circumference growth are associated with autism. To address this issue, we carried out a nested matched case-control study using data from national well baby clinics in Finland; autism cases were identified from the Finnish Hospital and Outpatient Discharge Registry.

METHODS

A nonparametric Bayesian method was used to construct growth velocity trajectories between birth and 2 years of age in autism cases and matched control subjects (n = 468 in main analyses, 1:1 matched control subjects). Estimates of odds ratios for autism risk in relation to the growth velocities were obtained using conditional logistic regression.

RESULTS

Growth velocity of head circumference at 3 months of age, adjusting for gestational age at birth and maternal age, is significantly associated with autism (p = .014); the finding was observed in subjects with comorbid intellectual disability (ID) (p = .025) but not in those without ID (p = .15). Height growth velocity among subjects with autism and without ID is significantly associated with autism at 6 months (p = .007), and weight growth velocity at 18 months without ID (p = .02) and 24 months without ID (p = .042) and with ID (p = .037).

CONCLUSIONS

Acceleration in head circumference growth is associated with autism with comorbid ID at 3 months but not subsequently. This association is unrelated to acceleration in height and weight, which are not strongly associated with autism until after 6 months.

Analyzing growth trajectories

Growth trajectories play a central role in life course epidemiology, often providing fundamental indicators of prenatal or childhood development, as well as an array of potential determinants of adult health outcomes. Statistical methods for the analysis of growth trajectories have been widely studied, but many challenging problems remain. Repeated measurements of length, weight and head circumference, for example, may be available on most subjects in a study, but usually only sparse temporal sampling of such variables is feasible. It can thus be challenging to gain a detailed understanding of growth patterns, and smoothing techniques are inevitably needed. Moreover, the problem is exacerbated by the presence of large fluctuations in growth velocity during early infancy, and high variability between subjects. Existing approaches, however, can be inflexible because of a reliance on parametric models, require computationally intensive methods that are unsuitable for exploratory analyses, or are only capable of examining each variable separately. This article proposes some new nonparametric approaches to analyzing sparse data on growth trajectories, with flexibility and ease of implementation being key features. The methods are illustrated using data on participants in the Collaborative Perinatal Project.