Unbalanced Experimental Design Research Articles

A unified strategy to rebalance multifactorial designs with unequal group sizes: application to analysis of variance multiblock orthogonal partial least squares

BackgroundAdequately handling unbalanced groups remains one of the major challenges for the analysis of multivariate data collected from multifactorial experimental designs. While partial least squares-based methods, such as analysis of variance multiblock orthogonal partial least squares (AMOPLS), can offer better discrimination between factor levels, they can be more heavily affected by this issue, and unbalanced designs of experiments may lead to a substantial confusion of the effects. Even state-of-the-art analysis of variance (ANOVA) decomposition methodologies using general linear models (GLM) lack the ability to efficiently disentangle these sources of variation when combined with AMOPLS. ResultsA versatile solution developed as an extension of a prior rebalancing strategy is proposed for the first decomposition step based on ANOVA. This approach has the advantage of yielding an unbiased estimation of the parameters and retaining the within-group variation in the rebalanced design, while preserving the orthogonality of effect matrices, even in presence of unequal group sizes. This property is of utmost importance for model interpretation because it avoids mixing sources of variation related to the different effects in the design. A real case study involving metabolomic data from in vitro toxicological experiments was used to demonstrate the potential of this strategy to handle unequal group sizes using a supervised approach. Primary 3D rat neural cell cultures were exposed to trimethyltin following a multifactorial design of experiments involving three fixed effect factors. Significance and NoveltyThe rebalancing strategy was demonstrated as a novel and potent solution to handle unbalanced experimental designs by offering unbiased parameter estimators and orthogonal submatrices, thus avoiding confusion of the effects and facilitating model interpretation. Moreover, it can be combined with any multivariate method used for the analysis of high-dimensional data collected from multifactorial designs.

Gdaphen, R pipeline to identify the most important qualitative and quantitative predictor variables from phenotypic data

BackgroundIn individuals or animals suffering from genetic or acquired diseases, it is important to identify which clinical or phenotypic variables can be used to discriminate between disease and non-disease states, the response to treatments or sexual dimorphism. However, the data often suffers from low number of samples, high number of variables or unbalanced experimental designs. Moreover, several parameters can be recorded in the same test. Thus, correlations should be assessed, and a more complex statistical framework is necessary for the analysis. Packages already exist that provide analysis tools, but they are not found together, rendering the decision method and implementation difficult for non-statisticians.ResultWe present Gdaphen, a fast joint-pipeline allowing the identification of most important qualitative and quantitative predictor variables to discriminate between genotypes, treatments, or sex. Gdaphen takes as input behavioral/clinical data and uses a Multiple Factor Analysis (MFA) to deal with groups of variables recorded from the same individuals or anonymize genotype-based recordings. Gdaphen uses as optimized input the non-correlated variables with 30% correlation or higher on the MFA-Principal Component Analysis (PCA), increasing the discriminative power and the classifier’s predictive model efficiency. Gdaphen can determine the strongest variables that predict gene dosage effects thanks to the General Linear Model (GLM)-based classifiers or determine the most discriminative not linear distributed variables thanks to Random Forest (RF) implementation. Moreover, Gdaphen provides the efficacy of each classifier and several visualization options to fully understand and support the results as easily readable plots ready to be included in publications. We demonstrate Gdaphen capabilities on several datasets and provide easily followable vignettes.ConclusionsGdaphen makes the analysis of phenotypic data much easier for medical or preclinical behavioral researchers, providing an integrated framework to perform: (1) pre-processing steps as data imputation or anonymization; (2) a full statistical assessment to identify which variables are the most important discriminators; and (3) state of the art visualizations ready for publication to support the conclusions of the analyses. Gdaphen is open-source and freely available at https://github.com/munizmom/gdaphen, together with vignettes, documentation for the functions and examples to guide you in each own implementation.

A new approach fits multivariate genomic prediction models efficiently

BackgroundFast, memory-efficient, and reliable algorithms for estimating genomic estimated breeding values (GEBV) for multiple traits and environments are needed to make timely decisions in breeding. Multivariate genomic prediction exploits genetic correlations between traits and environments to increase accuracy of GEBV compared to univariate methods. These genetic correlations are estimated simultaneously with GEBV, because they are specific to year, environment, and management. However, estimating genetic parameters is computationally demanding with restricted maximum likelihood (REML) and Bayesian samplers, and canonical transformations or orthogonalizations cannot be used for unbalanced experimental designs.MethodsWe propose a multivariate randomized Gauss–Seidel algorithm for simultaneous estimation of model effects and genetic parameters. Two previously proposed methods for estimating genetic parameters were combined with a Gauss–Seidel (GS) solver, and were called Tilde-Hat-GS (THGS) and Pseudo-Expectation-GS (PEGS). Balanced and unbalanced experimental designs were simulated to compare runtime, bias and accuracy of GEBV, and bias and standard errors of estimates of heritabilities and genetic correlations of THGS, PEGS, and REML. Models with 10 to 400 response variables, 1279 to 42,034 genetic markers, and 5990 to 1.85 million observations were fitted.ResultsRuntime of PEGS and THGS was a fraction of REML. Accuracies of GEBV were slightly lower than those from REML, but higher than those from the univariate approach, hence THGS and PEGS exploited genetic correlations. For 500 to 600 observations per response variable, biases of estimates of genetic parameters of THGS and PEGS were small, but standard errors of estimates of genetic correlations were higher than for REML. Bias and standard errors decreased as sample size increased. For balanced designs, GEBV and estimates of genetic correlations from THGS were unbiased when only an intercept and eigenvectors of genotype scores were fitted.ConclusionsTHGS and PEGS are fast and memory-efficient algorithms for multivariate genomic prediction for balanced and unbalanced experimental designs. They are scalable for increasing numbers of environments and genetic markers. Accuracy of GEBV was comparable to REML. Estimates of genetic parameters had little bias, but their standard errors were larger than for REML. More studies are needed to evaluate the proposed methods for datasets that contain selection.

Impact of in-field soil heterogeneity on biomass and yield of winter triticale in an intensively cropped hummocky landscape under temperate climate conditions

Crop cultivation provides ecosystem services on increasingly large fields. However, the effects of in-field spatial heterogeneity on crop yields, in particular triticale, have rarely been considered. The study assess the effects of in-field soil heterogeneity and elevation on triticale grown in an intensively cropped hummocky landscape. The field was classified into three soil classes: C1, C2, and C3, based on soil texture and available water capacity (AWC), which had high, moderate, and low yield potential, respectively. Three elevations (downslope (DS), midslope (MS), and upslope (US)) were considered as the second study factor. An unbalanced experimental design was adopted with a factorial analysis of variance for data analysis. Temporal growth analysis showed that soil classes and elevation had significant effects. Generally, better growth was observed in C1 compared to that of C3. DS had a lower yield potential than that of MS and US. In addition, the interactive effect was confirmed, as triticale had poor growth and yield in C3 on the DS, but not on US. Crop physiological parameters also confirmed the differences between soil classes and elevation. Similarly, soil moisture (SM) content in the plow layer measured at different points in time and AWC over the soil profile had a positive association with growth and yield. The results confirmed that spatial differences in AWC and SM can explain spatial variability in growth and yield. The mapping approach combining soil auguring techniques with a digital elevation model could be used to subdivide fields in hummocky landscapes for determining sub-field input intensities to guide precision farming.

Lcc: an R package to estimate the concordance correlation, Pearson correlation and accuracy over time

Background and ObjectiveObservational studies and experiments in medicine, pharmacology and agronomy are often concerned with assessing whether different methods/raters produce similar values over the time when measuring a quantitative variable. This article aims to describe the statistical package lcc, for are, that can be used to estimate the extent of agreement between two (or more) methods over the time, and illustrate the developed methodology using three real examples.MethodsThe longitudinal concordance correlation, longitudinal Pearson correlation, and longitudinal accuracy functions can be estimated based on fixed effects and variance components of the mixed-effects regression model. Inference is made through bootstrap confidence intervals and diagnostic can be done via plots, and statistical tests.ResultsThe main features of the package are estimation and inference about the extent of agreement using numerical and graphical summaries. Moreover, our approach accommodates both balanced and unbalanced experimental designs or observational studies, and allows for different within-group error structures, while allowing for the inclusion of covariates in the linear predictor to control systematic variations in the response. All examples show that our methodology is flexible and can be applied to many different data types.ConclusionsThe lcc package, available on the CRAN repository, proved to be a useful tool to describe the agreement between two or more methods over time, allowing the detection of changes in the extent of agreement. The inclusion of different structures for the variance-covariance matrices of random effects and residuals makes the package flexible for working with different types of databases.

Abstract A026: Effects of values-based messaging and an ecological approach to communicate about sugar as a strategy to prevent cancer among Latinas

Abstract Introduction: An important aspect of Latino cancer prevention is reducing consumption of the sugar sweetened beverages (SSB) that account for many of the excess calories consumed and contribute to high rates of diabetes, obesity and other cancer risks. SSB consumption is powerfully influenced by social context, including targeted advertising and marketing, yet health promotion approaches focus on individual behavior, ignoring the social determinants of health (SDOH). Social justice based empowerment approaches suggest that literacy empowers people both to make better individual behavioral choices and to engage in activities that result in improved health for the overall community. Such approaches lend themselves to messaging about SDOH consistent with an ecological approach to health. Moreover, recent research in cancer communication has suggested that values-based appeals may increase receptivity to and engagement with messages, which then improve literacy and empowerment. This approach may be particularly useful for addressing disparities populations like Latinos. Aim: We tested the efficacy of messages about SDOH that invoke the values of social justice, standing up to exploitative authority, and familism, three values held strongly by young adult Latinos. We hypothesized that values-based SDOH messages would be more effective than traditional fear-based individual messaging. Methods: An unbalanced experimental design with Mexican-American women aged 18-29 (N=434). Control condition (N=73): A typical fear-based appeal on the individual harms of obesity. Experimental condition (N=361): 5 distinct values-based messages on the social determinants of obesity and diabetes. Main Outcomes: Receptivity to and acceptance of the messages. Secondary Outcomes: Public health literacy, SSB media literacy, empowerment. Analyses: Simple and multiple linear regression models accounting for the unbalanced design. Results: Consistent with hypotheses, the values-based messages communicating an ecological model of public health were more effective than the traditional fear appeal individual behavior message: Participants were more receptive to (p<.001) and accepting of (p<.01) values-based messages relative to control. Values-based messages increased SSB media literacy (p<.05) and the perceived efficacy of civic actions such as boycotting SSB (p<.05) and using social media to advocate about SDOH and sugar (p<.001). Values-based messages appear to work by engendering identification (p<.001) and activating social justice values (p<.05). Conclusion: Values-based messages about the individual harms and social causes of SSB overconsumption resonate more than the traditional health communication approach among young adult Latinas who are at increased risk of diet-related cancer. An ecological approach to cancer communication incorporating SDOH and individual behavior holds considerable promise for addressing cancer disparities among Latinos. Citation Format: Deepti Chittamuru, Susana Ramirez. Effects of values-based messaging and an ecological approach to communicate about sugar as a strategy to prevent cancer among Latinas [abstract]. In: Proceedings of the Twelfth AACR Conference on the Science of Cancer Health Disparities in Racial/Ethnic Minorities and the Medically Underserved; 2019 Sep 20-23; San Francisco, CA. Philadelphia (PA): AACR; Cancer Epidemiol Biomarkers Prev 2020;29(6 Suppl_2):Abstract nr A026.

Comparison of PARAFASCA, AComDim, and AMOPLS approaches in the multivariate GLM modelling of multi-factorial designs

Data tables from experimental designs with multiple response variables and a large number of responses with respect to the number of observations are becoming more common, particularly in the omics and chemometrics fields. Traditional multivariate modelling approaches are not suitable for this type of data and more complex approaches like ANOVA Simultaneous Component Analysis (ASCA) and ANOVA Principal Component Analysis (APCA) have been developed to analyse them. They combine a matrix decomposition based on an ANOVA model with a multivariate step, Principal Component Analysis (PCA), which is applied to each decomposed matrix.This article compares ASCA and APCA to three other and less known techniques combining ANOVA and a multivariate step: PArallel Factor - Simultaneous Component Analysis (PARAFASCA), ANOVA Common Dimensions (AComDim), and ANOVA Multi-block Orthogonal Partial Least Squares (AMOPLS). The main advantages of these three methods are their ability to explore in a single and global procedure all (or a part) of the model effects, extract automatically the most important ones, interpret them visually and quantify their respective importance and significance. Theses approaches are presented in a common framework to make their comparison easier, some enhancements are introduced and they are also extended to unbalanced experimental designs thanks to a GLM version of the matrix decomposition.The three methods are applied to a 1H NMR data set with a three-factor unbalanced experimental design. Quantitative and visual results are compared for the three techniques and show that they are all suitable for the analysis of a complex model, but differ in the type of outputs and the ease of interpretation of the results. This opens perspectives for the analysis of even more complex data, including models with random or quantitative effects.

English

Heritability is a basic genetic parameter for quantitative traits that may determine their selection generation and intensity as well as predict their selection response and efficiency in plant breeding. Estimation of heritability varies based on experimental design. The type 2 modified augmented design (MAD2) as an unbalanced experimental design, has been proposed for evaluating numerous unreplicated test genotypes with several replicated control genotypes to adjust for soil heterogeneity. Here, we define an inter-environment correlation (r_E), that is, the mean Pearson’s correlation coefficient of trait performance for test genotypes between all pairs of environments, to approximate broad-sense heritability (H^2). Computer simulation and empirical results demonstrated that r_E was consistent with H^2 estimates on a plot basis by ANOVA for non-missing data sets, and similar to those by the restricted maximum likelihood (REML)-based method for missing data sets. The r_E  method was shown to generally outperform the ANOVA- and REML-based methods.    Key words: Broad-sense heritability, analysis of variance, inter-environment correlation, modified augmented design, restricted maximum likelihood, flax.

A bootstrap-based non-parametric ANOVA method with applications to factorial microarray data

Many microarray experiments have factorial designs, but there are few statistical methods developed explicitly to handle the factorial analysis in these experiments. We propose a bootstrap-based non-parametric ANOVA (NANOVA) method and a gene classification algorithm to classify genes into different groups according to the factor effects. The proposed method encompasses one-way and two-way models, as well as balanced and unbalanced experimental designs. False discovery rate (FDR) estimation is embedded in the procedure, and the method is robust to outliers. The gene classification algorithm is based on a series of NANOVA tests. The false discovery rate of each test is carefully controlled. Gene expression pattern in each group is modeled by a different ANOVA structure. We demonstrate the performance of NANOVA using simulated and microarray data.

The use of test day models with small size of contemporary groups

IntroductionFor many years genetic evaluation of dairy cattle has been based on the analysis of 305‐day lactation milk production. Thus, to account for environmental variance, records are usually grouped in herd–year–season (HYS) classes. The 305‐day milk yield is computed on the basis of single test day records. An alternative approach to genetic evaluation is an analysis of individual test day records (P tak and S chaeffer 1993). A complete set of records contains more information than 305‐day milk yield, and, in consequence, by including the single herd–test date (HTD) effect, this approach leads to an improvement in the accuracy of genetic evaluation. Modeling the time–herd effect in this way reduces residual variance. In populations with a small herd size a number of records with no contemporaries in HTD classes could appear. It should be noted that accurate estimation and prediction in mixed linear models requires both model adequacy and respective data structure. Unfortunately, inclusion of a HTD effect when herds are small (typical situation for European cattle breeding) causes a decomposition of data structure (more unbalanced experimental design). Hence, a modification to the grouping of the records was recommended (S walve 1995; S trabel 1997).When a lactation model is used various modifications to HYS definition could be implemented to improve its adjustment to environmental effects (S chmitz et al. 1991; S trandberg and G randinson 1997; C rump et al. 1997). The definition of herd–test day class is so precise that it does not allow for a different assignment of records to classes. What could be done is to combine HTD classes within the herd by joining the consecutive records (S walve 1995) or across herds looking for records from ‘similar’ herds taken at ‘similar’ periods of time (S trabel 1997). HTD effect can also be set as random to avoid the loss of information especially when the number of single HTD classes is high (R eents et al. 1995; P& ouml; s& ouml; et al. 1996). Finally, the HTD effect can be replaced by HYS, typical for the traditional model (P tak and Żarnecki 1998).The objective of the present study was to compare animal model evaluations using test day (TD) models with different definitions of contemporary groups (CG). Evaluations based on the 305‐day lactation model were also carried out.

Sweeping, alignment and the analysis of unbalanced data

The terms sweeping and alignment refer to the same process. Sweeping/alignment is used by data analysts as a technique for describing the effects of a model factor (e.g., treatments in a randomized block design) after the effects of nuisance parameters (e.g., blocks) have been removed from the data. In this paper sweeping/alignment is used as the basis for developing tests of factors in unbalanced experimental design models. Formulas are presented for treatment effects in randomized block designs with missing observations, and for interaction and main effects in unbalanced two-way factorial designs with empty cells.

The MISER criterion for imbalance in the analysis of covariance

This paper describes a new statistical technique for comparing unbalanced experimental designs that will be modeled by the univariate analysis of covariance. We propose treating the imbalance in the design by Minimizing the Inflation of the Standard Error of a contrast (MISER). We also discuss attributing the increased variance caused by imbalance in a design to particular covariates. The effect of implementing the proposed MISER criterion is to generate a design that is sensitive to treatment effect differences. The MISER criterion is applied to a social experiment involving offering cash incentives to induce high quality young men to enlist in the U.S. Army.