Distance-decay equations of antibiotic resistance genes across freshwater reservoirs.

Distance-decay (DD) equations can discern the biogeographical pattern of organisms and genes in a better way with advanced statistical methods. Here, we developed a data Compilation, Arrangement, and Statistics framework to advance quantile regression (QR) into the generation of DD equations for antibiotic resistance genes (ARGs) across various spatial scales using freshwater reservoirs as an illustration. We found that QR is superior at explaining dissemination potential of ARGs to the traditionally used least squares regression (LSR). This is because our model is based on the 'law of limiting factors', which reduces influence of unmeasured factors that reduce the efficacy of the LSR method. DD equations generated from the 99th QR model for ARGs were 'Sall = 90.03e-0.01Dall' in water and 'Sall = 92.31e-0.011Dall' in sediment. The 99th QR model was less impacted by uneven sample sizes, resulting in a better quantification of ARGs dissemination. Within an individual reservoir, the 99th QR model demonstrated that there is no dispersal limitation of ARGs at this smaller spatial scale. The QR method not only allows for construction of robust DD equations that better display dissemination of organisms and genes across ecosystems, but also provides new insights into the biogeography exhibited by key parameters, as well as the interactions between organisms and environment.

A Bayesian quantile joint modeling of multivariate longitudinal and time-to-event data.

Linear mixed models are traditionally used for jointly modeling (multivariate) longitudinal outcomes and event-time(s). However, when the outcomes are non-Gaussian a quantile regression model is more appropriate. In addition, in the presence of some time-varying covariates, it might be of interest to see how the effects of different covariates vary from one quantile level (of outcomes) to the other, and consequently how the event-time changes across different quantiles. For such analyses linear quantile mixed models can be used, and an efficient computational algorithm can be developed. We analyze a dataset from the Acute Lymphocytic Leukemia (ALL) maintenance study conducted by Tata Medical Center, Kolkata. In this study, the patients suffering from ALL were treated with two standard drugs (6MP and MTx) for the first two years, and three biomarkers (e.g. lymphocyte count, neutrophil count and platelet count) were longitudinally measured. After treatment the patients were followed nearly for the next three years, and the relapse-time (if any) for each patient was recorded. For this dataset we develop a Bayesian quantile joint model for the three longitudinal biomarkers and time-to-relapse. We consider an Asymmetric Laplace Distribution (ALD) for each outcome, and exploit the mixture representation of the ALD for developing a Gibbs sampler algorithm to estimate the regression coefficients. Our proposed model allows different quantile levels for different biomarkers, but still simultaneously estimates the regression coefficients corresponding to a particular quantile combination. We infer that a higher lymphocyte count accelerates the chance of a relapse while a higher neutrophil count and a higher platelet count (jointly) reduce it. Also, we infer that across (almost) all quantiles 6MP reduces the lymphocyte count, while MTx increases the neutrophil count. Simulation studies are performed to assess the effectiveness of the proposed approach.

A Bayesian joint model for multivariate longitudinal and time-to-event data with application to ALL maintenance studies.

The most common type of cancer diagnosed among children is the Acute Lymphocytic Leukemia (ALL). A study was conducted by Tata Translational Cancer Research Center (TTCRC) Kolkata, in which 236 children (diagnosed as ALL patients) were treated for the first two years (approximately) with two standard drugs (6MP and MTx) and were then followed nearly for the next 3 years. The goal is to identify the longitudinal biomarkers that are associated with time-to-relapse, and also to assess the effectiveness of the drugs. We develop a Bayesian joint model in which a linear mixed model is used to jointly model three biomarkers (i.e. white blood cell count, neutrophil count, and platelet count) and a semi-parametric proportional hazards model is used to model the time-to-relapse. Our proposed joint model can assess the effects of different covariates on the progression of the biomarkers, and the effects of the biomarkers (and the covariates) on time-to-relapse. In addition, the proposed joint model can impute the missing longitudinal biomarkers efficiently. Our analysis shows that the white blood cell (WBC) count is not associated with time-to-relapse, but the neutrophil count and the platelet count are significantly associated with it. We also infer that a lower dose of 6MP and a higher dose of MTx jointly result in a lower relapse probability in the follow-up period. Interestingly, we find that relapse probability is the lowest for the patients classified into the "high-risk" group at presentation. The effectiveness of the proposed joint model is assessed through the extensive simulation studies.

A Bayesian joint model for multivariate longitudinal and time-to-event data with application to ALL maintenance studies.

The most common type of cancer diagnosed among children is the acute lymphocytic leukemia (ALL). A study was conducted by Tata Translational Cancer Research Center (TTCRC) Kolkata, in which 236 children (diagnosed as ALL patients) were treated for the first two years (approximately) with two standard drugs (6MP and MTx) and were then followed nearly for the next three years. The goal is to identify the longitudinal biomarkers that are associated with time-to-relapse, and also to assess the effectiveness of the drugs. We develop a Bayesian joint model in which a linear mixed model is used to jointly model three biomarkers (i.e. white blood cell count, neutrophil count, and platelet count) and a semi-parametric proportional hazards model is used to model the time-to-relapse. Our proposed joint model can assess the effects of different covariates on the progression of the biomarkers, and the effects of the biomarkers (and the covariates) on time-to-relapse. In addition, the proposed joint model can impute the missing longitudinal biomarkers efficiently. Our analysis shows that the white blood cell (WBC) count is not associated with time-to-relapse, but the neutrophil count and the platelet count are significantly associated with it. We also infer that a lower dose of 6MP and a higher dose of MTx jointly result in a lower relapse probability in the follow-up period. Interestingly, we find that relapse probability is the lowest for the patients classified into the "high-risk" group at presentation. The effectiveness of the proposed joint model is assessed through the extensive simulation studies.

Activity and toxicity of intramuscular 1000 iu/m2 polyethylene glycol-E. coli L-asparaginase in the UKALL 2003 and UKALL 2011 clinical trials.

In successive UK clinical trials (UKALL 2003, UKALL 2011) for paediatric acute lymphoblastic leukaemia (ALL), polyethylene glycol-conjugated E. coli L-asparaginase (PEG-EcASNase) 1000 iu/m2 was administered intramuscularly with risk-stratified treatment. In induction, patients received two PEG-EcASNase doses, 14 days apart. Post-induction, non-high-risk patients (Regimens A, B) received 1-2 doses in delayed intensification (DI) while high-risk Regimen C patients received 6-10 PEG-EcASNase doses, including two in DI. Trial substudies monitored asparaginase (ASNase) activity, ASNase-related toxicity and ASNase-associated antibodies (total, 1112 patients). Median (interquartile range) trough plasma ASNase activity (14 ± 2 days post dose) following first and second induction doses and first DI dose was respectively 217 iu/l (144-307 iu/l), 265 iu/l (165-401 iu/l) and 292 iu/l (194-386 iu/l); 15% (138/910) samples showed subthreshold ASNase activity (<100 iu/l) at any trough time point. Older age was associated with lower (regression coefficient -9.5; p < 0.0001) and DI time point with higher ASNase activity (regression coefficient 29.9; p < 0.0001). Clinical hypersensitivity was observed in 3.8% (UKALL 2003) and 6% (UKALL 2011) of patients, and in 90% or more in Regimen C. A 7% (10/149) silent inactivation rate was observed in UKALL 2003. PEG-EcASNase schedule in UKALL paediatric trials is associated with low toxicity but wide interpatient variability. Therapeutic drug monitoring potentially permits optimisation through individualised asparaginase dosing.

Weighted False Discovery Rate Control in Large-Scale Multiple Testing.

The use of weights provides an effective strategy to incorporate prior domain knowledge in large-scale inference. This paper studies weighted multiple testing in a decision-theoretic framework. We develop oracle and data-driven procedures that aim to maximize the expected number of true positives subject to a constraint on the weighted false discovery rate. The asymptotic validity and optimality of the proposed methods are established. The results demonstrate that incorporating informative domain knowledge enhances the interpretability of results and precision of inference. Simulation studies show that the proposed method controls the error rate at the nominal level, and the gain in power over existing methods is substantial in many settings. An application to a genome-wide association study is discussed.

A Semiparametric Bayesian Approach for Analyzing Longitudinal Data from Multiple Related Groups.

Often the biological and/or clinical experiments result in longitudinal data from multiple related groups. The analysis of such data is quite challenging due to the fact that groups might have shared information on the mean and/or covariance functions. In this article, we consider a Bayesian semiparametric approach of modeling the mean trajectories for longitudinal response coming from multiple related groups. We consider matrix stick-breaking process priors on the group mean parameters which allows information sharing on the mean trajectories across the groups. Simulation studies are performed to demonstrate the effectiveness of the proposed approach compared to the more traditional approaches. We analyze data from a one-year follow-up of nutrition education for hypercholesterolemic children with three different treatments where the children are from different age-groups. Our analysis provides more clinically useful information than the previous analysis of the same dataset. The proposed approach will be a very powerful tool for analyzing data from clinical trials and other medical experiments.

A semiparametric approach to simultaneous covariance estimation for bivariate sparse longitudinal data.

Estimation of the covariance structure for irregular sparse longitudinal data has been studied by many authors in recent years but typically using fully parametric specifications. In addition, when data are collected from several groups over time, it is known that assuming the same or completely different covariance matrices over groups can lead to loss of efficiency and/or bias. Nonparametric approaches have been proposed for estimating the covariance matrix for regular univariate longitudinal data by sharing information across the groups under study. For the irregular case, with longitudinal measurements that are bivariate or multivariate, modeling becomes more difficult. In this article, to model bivariate sparse longitudinal data from several groups, we propose a flexible covariance structure via a novel matrix stick-breaking process for the residual covariance structure and a Dirichlet process mixture of normals for the random effects. Simulation studies are performed to investigate the effectiveness of the proposed approach over more traditional approaches. We also analyze a subset of Framingham Heart Study data to examine how the blood pressure trajectories and covariance structures differ for the patients from different BMI groups (high, medium, and low) at baseline.

Statistical challenges in the analysis of dynamic traits: implications for pharmacogenomic clinics.

Analysis of dynamic traits is statistically challenging for several reasons. Since most of the dynamic traits result in irregular sparse longitudinal measurements, a unified approach for jointly modeling the mean trajectories and the underlying covariance structure is essential. When the traits are bivariate or multivariate in nature, modeling the covariance structure is really challenging. For the pharmacogenomic clinics, it is extremely important to have a comprehensive study of the whole biological system. In other words, if the traits under consideration result in some events (e.g., death, disease), then a joint analysis is required for the observed dynamic traits and the event-time. In statistics, there is a vast literature on such joint modeling using parametric, nonparametric and semiparametric approaches. In this article, we will discuss different aspects of modeling the longitudinal traits, their limitations and importance to pharmacogenomic clinics.

A Bayesian semiparametric model for bivariate sparse longitudinal data.

Mixed-effects models have recently become popular for analyzing sparse longitudinal data that arise naturally in biological, agricultural and biomedical studies. Traditional approaches assume independent residuals over time and explain the longitudinal dependence by random effects. However, when bivariate or multivariate traits are measured longitudinally, this fundamental assumption is likely to be violated because of intertrait dependence over time. We provide a more general framework where the dependence of the observations from the same subject over time is not assumed to be explained completely by the random effects of the model. We propose a novel, mixed model-based approach and estimate the error-covariance structure nonparametrically under a generalized linear model framework. We use penalized splines to model the general effect of time, and we consider a Dirichlet process mixture of normal prior for the random-effects distribution. We analyze blood pressure data from the Framingham Heart Study where body mass index, gender and time are treated as covariates. We compare our method with traditional methods including parametric modeling of the random effects and independent residual errors over time. We conduct extensive simulation studies to investigate the practical usefulness of the proposed method. The current approach is very helpful in analyzing bivariate irregular longitudinal traits.

Dynamic semiparametric Bayesian models for genetic mapping of complex trait with irregular longitudinal data.

Many phenomena of fundamental importance to biology and biomedicine arise as a dynamic curve, such as organ growth and HIV dynamics. The genetic mapping of these traits is challenged by longitudinal variables measured at irregular and possibly subject-specific time points, in which case nonnegative definiteness of the estimated covariance matrix needs to be guaranteed. We present a semiparametric approach for genetic mapping within the mixture-model setting by jointly modeling mean and covariance structures for irregular longitudinal data. Penalized spline is used to model the mean functions of individual quantitative trait locus (QTL) genotypes as latent variables, whereas an extended generalized linear model is used to approximate the covariance matrix. The parameters for modeling the mean-covariances are estimated by MCMC, using the Gibbs sampler and the Metropolis-Hastings algorithm. We derive the full conditional distributions for the mean and covariance parameters and compute Bayes factors to test the hypothesis about the existence of significant QTLs. We used the model to screen the existence of specific QTLs for age-specific change of body mass index with a sparse longitudinal data set. The new model provides powerful means for broadening the application of genetic mapping to reveal the genetic control of dynamic traits.

A Bayesian Framework for Functional Mapping through Joint Modeling of Longitudinal and Time-to-Event Data.

The most powerful and comprehensive approach of study in modern biology is to understand the whole process of development and all events of importance to development which occur in the process. As a consequence, joint modeling of developmental processes and events has become one of the most demanding tasks in statistical research. Here, we propose a joint modeling framework for functional mapping of specific quantitative trait loci (QTLs) which controls developmental processes and the timing of development and their causal correlation over time. The joint model contains two submodels, one for a developmental process, known as a longitudinal trait, and the other for a developmental event, known as the time to event, which are connected through a QTL mapping framework. A nonparametric approach is used to model the mean and covariance function of the longitudinal trait while the traditional Cox proportional hazard (PH) model is used to model the event time. The joint model is applied to map QTLs that control whole-plant vegetative biomass growth and time to first flower in soybeans. Results show that this model should be broadly useful for detecting genes controlling physiological and pathological processes and other events of interest in biomedicine.

Functional mapping of developmental processes: theory, applications, and prospects.

Functional mapping is a statistical tool for mapping quantitative trait loci (QTLs) that control the developmental pattern and process of a complex trait. Functional mapping has two significant advantages beyond traditional QTL mapping approaches. First, it integrates biological principles of trait formation into the model, enabling the biological interpretation of QTLs detected. Second, functional mapping is based on parsimonious modeling of mean-covariance structures, which enhances the statistical power of QTL detection. Here, we review the basic theory of functional mapping and describe one of its applications to plant genetics. We pinpoint several areas in which functional mapping can be integrated with systems biology to further our understanding of the genetic and genetic regulatory underpinnings of development.

Statistical models for genetic mapping in polyploids: challenges and opportunities.

Statistical methods for genetic mapping have well been developed for diploid species but are lagging in the more complex polyploids. The genetic mapping of polyploids, where genome number is higher than two, is complicated by uncertainty about the genotype-phenotype correspondence, inconsistent meiotic mechanisms, heterozygous genome structures, and increased allelic (action) and nonallelic (interaction) combinations. According to their meiotic configurations, polyploids can be classified as bivalent polyploids, in which only two chromosomes pair during meiosis at a time, and multivalent polyploids, where multiple chromosomes pair simultaneously. For some polyploids, these two types of pairing occur at the same time, leading to a mixed category. This chapter reviews several challenges due to the complexities of linkage analysis in polyploids and describes statistical models and algorithms that have been developed for linkage mapping based on their distinct meiotic characteristics. We discuss several issues that should be addressed to better understand the genome structure and organization of polyploids and the genetic architecture of complex traits for this unique group of plants.

Genome-wide association studies for bivariate sparse longitudinal data.

OBJECTIVE: Longitudinal measurements with bivariate response have been analyzed by several authors using two separate models for each response. However, for most of the biological or medical experiments, the two responses are highly correlated and hence a separate model for each response might not be a desirable way to analyze such data. A single model considering a bivariate response provides a more powerful inference as the correlation between the responses is modeled appropriately. In this article, we propose a dynamic statistical model to detect the genes controlling human blood pressure (systolic and diastolic). METHODS: By modeling the mean function with orthogonal Legendre polynomials and the covariance matrix with a stationary parametric structure, we incorporate the statistical ideas in functional genome-wide association studies to detect SNPs which have significant control on human blood pressure. The traditional false discovery rate is used for multiple comparisons. RESULTS: We analyze the data from the Framingham Heart Study to detect such SNPs by appropriately considering gender-gene interaction. We detect 8 SNPs for males and 7 for females which are most significant in controlling blood pressure. The genotype-specific mean curves and additive and dominant effects over time are shown for each significant SNP for both genders. Simulation studies are performed to examine the statistical properties of our model. The current model will be extremely useful in detecting genes controlling different traits and diseases for humans or non-human subjects.

A dynamic model for functional mapping of biological rhythms.

Functional mapping is a statistical method for mapping quantitative trait loci (QTLs) that regulate the dynamic pattern of a biological trait. This method integrates mathematical aspects of biological complexity into a mixture model for genetic mapping and tests the genetic effects of QTLs by comparing genotype-specific curve parameters. As a way of quantitatively specifying the dynamic behavior of a system, differential equations have proven to be powerful for modeling and unraveling the biochemical, molecular, and cellular mechanisms of a biological process, such as biological rhythms. The equipment of functional mapping with biologically meaningful differential equations provides new insights into the genetic control of any dynamic processes. We formulate a new functional mapping framework for a dynamic biological rhythm by incorporating a group of ordinary differential equations (ODE). The Runge-Kutta fourth order algorithm was implemented to estimate the parameters that define the system of ODE. The new model will find its implications for understanding the interplay between gene interactions and developmental pathways in complex biological rhythms.

A dynamic model for genome-wide association studies.

Although genome-wide association studies (GWAS) are widely used to identify the genetic and environmental etiology of a trait, several key issues related to their statistical power and biological relevance have remained unexplored. Here, we describe a novel statistical approach, called functional GWAS or fGWAS, to analyze the genetic control of traits by integrating biological principles of trait formation into the GWAS framework through mathematical and statistical bridges. fGWAS can address many fundamental questions, such as the patterns of genetic control over development, the duration of genetic effects, as well as what causes developmental trajectories to change or stop changing. In statistics, fGWAS displays increased power for gene detection by capitalizing on cumulative phenotypic variation in a longitudinal trait over time and increased robustness for manipulating sparse longitudinal data.

Functional mapping of reaction norms to multiple environmental signals through nonparametric covariance estimation.

BACKGROUND: The identification of genes or quantitative trait loci that are expressed in response to different environmental factors such as temperature and light, through functional mapping, critically relies on precise modeling of the covariance structure. Previous work used separable parametric covariance structures, such as a Kronecker product of autoregressive one [AR(1)] matrices, that do not account for interaction effects of different environmental factors. RESULTS: We implement a more robust nonparametric covariance estimator to model these interactions within the framework of functional mapping of reaction norms to two signals. Our results from Monte Carlo simulations show that this estimator can be useful in modeling interactions that exist between two environmental signals. The interactions are simulated using nonseparable covariance models with spatio-temporal structural forms that mimic interaction effects. CONCLUSIONS: The nonparametric covariance estimator has an advantage over separable parametric covariance estimators in the detection of QTL location, thus extending the breadth of use of functional mapping in practical settings.