Predictive Functional Linear Models with Diverging Number of Semiparametric Single-Index Interactions.

When predicting crop yield using both functional and multivariate predictors, the prediction performances benefit from the inclusion of the interactions between the two sets of predictors. We assume the interaction depends on a nonparametric, single-index structure of the multivariate predictor and reduce each functional predictor's dimension using functional principal component analysis (FPCA). Allowing the number of FPCA scores to diverge to infinity, we consider a sequence of semiparametric working models with a diverging number of predictors, which are FPCA scores with estimation errors. We show that the parametric component of the model is root-n consistent and asymptotically normal, the overall prediction error is dominated by the estimation of the nonparametric interaction function, and justify a CV-based procedure to select the tuning parameters.

Improving Prediction Efficacy through Abnormality Detection and Data Preprocessing.

Abnormal testing data can severely reduce model performance if not processed properly. In this work, we propose a preprocessing system to handle different types of commonly seen abnormal testing data. The system consists of an aberrant data detector and an aberrant data corrector. The aberrant data detector is responsible for classifying the type of incoming data. Based on the data type, the aberrant data corrector will take different actions to amend testing data. Users can then apply their preferred prediction methods on the corrected testing data. Specifically, corrupted and adversarial images are used as examples of abnormal data. We show that corrupted data can be reconstructed through a Gaussian Locally Linear Mappings method, and the prediction performance of adversarial samples can be improved by using the nearest neighbors as a surrogate. We compare the proposed aberrant data detector and corrector with existing and well-recognized alternatives. These approaches are published individually and do not put two components together as a pre-processing system. The numerical outcomes show that our proposed components, standing alone, are competitive. The proposed system is a generic method that can be applied to different downstream predictive models. We use three existing prediction methods to illustrate the general usage of the proposed system and its capability of improving prediction efficacy.

Doubly regularized estimation and selection in linear mixed-effects models for high-dimensional longitudinal data.

The linear mixed-effects model (LMM) is widely used in the analysis of clustered or longitudinal data. This paper aims to address analytic challenges arising from estimation and selection in the application of the LMM to high-dimensional longitudinal data. We develop a doubly regularized approach in the LMM to simultaneously select fixed and random effects. On the theoretical front, we establish large sample properties for the proposed method under the high-dimensional setting, allowing both numbers of fixed effects and random effects to be much larger than the sample size. We present new regularity conditions for the diverging rates, under which the proposed method achieves both estimation and selection consistency. In addition, we propose a new algorithm that solves the related optimization problem effectively so that its computational cost is comparable with that of the Newton-Raphson algorithm for maximum likelihood estimator in the LMM. Through simulation studies we assess performances of the proposed regularized LMM in both aspects of variable selection and estimation. We also illustrate the proposed method by two data analysis examples.

Bayesian estimation of associations between identified longitudinal hormone subgroups and age at final menstrual period.

BACKGROUND: Although follicle stimulating hormone (FSH) is known to be predictive of age at final menstrual period (FMP), previous methods use FSH levels measured at time points that are defined relative to the age at FMP, and hence are not useful for prospective prediction purposes in clinical settings where age at FMP is an unknown outcome. This study is aimed at assessing whether FSH trajectory feature subgroups identified relative to chronological age can be used to improve the prediction of age at FMP. METHODS: We develop a Bayesian model to identify latent subgroups in longitudinal FSH trajectories, and study the relationship between subgroup membership and age at FMP. Data for our study is taken from the Penn Ovarian Aging study, 1996-2010. The proposed model utilizes mixture modeling and nonparametric smoothing methods to capture hypothesized latent subgroup features of the FSH longitudinal trajectory; and simultaneously studies the prognostic value of these latent subgroup features to predict age at FMP. RESULTS: The analysis identified two FSH trajectory subgroups that were significantly associated with FMP age: 1) early FSH class (15%), which displayed initial increases in FSH shortly after age 40; and 2) late FSH class (85%), which did not have a rise in FSH until after age 45. The use of FSH subgroup memberships, along with class-specific characteristics, i.e., level and rate of FSH change at class-specific pre-specified ages, improved prediction of FMP age by 20-22% in comparison to the prediction based on previously identified risk factors (BMI, smoking and pre-menopausal levels of anti-mullerian hormone (AMH)). CONCLUSIONS: To the best of our knowledge, this work is the first in the area to demonstrate the existence of subgroups in FSH trajectory patterns relative to chronological age and the fact that such a subgroup membership possesses prediction power for age at FMP. Earlier ages at FMP were found in a subgroup of women with rise in FSH levels commencing shortly after age 40, in comparison to women who did not exhibit an increase in FSH until after 45 years of age. Periodic evaluations of FSH in these age ranges are potentially useful for predicting age at FMP.

Modeling Short- and Long-Term Characteristics of Follicle Stimulating Hormone as Predictors of Severe Hot Flashes in Penn Ovarian Aging Study.

The Penn Ovarian Aging Study tracked a population-based sample of 436 women aged 35-47 years to determine associations between reproductive hormone levels and menopausal symptoms. We develop a joint modeling method that uses the individual-level longitudinal measurements of follicle stimulating hormone (FSH) to predict the risk of severe hot flashes in a manner that distinguishes long-term trends of the mean trajectory, cumulative changes captured by the derivative of mean trajectory, and short-term residual variability. Our method allows the potential effects of longitudinal trajectories on the health risks to vary and accumulate over time. We further utilize the proposed methods to narrow the critical time windows of increased health risks. We find that high residual variation of FSH is a strong predictor of hot flash risk, and that the high cumulative changes of the FSH mean trajectories in the 52.5-55 year age range also provides evidence of increased risk above and beyond that of short-term FSH residual variation by itself.

Regularized Semiparametric Estimation for Ordinary Differential Equations.

Ordinary differential equations (ODEs) are widely used in modeling dynamic systems and have ample applications in the fields of physics, engineering, economics and biological sciences. The ODE parameters often possess physiological meanings and can help scientists gain better understanding of the system. One key interest is thus to well estimate these parameters. Ideally, constant parameters are preferred due to their easy interpretation. In reality, however, constant parameters can be too restrictive such that even after incorporating error terms, there could still be unknown sources of disturbance that lead to poor agreement between observed data and the estimated ODE system. In this paper, we address this issue and accommodate short-term interferences by allowing parameters to vary with time. We propose a new regularized estimation procedure on the time-varying parameters of an ODE system so that these parameters could change with time during transitions but remain constants within stable stages. We found, through simulation studies, that the proposed method performs well and tends to have less variation in comparison to the non-regularized approach. On the theoretical front, we derive finite-sample estimation error bounds for the proposed method. Applications of the proposed method to modeling the hare-lynx relationship and the measles incidence dynamic in Ontario, Canada lead to satisfactory and meaningful results.

Joint modeling of cross-sectional health outcomes and longitudinal predictors via mixtures of means and variances.

Joint modeling methods have become popular tools to link important features extracted from longitudinal data to a primary event. While most modeling strategies have focused on the association between the longitudinal mean trajectories and risk of an event, we consider joint models that incorporate information from both long-term trends and short-term variability in a longitudinal submodel. We also consider both shared random effect and latent class (LC) approaches in the primary-outcome model to predict a binary outcome of interest. We develop simulation studies to compare and contrast these two modeling strategies; in particular, we study in detail the effects of the primary-outcome model misspecification. Among other findings, we note that when we analyze data from a shared random-effect using a LC model while the information from the longitudinal data is weak, the LC approach is more sensitive to such a model misspecification. Under this setting, the LC model has a superior performance in within-sample prediction that cannot be duplicated when predicting new samples. This is a unique feature of the LC approach that is new as far as we know to the existing literature. Finally, we use the proposed models to study how follicle stimulating hormone (FSH) trajectories are related to the risk of developing severe hot flashes for participating women in the Penn Ovarian Aging Study.

Estimation of mean response via effective balancing score.

We introduce effective balancing scores for estimation of the mean response under a missing at random mechanism. Unlike conventional balancing scores, the effective balancing scores are constructed via dimension reduction free of model specification. Three types of effective balancing scores are introduced: those that carry the covariate information about the missingness, the response, or both. They lead to consistent estimation with little or no loss in efficiency. Compared to existing estimators, the effective balancing score based estimator relieves the burden of model specification and is the most robust. It is a near-automatic procedure which is most appealing when high dimensional covariates are involved. We investigate both the asymptotic and the numerical properties, and demonstrate the proposed method in a study on Human Immunodeficiency Virus disease.

Selecting the Number of Principal Components in Functional Data.

Functional principal component analysis (FPCA) has become the most widely used dimension reduction tool for functional data analysis. We consider functional data measured at random, subject-specific time points, contaminated with measurement error, allowing for both sparse and dense functional data, and propose novel information criteria to select the number of principal component in such data. We propose a Bayesian information criterion based on marginal modeling that can consistently select the number of principal components for both sparse and dense functional data. For dense functional data, we also developed an Akaike information criterion (AIC) based on the expected Kullback-Leibler information under a Gaussian assumption. In connecting with factor analysis in multivariate time series data, we also consider the information criteria by Bai & Ng (2002) and show that they are still consistent for dense functional data, if a prescribed undersmoothing scheme is undertaken in the FPCA algorithm. We perform intensive simulation studies and show that the proposed information criteria vastly outperform existing methods for this type of data. Surprisingly, our empirical evidence shows that our information criteria proposed for dense functional data also perform well for sparse functional data. An empirical example using colon carcinogenesis data is also provided to illustrate the results.

Functional Linear Model with Zero-value Coefficient Function at Sub-regions.

We propose a shrinkage method to estimate the coefficient function in a functional linear regression model when the value of the coefficient function is zero within certain sub-regions. Besides identifying the null region in which the coefficient function is zero, we also aim to perform estimation and inferences for the nonparametrically estimated coefficient function without over-shrinking the values. Our proposal consists of two stages. In stage one, the Dantzig selector is employed to provide initial location of the null region. In stage two, we propose a group SCAD approach to refine the estimated location of the null region and to provide the estimation and inference procedures for the coefficient function. Our considerations have certain advantages in this functional setup. One goal is to reduce the number of parameters employed in the model. With a one-stage procedure, it is needed to use a large number of knots in order to precisely identify the zero-coefficient region; however, the variation and estimation difficulties increase with the number of parameters. Owing to the additional refinement stage, we avoid this necessity and our estimator achieves superior numerical performance in practice. We show that our estimator enjoys the Oracle property; it identifies the null region with probability tending to 1, and it achieves the same asymptotic normality for the estimated coefficient function on the non-null region as the functional linear model estimator when the non-null region is known. Numerically, our refined estimator overcomes the shortcomings of the initial Dantzig estimator which tends to under-estimate the absolute scale of non-zero coefficients. The performance of the proposed method is illustrated in simulation studies. We apply the method in an analysis of data collected by the Johns Hopkins Precursors Study, where the primary interests are in estimating the strength of association between body mass index in midlife and the quality of life in physical functioning at old age, and in identifying the effective age ranges where such associations exist.

A chemoprotective fish oil- and pectin-containing diet temporally alters gene expression profiles in exfoliated rat colonocytes throughout oncogenesis.

We have demonstrated that fish oil- and pectin-containing (FO/P) diets protect against colon cancer compared with corn oil and cellulose (CO/C) by upregulating apoptosis and suppressing proliferation. To elucidate the mechanisms whereby FO/P diets induce apoptosis and suppress proliferation during the tumorigenic process, we analyzed the temporal gene expression profiles from exfoliated rat colonocytes. Rats consumed diets containing FO/P or CO/C and were injected with azoxymethane (AOM; 2 times, 15 mg/kg body weight, subcutaneously). Feces collected at initiation (24 h after AOM injection) and at aberrant crypt foci (ACF) (7 wk postinjection) and tumor (28 wk postinjection) stages of colon cancer were used for poly (A)+ RNA extraction. Gene expression signatures were determined using Codelink arrays. Changes in phenotypes (ACF, apoptosis, proliferation, and tumor incidence) were measured to establish the regulatory controls contributing to the chemoprotective effects of FO/P. At initiation, FO/P downregulated the expression of 3 genes involved with cell adhesion and enhanced apoptosis compared with CO/C. At the ACF stage, the expression of genes involved in cell cycle regulation was modulated by FO/P and the zone of proliferation was reduced in FO/P rats compared with CO/C rats. FO/P also increased apoptosis and the expression of genes that promote apoptosis at the tumor endpoint compared with CO/C. We conclude that the effects of chemotherapeutic diets on epithelial cell gene expression can be monitored noninvasively throughout the tumorigenic process and that a FO/P diet is chemoprotective in part due to its ability to affect expression of genes involved in apoptosis and cell cycle regulation throughout all stages of tumorigenesis.

Effects of location for collection of air samples on a farm and time of day of sample collection on airborne concentrations of virulent Rhodococcus equi at two horse breeding farms.

OBJECTIVE: To determine whether airborne concentrations of virulent Rhodococcus equi at 2 horse breeding farms varied on the basis of location, time of day, and month. SAMPLE POPULATION: 2 farms in central Kentucky with recurrent R equi-induced pneumonia in foals. PROCEDURES: From February through July 2008, air samples were collected hourly for a 24-hour period each month from stalls and paddocks used to house mares and their foals. Concentrations of airborne virulent R equi were determined via a modified colony immunoblot technique. Differences were compared by use of zero-inflated negative binomial methods to determine effects of location, time, and month. RESULTS: Whether mares and foals were housed predominantly in stalls or paddocks significantly affected results for location of sample collection (stall vs paddock) by increasing airborne concentrations of virulent R equi at the site where horses were predominantly housed. Airborne concentrations of virulent R equi were significantly higher from 6:00 pm through 11:59 pm than for the period from midnight through 5:59 am. Airborne concentrations of virulent R equi did not differ significantly between farms or among months. CONCLUSIONS AND CLINICAL RELEVANCE: Airborne concentrations of virulent R equi were significantly increased when horses were predominantly housed at the site for collection of air samples (ie, higher in stalls when horses were predominantly housed in stalls and higher in paddocks when horses were predominantly housed in paddocks). Concentrations of virulent R equi among air samples collected between the hours of 6:00 am and midnight appeared similar.

Generalized Functional Linear Models with Semiparametric Single-Index Interactions.

We introduce a new class of functional generalized linear models, where the response is a scalar and some of the covariates are functional. We assume that the response depends on multiple covariates, a finite number of latent features in the functional predictor, and interaction between the two. To achieve parsimony, the interaction between the multiple covariates and the functional predictor is modeled semiparametrically with a single-index structure. We propose a two step estimation procedure based on local estimating equations, and investigate two situations: (a) when the basis functions are pre-determined, e.g., Fourier or wavelet basis functions and the functional features of interest are known; and (b) when the basis functions are data driven, such as with functional principal components. Asymptotic properties are developed. Notably, we show that when the functional features are data driven, the parameter estimates have an increased asymptotic variance, due to the estimation error of the basis functions. Our methods are illustrated with a simulation study and applied to an empirical data set, where a previously unknown interaction is detected. Technical proofs of our theoretical results are provided in the online supplemental materials.

A two-component nonlinear mixed effects model for longitudinal data, with application to gastric emptying studies.

Gastric emptying studies are of great interest in human and veterinary medical research to evaluate effects of medications or diets for promoting gastrointestinal motility and to examine unintended side-effects of new or existing medications, diets, or procedures. Summarizing gastric emptying data is important to allow easier comparison between treatments or groups of subjects and comparisons of results among studies. The standard method for assessing gastric emptying is by using scintigraphy and summarizing the nonlinear emptying of the radioisotope. A popular model for fitting gastric emptying data is the power exponential model. This model can only describes a globally decreasing pattern and thus has the limitation of poorly describing localized intragastric events that can occur during emptying. Hence, we develop a new model for gastric emptying studies to improve population and individual inferences using a mixture of nonlinear mixed effects models. One mixture component is based on a power exponential model which captures globally decreasing patterns. The other is based on a locally extended power exponential model which captures both local bumping and rapid decay. We refer to this mixture model as a two-component nonlinear mixed effects model. The parameters in our model have clear graphical interpretations that provide a more accurate representation and summary of the curves of gastric emptying pattern. Two methods are developed to fit our proposed model: one is the mixture of an Expectation Maximization algorithm and a global two-stage method and the other is the mixture of an Expectation Maximization algorithm and the Monte Carlo Expectation Maximization algorithm. We compare our methods using simulation, showing that the two approaches are comparable to one another. For estimating the variance and covariance matrix, the second approach appears approximately more efficient and is also numerically more stable in some cases. Our new model and approaches are applicable for assessing gastric emptying in human and veterinary medical research and in many other biomedical fields such as pharmacokinetics, toxicokinetics, and physiological research. An example of gastric emptying data from equine medicine is used to demonstrate the advantage of our approaches.

Apigenin and naringenin suppress colon carcinogenesis through the aberrant crypt stage in azoxymethane-treated rats.

Epidemiological evidence suggests that a diet abundant in fruits and vegetables may protect against colon cancer. Bioactive compounds, including flavonoids and limonoids, have been shown to possess antiproliferative and antitumorigenic effects in various cancer models. This experiment investigated the effects of four citrus flavonoids and one limonoid mixture at the promotion stage of chemically induced colon cancer in rats. Male Sprague-Dawley rats (n = 10 rats/group) were randomly allocated to one of six diets formulated to contain 0.1% apigenin, 0.02% naringenin, 0.1% hesperidin, 0.01% nobiletin, 0.035% limonin glucoside/obacunone glucoside mixture or a control diet (0% flavonoid/limonoid). Rats received experimental diets for 10 weeks and were injected with azoxymethane (15 mg/kg) at weeks 3 and 4. Excised colons were evaluated for aberrant crypt foci (ACF) formation, colonocyte proliferation (proliferating cell nuclear antigen assay), apoptosis (terminal deoxynucleotidyl transferase dUTP nick end labeling assay) and expression of inducible nitric oxide synthase (iNOS) and cyclooxygenase-2 (COX-2) (immunoblotting). When compared with the control diet, apigenin lowered the number of high multiplicity ACF (HMACF >4 aberrant crypts/focus) by 57% (P < 0.05), while naringenin lowered both the number of HMACF by 51% (P < 0.05) and the proliferative index by 32% (P < 0.05). Both apigenin and naringenin increased apoptosis of luminal surface colonocytes (78% and 97%, respectively; P < 0.05) when compared with the control diet. Hesperidin, nobiletin and the limonin glucoside/obacunone glucoside mixture did not affect these variables. The colonic mucosal protein levels of iNOS or COX-2 were not different among the six diet groups. The ability of dietary apigenin and naringenin to reduce HMACF, lower proliferation (naringenin only) and increase apoptosis may contribute toward colon cancer prevention. However, these effects were not due to mitigation of iNOS and COX-2 protein levels at the ACF stage of colon cancer.

Inference from Multiple Imputation for Missing Data Using Mixtures of Normals.

We consider two difficulties with standard multiple imputation methods for missing data based on Rubin's t method for confidence intervals: their often excessive width, and their instability. These problems are present most often when the number of copies is small, as is often the case when a data collection organization is making multiple completed datasets available for analysis. We suggest using mixtures of normals as an alternative to Rubin's t. We also examine the performance of improper imputation methods as an alternative to generating copies from the true posterior distribution for the missing observations. We report the results of simulation studies and analyses of data on health-related quality of life in which the methods suggested here gave narrower confidence intervals and more stable inferences, especially with small numbers of copies or non-normal posterior distributions of parameter estimates. A free R software package called MImix that implements our methods is available from CRAN.

Regulatory activity of polyunsaturated fatty acids in T-cell signaling.

n-3 Polyunsaturated fatty acids (PUFA) are considered to be authentic immunosuppressors and appear to exert beneficial effects with respect to certain immune-mediated diseases. In addition to promoting T-helper 1 (Th1) cell to T-helper 2 (Th2) cell effector T-cell differentiation, n-3 PUFA may also exert anti-inflammatory actions by inducing apoptosis in Th1 cells. With respect to mechanisms of action, effects range from the modulation of membrane receptors to gene transcription via perturbation of a number of second messenger cascades. In this review, the putative targets of anti-inflammatory n-3 PUFA, activated during early and late events of T-cell activation will be discussed. Studies have demonstrated that these fatty acids alter plasma membrane micro-organization (lipid rafts) at the immunological synapse, the site where T-cells and antigen-presenting cells (APC) form a physical contact for antigen initiated T-cell signaling. In addition, the production of diacylglycerol and the activation of different isoforms of protein kinase C (PKC), mitogen-activated protein kinase (MAPK), calcium signaling, and nuclear translocation/activation of transcriptional factors, can be modulated by n-3 PUFA. Advantages and limitations of diverse methodologies to study the membrane lipid raft hypothesis, as well as apparent contradictions regarding the effect of n-3 PUFA on lipid rafts will be critically presented.

Evaluation of fecal mRNA reproducibility via a marginal transformed mixture modeling approach.

BACKGROUND: Developing and evaluating new technology that enables researchers to recover gene-expression levels of colonic cells from fecal samples could be key to a non-invasive screening tool for early detection of colon cancer. The current study, to the best of our knowledge, is the first to investigate and report the reproducibility of fecal microarray data. Using the intraclass correlation coefficient (ICC) as a measure of reproducibility and the preliminary analysis of fecal and mucosal data, we assessed the reliability of mixture density estimation and the reproducibility of fecal microarray data. Using Monte Carlo-based methods, we explored whether ICC values should be modeled as a beta-mixture or transformed first and fitted with a normal-mixture. We used outcomes from bootstrapped goodness-of-fit tests to determine which approach is less sensitive toward potential violation of distributional assumptions. RESULTS: The graphical examination of both the distributions of ICC and probit-transformed ICC (PT-ICC) clearly shows that there are two components in the distributions. For ICC measurements, which are between 0 and 1, the practice in literature has been to assume that the data points are from a beta-mixture distribution. Nevertheless, in our study we show that the use of a normal-mixture modeling approach on PT-ICC could provide superior performance. CONCLUSIONS: When modeling ICC values of gene expression levels, using mixture of normals in the probit-transformed (PT) scale is less sensitive toward model mis-specification than using mixture of betas. We show that a biased conclusion could be made if we follow the traditional approach and model the two sets of ICC values using the mixture of betas directly. The problematic estimation arises from the sensitivity of beta-mixtures toward model mis-specification, particularly when there are observations in the neighborhood of the the boundary points, 0 or 1. Since beta-mixture modeling is commonly used in approximating the distribution of measurements between 0 and 1, our findings have important implications beyond the findings of the current study. By using the normal-mixture approach on PT-ICC, we observed the quality of reproducible genes in fecal array data to be comparable to those in mucosal arrays.

Identification of actively translated mRNA transcripts in a rat model of early-stage colon carcinogenesis.

With respect to functional mapping of gene expression signatures, the steady-state mRNA expression level does not always accurately reflect the status of critical signaling proteins. In these cases, control is exerted at the epigenetic level of recruitment of mRNAs to polysomes, the factories of ribosomes that mediate efficient translation of many cellular messages. However, to date, a genome-wide perspective of the effect of carcinogen and chemoprotective bioactive diets on actively translated (polysomal) mRNA populations has not been done. Therefore, we used an established colon cancer model, i.e., the azoxymethane (AOM)-treated rat, in combination with a chemoprotective diet extensively studied in our laboratory, i.e., n-3 polyunsaturated fatty acids, to characterize the molecular processes underlying the transformation of normal colonic epithelium. The number of genes affected by AOM treatment 10 weeks after carcinogen injection was significantly greater in the polysome RNA fraction compared with the total RNA fraction as determined using a high-density microarray platform. In particular, polysomal loading patterns of mRNAs associated with the Wnt-beta catenin, phospholipase A(2)-eicosanoid and the mitogen-activated protein kinase signaling axes were significantly upregulated at a very early period of tumor development in the colon. These data indicate that translational alterations are far more extensive relative to transcriptional alterations in mediating malignant transformation. In contrast, transcriptional alterations were found to be more extensive relative to translational alterations in mediating the effects of diet. Therefore, during early stage colonic neoplasia, diet and carcinogen seem to predominantly regulate gene expression at multiple levels via unique mechanisms.