Plmmr: an R package to fit penalized linear mixed models for genome-wide association data with complex correlation structure

Prediction of spatial soil property information from ancillary sensor data using ordinary linear regression: Model derivations, residual assumptions and model validation tests

This paper studies linear regression models for high dimensional multi-response data with a hybrid quantum computing algorithm. We propose an intuitively appealing estimation method based on identifying the linearly independent columns in the coefficient matrix. Our method relaxes the low rank constraint in the existing literature and allows the rank to diverge with dimensions. The linearly independent columns are selected by a novel non-oracular quantum search (NQS) algorithm which is significantly faster than classical search methods implemented on electronic computers. Besides, NQS achieves a near optimal computational complexity as existing quantum search algorithms but does not require any oracle information of the solution state. We prove the proposed estimation procedure enjoys desirable theoretical properties. Intensive numerical experiments are also conducted to demonstrate the finite sample performance of the proposed method, and a comparison is made with some popular competitors. The results show that our method outperforms all of the alternative methods under various circumstances.

Exponomial forecasts of nonstationary time series

We propose a novel computational method for genomic selection that combines identical-by-state (IBS)-based Haseman-Elston (HE) regression and best linear prediction (BLP), called HE-BLP. Genomic best linear unbiased prediction (GBLUP) has been widely used in whole-genome prediction for breeding programs. To determine the total genetic variance of a training population, a linear mixed model (LMM) should be solved via restricted maximum likelihood (REML), whose computational complexity is the cube of the sample size. We proposed a novel computational method combining identical-by-state (IBS)-based Haseman-Elston (HE) regression and best linear prediction (BLP), called HE-BLP. With this method, the total genetic variance can be estimated by solving a simple HE linear regression, which has a computational complex of the sample size squared; therefore, it is suitable for large-scale genomic data, except those with which environmental effects need to be estimated simultaneously, because it does not allow for this estimation. In Monte Carlo simulation studies, the estimated heritability based on HE was identical to that based on REML, and the prediction accuracy via HE-BLP and traditional GBLUP was also quite similar when quantitative trait loci (QTLs) were randomly distributed along the genome and their effects followed a normal distribution. In addition, the kernel row number (KRN) trait in a maize IBM population was used to evaluate the performance of the two methods; the results showed similar prediction accuracy of breeding values despite slightly different estimated heritability via HE and REML, probably due to the underlying genetic architecture. HE-BLP can be a future genomic selection method choice for even larger sets of genomic data in certain special cases where environmental effects can be ignored. The software for HE regression and the simulation program is available online in the Genetic Analysis Repository (GEAR; https://github.com/gc5k/GEAR/wiki).

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.

BackgroundIdentifying variants associated with complex human traits in high-dimensional data is a central goal of genome-wide association studies. However, complicated etiologies such as gene-gene interactions are ignored by the univariate analysis usually applied in these studies. Random Forests (RF) are a popular data-mining technique that can accommodate a large number of predictor variables and allow for complex models with interactions. RF analysis produces measures of variable importance that can be used to rank the predictor variables. Thus, single nucleotide polymorphism (SNP) analysis using RFs is gaining popularity as a potential filter approach that considers interactions in high-dimensional data. However, the impact of data dimensionality on the power of RF to identify interactions has not been thoroughly explored. We investigate the ability of rankings from variable importance measures to detect gene-gene interaction effects and their potential effectiveness as filters compared to p-values from univariate logistic regression, particularly as the data becomes increasingly high-dimensional.ResultsRF effectively identifies interactions in low dimensional data. As the total number of predictor variables increases, probability of detection declines more rapidly for interacting SNPs than for non-interacting SNPs, indicating that in high-dimensional data the RF variable importance measures are capturing marginal effects rather than capturing the effects of interactions.ConclusionsWhile RF remains a promising data-mining technique that extends univariate methods to condition on multiple variables simultaneously, RF variable importance measures fail to detect interaction effects in high-dimensional data in the absence of a strong marginal component, and therefore may not be useful as a filter technique that allows for interaction effects in genome-wide data.

Model-based and model-assisted methods of survey estimation aim to improve the precision of estimators of the population total or mean relative to methods based on the nonparametric Horvitz-Thompson estimator. These methods often use a linear regression model defined in terms of auxiliary variables whose values are assumed known for all population units. Information on networks represents another form of auxiliary information that might increase the precision of these estimators, particularly if it is reasonable to assume that networked population units have similar values of the survey variable. Linear models that use networks as a source of auxiliary information include autocorrelation, disturbance, and contextual models. In this article we focus on social networks, and investigate how much of the population structure of the network needs to be known for estimation methods based on these models to be useful. In particular, we use simulation to compare the performance of the best linear unbiased predictor under a model that ignores the network with model-based estimators that incorporate network information. Our results show that incorporating network information via a contextual model seems to be the most appropriate approach. We also show that one does not need to know the full population network, but that knowledge of the partial network linking the sampled population units to the non-sampled population units is necessary. Finally, we also provide an estimator for the mean-squared error to make an informed decision about using the contextual information, as well as the results showing that this adaptive strategy leads to higher precision.

Soybean [Glycine max (L.) Merril] is one of the main crops produced worldwide, and on‐farm yields have increased considerably in the last decades in Brazil. We evaluated the genetic gain for agronomic, phenological, and end‐use quality traits in 29 cultivars in the South Region, and in 38 cultivars in the Midwest Region in Brazil, released from 1966 to 2011. Field trials were conducted in Macroregions 1, 2, and 4, in 2016–2017, 2017–2018, and 2018–2019 crop seasons. The best linear unbiased predictors (BLUP) of the cultivars were obtained for each trait using a linear model. The BLUPs were regressed with the year of release using linear and quadratic regression models. The rates of genetic gain for seed yield ranged from 11.98 to 15.31 kg ha–1 yr–1 (0.33 to 0.42% yr–1) in the South Region, and from 13.58 to 21.84 kg ha–1 yr–1 (0.47 to 0.77% yr–1) in the Midwest Region. New cultivars presented taller plants and more seed oil content, oil and protein yield, and lower seed weight, days to flowering, days to maturity, and seed protein content than old cultivars in the South Region, although with differences between the Macroregions. In the Midwest Region, new cultivars showed higher seed oil content, oil and protein yield, and lower bottom pod height and seed protein content than old cultivars. Our results showed that breeding programs have been efficient to improve soybean yield and other traits across the years, without yield plateaus in sight.

We collected 3180 records of oleic acid (C18:1) and monounsaturated fatty acid (MUFA) measured using gas chromatography (GC) and 6960 records of C18:1 and MUFA measured using near-infrared spectroscopy (NIRS) in intermuscular fat samples of Japanese Black cattle. We compared genomic prediction performance for four linear models (genomic best linear unbiased prediction [GBLUP], kinship-adjusted multiple loci [KAML], BayesC, and BayesLASSO) and five machine learning models (Gaussian kernel [GK], deep kernel [DK], random forest [RF], extreme gradient boost [XGB], and convolutional neural network [CNN]). For GC-based C18:1 and MUFA, KAML showed the highest accuracies, followed by BayesC, XGB, DK, GK, and BayesLASSO, with more than 6% gain of accuracy by KAML over GBLUP. Meanwhile, DK had the highest prediction accuracy for NIRS-based C18:1 and MUFA, but the difference in accuracies between DK and KAML was slight. For all traits, accuracies of RF and CNN were lower than those of GBLUP. The KAML extends GBLUP methods, of which marker effects are weighted, and involves only additive genetic effects; whereas machine learning methods capture non-additive genetic effects. Thus, KAML is the most suitable method for breeding of fatty acid composition in Japanese Black cattle.

Power calculation for stepped-wedge cluster randomized trials (SW-CRTs) presents unique challenges, beyond those of standard parallel cluster randomized trials, due to the need to consider temporal within cluster correlations and background period effects. To date, power calculation methods specific to SW-CRTs have primarily been developed under a linear model. When the outcome is binary, the use of a linear model corresponds to assessing a prevalence difference; yet trial analysis often employs a nonlinear link function. We propose power calculation methods for cross-sectional SW-CRTs under a logistic model fitted by generalized estimating equations. Firstly, under an exchangeable correlation structure, we show the power based on a logistic model is lower than that from assuming a linear model in the absence of period effects. We then evaluate the impact of background prevalence changes over time on power. To allow the correlation among outcomes in the same cluster to change over time and with treatment status, we generalize the methods to more complex correlation structures. Our simulation studies demonstrate that the proposed power calculation methods perform well with the model-based variance under the true correlation structure and reveal that a working independence structure can result in substantial efficiency loss, while a working exchangeable structure performs well even when the underlying correlation structure deviates from exchangeable. An extension to our methods accounts for variable cluster sizes and reveals that unequal cluster sizes have a modest impact on power. We illustrate the approaches by application to a quality of care improvement trial for acute coronary syndrome.

We develop a doubly robust estimation of generalized partial linear models for longitudinal data with dropouts. Our method extends the highly efficient aggregate unbiased estimating function approach proposed in Qu et al. (2010) to a doubly robust one in the sense that under missing at random (MAR), our estimator is consistent when either the linear conditional mean condition is satisfied or a model for the dropout process is correctly specified. We begin with a generalized linear model for the marginal mean, and then move forward to a generalized partial linear model, allowing for nonparametric covariate effect by using the regression spline smoothing approximation. We establish the asymptotic theory for the proposed method and use simulation studies to compare its finite sample performance with that of Qu's method, the complete-case generalized estimating equation (GEE) and the inverse-probability weighted GEE. The proposed method is finally illustrated using data from a longitudinal cohort study.

Multiple environment phenotypes may be utilized to implement genomic prediction in plant breeding, while it is unclear about optimal utilization strategies according to its different availability. It is necessary to assess the utilization strategies of genomic prediction models based on different availability of multiple environment phenotypes. Here, we compared the prediction accuracy of three genomic prediction models (genomic prediction model (genomic best linear unbiased prediction (GBLUP), genomic best linear unbiased prediction (GFBLUP), and multi-trait genomic best linear unbiased prediction (mtGBLUP)) which leveraged diverse information from multiple environment phenotypes using a rice dataset containing 19 agronomic traits in two disparate seasons. We found that the prediction accuracy of genomic prediction models considering multiple environment phenotypes (GFBLUP and mtGBLUP) was better than the classical genomic prediction model (GBLUP model). The deviation of prediction accuracy of between GBLUP and mtGBLUP or GFBLUP was associated with the phenotypic correlation. In summary, the genomic prediction models considering multiple environment phenotypes (GFBLUP and mtGBLUP) demonstrated better prediction accuracy. In addition, we could utilize different genomic prediction strategies according to different availability of multiple environment phenotypes.

The best linear unbiased estimator (BLUE) and the best linear unbiased predictor (BLUP) are used to estimate, respectively, the parameter vectors of fixed and random effects in linear mixed models. But, when multicollinearity problem is arised, alternative estimators and predictors to BLUE and BLUP are preferred because of bad variance property of BLUE. Commonly used prediction approaches are the ridge and Liu prediction under multicollinearityin linear mixed models and in this article, we suggest a new prediction approachto combat multicollinearity problem by expanding the Kibria–Lukman (KL) prediction approach in linear regression models to linear mixed models. We do comparisons between the KL estimator/predictor and several other estimators/predictors, namely BLUE/BLUP, ridge and Liu estimators/predictors by using the matrix mean square error criterion. We give the selection of the ridge biasing parameter. Lastly, to demonstrate the performance of our new suggested prediction approach, we make greenhouse gases data analysis and a Monte-Carlo simulation study.

India being a vegetarian country, milk is the major source of dietary bio-energy, but majority of animals are routinely being evaluated on the basis of their milk producing ability. The present study was aimed to come up with a sire evaluation methodology based on first lactation Fat Energy Corrected Milk Yield (FBE) in order to obtain an accurate and unbiased estimate of breeding value of Mehsana buffalo bulls and ranking them on the basis of their daughter's performance for future herd improvement. Data for the present study included 7825 she buffaloes in their first lactations, extended over a period of 25 years (1989 to 2013), from field progeny testing programme of Dudhsagar Research and Development Association (DURDA), Dudhsagar Dairy, Mehsana, Gujarat. The data were classified into different subclasses based on period, season, cluster and age at first calving group. The average breeding values of Mehsana buffalo bulls evaluated for FBE by least squares method (LSM), best linear unbiased prediction sire model (BLUP-SM) and best linear unbiased prediction animal model (BLUP-AM) methods were 1215.89, 1185.7 and 1185.7 kcal, respectively. BLUP-AM method had lowest error variance as compared to LSM and BLUP-SM methods of sire evaluation. This indicated that BLUP-AM was most efficient method.

Standardized Feeding Approach Mitigates Weight Loss in Infants with Congenital Heart Disease