Partial least squares for functional joint models with applications to the Alzheimer's disease neuroimaging initiative study

Many biomedical studies have identified important imaging biomarkers that are associated with both repeated clinical measures and a survival outcome. The functional joint model (FJM) framework, proposed by Li and Luo in 2017, investigates the association between repeated clinical measures and survival data, while adjusting for both high-dimensional images and low-dimensional covariates based on the functional principal component analysis (FPCA). In this paper, we propose a novel algorithm for the estimation of FJM based on the functional partial least squares (FPLS). Our numerical studies demonstrate that, compared to FPCA, the proposed FPLS algorithm can yield more accurate and robust estimation and prediction performance in many important scenarios. We apply the proposed FPLS algorithm to a neuroimaging study. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.     

Joint prediction of multiple quantitative traits using a Bayesian multivariate antedependence model

Predicting organismal phenotypes from genotype data is important for preventive and personalized medicine as well as plant and animal breeding. Although genome-wide association studies (GWAS) for complex traits have discovered a large number of trait- and disease-associated variants, phenotype prediction based on associated variants is usually in low accuracy even for a high-heritability trait because these variants can typically account for a limited fraction of total genetic variance. In comparison with GWAS, the whole-genome prediction (WGP) methods can increase prediction accuracy by making use of a huge number of variants simultaneously. Among various statistical methods for WGP, multiple-trait model and antedependence model show their respective advantages. To take advantage of both strategies within a unified framework, we proposed a novel multivariate antedependence-based method for joint prediction of multiple quantitative traits using a Bayesian algorithm via modeling a linear relationship of effect vector between each pair of adjacent markers. Through both simulation and real-data analyses, our studies demonstrated that the proposed antedependence-based multiple-trait WGP method is more accurate and robust than corresponding traditional counterparts (Bayes A and multi-trait Bayes A) under various scenarios. Our method can be readily extended to deal with missing phenotypes and resequence data with rare variants, offering a feasible way to jointly predict phenotypes for multiple complex traits in human genetic epidemiology as well as plant and livestock breeding.     

IL-4 augments anisomycin-induced p38 activation via Akt pathway in a follicular dendritic cell (FDC)-like line

Prediction of medulloblastoma clinical outcome is crucial to personalizing treatment, both to identify high-risk patients for aggressive or alternative therapy and to spare those at low risk from excessive treatment. The best predictors [Pomeroy et al. (2002) Nature 415, 436-442], based on gene expression monitoring at diagnosis, have shown much less accuracy in recognizing patients with eventual failed outcomes - <50% for the predictor making fewest total errors - than those who would survive, while a single gene predictor exhibited reverse asymmetry. Such inaccuracy in recognizing one of the outcomes is a problem for clinical use. We hypothesized that a non-linear model could be built to significantly improve prediction of medulloblastoma outcome, thereby promoting use of gene-expression-based predictors in a clinical setting. In fact, this approach resulted in fewer errors and much less asymmetry in prediction, and bidirectional accuracy of about 80% could be obtained via its combination with other methods. Indeed, three combinations of methods were identified that yielded significantly better predictions of clinical outcome than previously attained, making feasible predictors of medulloblastoma treatment response with greatly improved bidirectional accuracy essential for clinical use.     

Gene expression monitoring accurately predicts medulloblastoma positive and negative clinical outcomes

Prediction of medulloblastoma clinical outcome is crucial to personalizing treatment, both to identify high-risk patients for aggressive or alternative therapy and to spare those at low risk from excessive treatment. The best predictors [Pomeroy et al. (2002) Nature 415, 436–442], based on gene expression monitoring at diagnosis, have shown much less accuracy in recognizing patients with eventual failed outcomes – <50% for the predictor making fewest total errors – than those who would survive, while a single gene predictor exhibited reverse asymmetry. Such inaccuracy in recognizing one of the outcomes is a problem for clinical use. We hypothesized that a non-linear model could be built to significantly improve prediction of medulloblastoma outcome, thereby promoting use of gene-expression-based predictors in a clinical setting. In fact, this approach resulted in fewer errors and much less asymmetry in prediction, and bidirectional accuracy of about 80% could be obtained via its combination with other methods. Indeed, three combinations of methods were identified that yielded significantly better predictions of clinical outcome than previously attained, making feasible predictors of medulloblastoma treatment response with greatly improved bidirectional accuracy essential for clinical use.     

Functional mixture regression

In functional linear models (FLMs), the relationship between the scalar response and the functional predictor process is often assumed to be identical for all subjects. Motivated by both practical and methodological considerations, we relax this assumption and propose a new class of functional regression models that allow the regression structure to vary for different groups of subjects. By projecting the predictor process onto its eigenspace, the new functional regression model is simplified to a framework that is similar to classical mixture regression models. This leads to the proposed approach named as functional mixture regression (FMR). The estimation of FMR can be readily carried out using existing software implemented for functional principal component analysis and mixture regression. The practical necessity and performance of FMR are illustrated through applications to a longevity analysis of female medflies and a human growth study. Theoretical investigations concerning the consistent estimation and prediction properties of FMR along with simulation experiments illustrating its empirical properties are presented in the supplementary material available at Biostatistics online. Corresponding results demonstrate that the proposed approach could potentially achieve substantial gains over traditional FLMs.     

Why are rare variants hard to impute? Coalescent models reveal theoretical limits in existing algorithms

Genotype imputation is an indispensable step in human genetic studies. Large reference panels with deeply sequenced genomes now allow interrogating variants with minor allele frequency < 1% without sequencing. Although it is critical to consider limits of this approach, imputation methods for rare variants have only done so empirically; the theoretical basis of their imputation accuracy has not been explored. To provide theoretical consideration of imputation accuracy under the current imputation framework, we develop a coalescent model of imputing rare variants, leveraging the joint genealogy of the sample to be imputed and reference individuals. We show that broadly used imputation algorithms include model misspecifications about this joint genealogy that limit the ability to correctly impute rare variants. We develop closed-form solutions for the probability distribution of this joint genealogy and quantify the inevitable error rate resulting from the model misspecification across a range of allele frequencies and reference sample sizes. We show that the probability of a falsely imputed minor allele decreases with reference sample size, but the proportion of falsely imputed minor alleles mostly depends on the allele count in the reference sample. We summarize the impact of this error on genotype imputation on association tests by calculating the r² between imputed and true genotype and show that even when modeling other sources of error, the impact of the model misspecification has a significant impact on the r² of rare variants. To evaluate these predictions in practice, we compare the imputation of the same dataset across imputation panels of different sizes. Although this empirical imputation accuracy is substantially lower than our theoretical prediction, modeling misspecification seems to further decrease imputation accuracy for variants with low allele counts in the reference. These results provide a framework for developing new imputation algorithms and for interpreting rare variant association analyses.     

Latent class models for joint analysis of disease prevalence and high-dimensional semicontinuous biomarker data

High-dimensional biomarker data are often collected in epidemiological studies when assessing the association between biomarkers and human disease is of interest. We develop a latent class modeling approach for joint analysis of high-dimensional semicontinuous biomarker data and a binary disease outcome. To model the relationship between complex biomarker expression patterns and disease risk, we use latent risk classes to link the 2 modeling components. We characterize complex biomarker-specific differences through biomarker-specific random effects, so that different biomarkers can have different baseline (low-risk) values as well as different between-class differences. The proposed approach also accommodates data features that are common in environmental toxicology and other biomarker exposure data, including a large number of biomarkers, numerous zero values, and complex mean-variance relationship in the biomarkers levels. A Monte Carlo EM (MCEM) algorithm is proposed for parameter estimation. Both the MCEM algorithm and model selection procedures are shown to work well in simulations and applications. In applying the proposed approach to an epidemiological study that examined the relationship between environmental polychlorinated biphenyl (PCB) exposure and the risk of endometriosis, we identified a highly significant overall effect of PCB concentrations on the risk of endometriosis.     

Chloroplast transit peptide prediction: a peek inside the black box

Previous work in predicting protein localization to the chloroplast organelle in plants led to the development of an artificial neural network-based approach capable of remarkable accuracy in its prediction (ChloroP). A common criticism against such neural network models is that it is difficult to interpret the criteria that are used in making predictions. We address this concern with several new prediction methods that base predictions explicitly on the abundance of different amino acid types in the N-terminal region of the protein. Our successful prediction accuracy suggests that ChloroP uses little positional information in its decision-making; an unexpected result given the elaborate ChloroP input scheme. By removing positional information, our simpler methods allow us to identify those amino acids that are useful for successful prediction. The identification of important sequence features, such as amino acid content, is advantageous if one of the goals of localization predictors is to gain an understanding of the biological process of chloroplast localization. Our most accurate predictor combines principal component analysis and logistic regression. Web-based prediction using this method is available online at http://apicoplast.cis.upenn.edu/pclr/.     

Logistic regression when covariates are random effects from a non‐linear mixed model

In many studies, the association of longitudinal measurements of a continuous response and a binary outcome are often of interest. A convenient framework for this type of problems is the joint model, which is formulated to investigate the association between a binary outcome and features of longitudinal measurements through a common set of latent random effects. The joint model, which is the focus of this article, is a logistic regression model with covariates defined as the individual‐specific random effects in a non‐linear mixed‐effects model (NLMEM) for the longitudinal measurements. We discuss different estimation procedures, which include two‐stage, best linear unbiased predictors, and various numerical integration techniques. The proposed methods are illustrated using a real data set where the objective is to study the association between longitudinal hormone levels and the pregnancy outcome in a group of young women. The numerical performance of the estimating methods is also evaluated by means of simulation.     

Accounting for post-randomization variables in meta-analysis: A joint meta-regression approach

Meta-regression is widely used in systematic reviews to investigate sources of heterogeneity and the association of study-level covariates with treatment effectiveness. Existing meta-regression approaches are successful in adjusting for baseline covariates, which include real study-level covariates (e.g., publication year) that are invariant within a study and aggregated baseline covariates (e.g., mean age) that differ for each participant but are measured before randomization within a study. However, these methods have several limitations in adjusting for post-randomization variables. Although post-randomization variables share a handful of similarities with baseline covariates, they differ in several aspects. First, baseline covariates can be aggregated at the study level presumably because they are assumed to be balanced by the randomization, while post-randomization variables are not balanced across arms within a study and are commonly aggregated at the arm level. Second, post-randomization variables may interact dynamically with the primary outcome. Third, unlike baseline covariates, post-randomization variables are themselves often important outcomes under investigation. In light of these differences, we propose a Bayesian joint meta-regression approach adjusting for post-randomization variables. The proposed method simultaneously estimates the treatment effect on the primary outcome and on the post-randomization variables. It takes into consideration both between- and within-study variability in post-randomization variables. Studies with missing data in either the primary outcome or the post-randomization variables are included in the joint model to improve estimation. Our method is evaluated by simulations and a real meta-analysis of major depression disorder treatments.     

Survival prediction of diffuse large-B-cell lymphoma based on both clinical and gene expression information

MOTIVATION: It is important to predict the outcome of patients with diffuse large-B-cell lymphoma after chemotherapy, since the survival rate after treatment of this common lymphoma disease is <50%. Both clinically based outcome predictors and the gene expression-based molecular factors have been proposed independently in disease prognosis. However combining the high-dimensional genomic data and the clinically relevant information to predict disease outcome is challenging. RESULTS: We describe an integrated clinicogenomic modeling approach that combines gene expression profiles and the clinically based International Prognostic Index (IPI) for personalized prediction in disease outcome. Dimension reduction methods are proposed to produce linear combinations of gene expressions, while taking into account clinical IPI information. The extracted summary measures capture all the regression information of the censored survival phenotype given both genomic and clinical data, and are employed as covariates in the subsequent survival model formulation. A case study of diffuse large-B-cell lymphoma data, as well as Monte Carlo simulations, both demonstrate that the proposed integrative modeling improves the prediction accuracy, delivering predictions more accurate than those achieved by using either clinical data or molecular predictors alone.     

In vivo serial MRI-based models and statistical methods to quantify sensitivity and specificity of mechanical predictors for carotid plaque rupture: location and beyond

It has been hypothesized that mechanical risk factors may be used to predict future atherosclerotic plaque rupture. Truly predictive methods for plaque rupture and methods to identify the best predictor(s) from all the candidates are lacking in the literature. A novel combination of computational and statistical models based on serial magnetic resonance imaging (MRI) was introduced to quantify sensitivity and specificity of mechanical predictors to identify the best candidate for plaque rupture site prediction. Serial in vivo MRI data of carotid plaque from one patient was acquired with follow-up scan showing ulceration. 3D computational fluid-structure interaction (FSI) models using both baseline and follow-up data were constructed and plaque wall stress (PWS) and strain (PWSn) and flow maximum shear stress (FSS) were extracted from all 600 matched nodal points (100 points per matched slice, baseline matching follow-up) on the lumen surface for analysis. Each of the 600 points was marked "ulcer" or "nonulcer" using follow-up scan. Predictive statistical models for each of the seven combinations of PWS, PWSn, and FSS were trained using the follow-up data and applied to the baseline data to assess their sensitivity and specificity using the 600 data points for ulcer predictions. Sensitivity of prediction is defined as the proportion of the true positive outcomes that are predicted to be positive. Specificity of prediction is defined as the proportion of the true negative outcomes that are correctly predicted to be negative. Using probability 0.3 as a threshold to infer ulcer occurrence at the prediction stage, the combination of PWS and PWSn provided the best predictive accuracy with (sensitivity, specificity)?=?(0.97, 0.958). Sensitivity and specificity given by PWS, PWSn, and FSS individually were (0.788, 0.968), (0.515, 0.968), and (0.758, 0.928), respectively. The proposed computational-statistical process provides a novel method and a framework to assess the sensitivity and specificity of various risk indicators and offers the potential to identify the optimized predictor for plaque rupture using serial MRI with follow-up scan showing ulceration as the gold standard for method validation. While serial MRI data with actual rupture are hard to acquire, this single-case study suggests that combination of multiple predictors may provide potential improvement to existing plaque assessment schemes. With large-scale patient studies, this predictive modeling process may provide more solid ground for rupture predictor selection strategies and methods for image-based plaque vulnerability assessment.     

Variable selection in nonlinear function-on-scalar regression

We develop a new method for variable selection in a nonlinear additive function-on-scalar regression (FOSR) model. Existing methods for variable selection in FOSR have focused on the linear effects of scalar predictors, which can be a restrictive assumption in the presence of multiple continuously measured covariates. We propose a computationally efficient approach for variable selection in existing linear FOSR using functional principal component scores of the functional response and extend this framework to a nonlinear additive function-on-scalar model. The proposed method provides a unified and flexible framework for variable selection in FOSR, allowing nonlinear effects of the covariates. Numerical analysis using simulation study illustrates the advantages of the proposed method over existing variable selection methods in FOSR even when the underlying covariate effects are all linear. The proposed procedure is demonstrated on accelerometer data from the 2003–2004 cohorts of the National Health and Nutrition Examination Survey (NHANES) in understanding the association between diurnal patterns of physical activity and demographic, lifestyle, and health characteristics of the participants.     

Rate matrices for analyzing large families of protein sequences.

We propose and study a new approach for the analysis of families of protein sequences. This method is related to the LogDet distances used in phylogenetic reconstructions; it can be viewed as an attempt to embed these distances into a multidimensional framework. The proposed method starts by associating a Markov matrix to each pairwise alignment deduced from a given multiple alignment. The central objects under consideration here are matrix-valued logarithms L of these Markov matrices, which exist under conditions that are compatible with fairly large divergence between the sequences. These logarithms allow us to compare data from a family of aligned proteins with simple models (in particular, continuous reversible Markov models) and to test the adequacy of such models. If one neglects fluctuations arising from the finite length of sequences, any continuous reversible Markov model with a single rate matrix Q over an arbitrary tree predicts that all the observed matrices L are multiples of Q. Our method exploits this fact, without relying on any tree estimation. We test this prediction on a family of proteins encoded by the mitochondrial genome of 26 multicellular animals, which include vertebrates, arthropods, echinoderms, molluscs, and nematodes. A principal component analysis of the observed matrices L shows that a single rate model can be used as a rough approximation to the data, but that systematic deviations from any such model are unmistakable and related to the evolutionary history of the species under consideration.     

Analysis of Genome-Wide Association Studies with Multiple Outcomes Using Penalization

Genome-wide association studies have been extensively conducted, searching for markers for biologically meaningful outcomes and phenotypes. Penalization methods have been adopted in the analysis of the joint effects of a large number of SNPs (single nucleotide polymorphisms) and marker identification. This study is partly motivated by the analysis of heterogeneous stock mice dataset, in which multiple correlated phenotypes and a large number of SNPs are available. Existing penalization methods designed to analyze a single response variable cannot accommodate the correlation among multiple response variables. With multiple response variables sharing the same set of markers, joint modeling is first employed to accommodate the correlation. The group Lasso approach is adopted to select markers associated with all the outcome variables. An efficient computational algorithm is developed. Simulation study and analysis of the heterogeneous stock mice dataset show that the proposed method can outperform existing penalization methods.     

A Joint Location-Scale Test Improves Power to Detect Associated SNPs,Gene Sets,and Pathways

Gene-based, pathway, and other multivariate association methods are motivated by the possibility of GxG and GxE interactions; however, accounting for such interactions is limited by the challenges associated with adequate modeling information. Here we propose an easy-to-implement joint location-scale (JLS) association testing framework for single-variant and multivariate analysis that accounts for interactions without explicitly modeling them. We apply the JLS method to a gene-set analysis of cystic fibrosis (CF) lung disease, which is influenced by multiple environmental and genetic factors. We identify and replicate an association between the constituents of the apical plasma membrane and CF lung disease (p = 0.0099 and p = 0.0180, respectively) and highlight a role for the SLC9A3-SLC9A3R1/2-EZR complex in contributing to CF lung disease. Many association studies could benefit from re-analysis with the JLS method that leverages complex genetic architecture for SNP, gene, and pathway identification. Analytical verification, simulation, and additional proof-of-principle applications support our approach.     

Nonlinear modeling and adaptive monitoring with fuzzy and multivariate statistical methods in biological wastewater treatment plants

A new approach to nonlinear modeling and adaptive monitoring using fuzzy principal component regression (FPCR) is proposed and then applied to a real wastewater treatment plant (WWTP) data set. First, principal component analysis (PCA) is used to reduce the dimensionality of data and to remove collinearity. Second, the adaptive credibilistic fuzzy-c-means method is used to appropriately monitor diverse operating conditions based on the PCA score values. Then a new adaptive discrimination monitoring method is proposed to distinguish between a large process change and a simple fault. Third, a FPCR method is proposed, where the Takagi-Sugeno-Kang (TSK) fuzzy model is employed to model the relation between the PCA score values and the target output to avoid the over-fitting problem with original variables. Here, the rule bases, the centers and the widths of TSK fuzzy model are found by heuristic methods. The proposed FPCR method is applied to predict the output variable, the reduction of chemical oxygen demand in the full-scale WWTP. The result shows that it has the ability to model the nonlinear process and multiple operating conditions and is able to identify various operating regions and discriminate between a sustained fault and a simple fault (or abnormalities) occurring within the process data.     

A simple approach to guide factor retention decisions when applying principal component analysis to biomechanical data

The use of principal component analysis (PCA) as a multivariate statistical approach to reduce complex biomechanical data-sets is growing. With its increased application in biomechanics, there has been a concurrent divergence in the use of criteria to determine how much the data is reduced (i.e. how many principal factors are retained). This short communication presents power equations to support the use of a parallel analysis (PA) criterion as a quantitative and transparent method for determining how many factors to retain when conducting a PCA. Monte Carlo simulation was used to carry out PCA on random data-sets of varying dimension. This process mimicked the PA procedure that would be required to determine principal component (PC) retention for any independent study in which the data-set dimensions fell within the range tested here. A surface was plotted for each of the first eight PCs, expressing the expected outcome of a PA as a function of the dimensions of a data-set. A power relationship was used to fit the surface, facilitating the prediction of the expected outcome of a PA as a function of the dimensions of a data-set. Coefficients used to fit the surface and facilitate prediction are reported. These equations enable the PA to be freely adopted as a criterion to inform PC retention. A transparent and quantifiable criterion to determine how many PCs to retain will enhance the ability to compare and contrast between studies.     

A joint fairness model with applications to risk predictions for underrepresented populations

In data collection for predictive modeling, underrepresentation of certain groups, based on gender, race/ethnicity, or age, may yield less accurate predictions for these groups. Recently, this issue of fairness in predictions has attracted significant attention, as data-driven models are increasingly utilized to perform crucial decision-making tasks. Existing methods to achieve fairness in the machine learning literature typically build a single prediction model in a manner that encourages fair prediction performance for all groups. These approaches have two major limitations: (i) fairness is often achieved by compromising accuracy for some groups; (ii) the underlying relationship between dependent and independent variables may not be the same across groups. We propose a joint fairness model (JFM) approach for logistic regression models for binary outcomes that estimates group-specific classifiers using a joint modeling objective function that incorporates fairness criteria for prediction. We introduce an accelerated smoothing proximal gradient algorithm to solve the convex objective function, and present the key asymptotic properties of the JFM estimates. Through simulations, we demonstrate the efficacy of the JFM in achieving good prediction performance and across-group parity, in comparison with the single fairness model, group-separate model, and group-ignorant model, especially when the minority group's sample size is small. Finally, we demonstrate the utility of the JFM method in a real-world example to obtain fair risk predictions for underrepresented older patients diagnosed with coronavirus disease 2019 (COVID-19).