A Simple Approach to Analyse Non-Orthogonal Data

The present paper deals with an alternative and simple procedure to analyse the non-orthogonal data. The procedure is general in nature but has some advantages for the non-orthogonal data due to some missing observations. The procedure is applied to (i) two way classification with unequal number of observations per cell; (ii) randomized block designs with some missing observations and (iii) balanced incomplete block designs and also illustrated with the help of numerical examples.     

Efficient two-sample designs for microarray experiments with biological replications

In the last years, biostatistical research has begun to apply linear models and design theory to develop efficient experimental designs and analysis tools for gene expression microarray data. With two-colour microarrays, direct comparisons of RNA-targets are possible and lead to incomplete block designs. In this setting, efficient designs for simple and factorial microarray experiments have mainly been proposed for technical replicates. But for biological replicates, which are crucial to obtain inference that can be generalised to a biological population, this question has only been discussed recently and is not fully solved yet. In this paper, we propose efficient designs for independent two-sample experiments using two-colour microarrays enabling biologists to measure their biological random samples in an efficient manner to draw generalisable conclusions. We give advice for experimental situations with differing group sizes and show the impact of different designs on the variance and degrees of freedom of the test statistics. The designs proposed in this paper can be evaluated using SAS PROC MIXED or S+/R lme.     

Analysis of data from incomplete block designs

This paper presents an organized solution to the problem of computing inter- and intrablock analyses of incomplete block designs, based on the modified maximum likelihood principle proposed by Patterson and Thompson (1971, Biometrika 58, 545-554). The calculations are set out to be easily programmed on a microcomputer. The method is attractive because it is simple, yet sufficiently general to handle a wide class of designs, including partially balanced incomplete block designs, designs with unequal block sizes, designs with missing values, and generally unbalanced split-plot experiments.     

Dual Designs and Their Application in Genetical Experiments

The dual of incomplete block designs has been studied with th́eir applications in genetical experiments. Partial diallel crosses (PDC) of type I have been constructed using balanced incomplete block (BIB) designs, partially balanced incomplete block (PBIB) designs and their dual designs. Simplified analysis of PDC has been presented using the dual property of these designs. List of optimal PDC having simple analysis has been given.     

A Simple Procedure for Constructing Experiment Designs with Incomplete Blocks of Sizes 2 and 3

In order to maximize control of heterogeneity within complete blocks, an experimenter could use incomplete blocks of size k = 2 or 3. In certain situations, incomplete blocks of this nature would eliminate the need for such spatial types of analyses as nearest neighbor. The intrablock efficiency factors for such designs are relatively low. However, with recovery of interblock information, FEDERER and SPEED (1987) have presented measures of design efficiency factors which demonstrate that efficiency factors approach unity for certain ratios of the intrablock and interblock variance components. Hence with recovery of interblock information, even incomplete block designs with k = 2 or 3 have relatively high efficiency factors. The reduction in the intrablock error variance over the complete block error variance in many situations will provide designs with high efficiency. A simple procedure for constructing incomplete blocks of sizes 2 and 3 is presented. It is shown how to obtain additional zero-one association confounding arrangements when v = 4 t, t an integer, and for v = pk, k ≤ p. It is indicated how to do the statistical analysis for these designs.     

Evaluation of experimental designs and spatial analyses in wheat breeding trials

Thirty-three wheat breeding trials were conducted from 1994 to 1996 in the Northern Grains Region (QLD and Northern NSW) of Australia to evaluate the influence of experimental designs and spatial analyses on the estimation of genotype effects for yield and their impact on selection decisions. The relative efficiency of the alternative designs and analyses was best measured by the average standard error of difference between line means. Both more effective designs and spatial analyses significantly improved the efficiency relative to the randomised complete block model, with the preferred model (which combined the design information and spatial trends) giving an average relative efficiency of 138% over all 33 trials. When the Czekanowski similarity coefficient was used, none of the studied models were in full agreement with the randomised complete block model in the selection of the top lines. The agreement was influenced by selection proportions. Hence, the use of these methodologies can impact on the selection decisions in plant breeding. Received: 17 December 1998 / Accepted: 29 July 1999     

A comparison of experimental designs for selection in breeding trials with nested treatment structure

Plant breeders frequently evaluate large numbers of entries in field trials for selection. Generally, the tested entries are related by pedigree. The simplest case is a nested treatment structure, where entries fall into groups or families such that entries within groups are more closely related than between groups. We found that some plant breeders prefer to plant close relatives next to each other in the field. This contrasts with common experimental designs such as the α-design, where entries are fully randomized. A third design option is to randomize in such a way that entries of the same group are separated as much as possible. The present paper compares these design options by simulation. Another important consideration is the type of model used for analysis. Most of the common experimental designs were optimized assuming that the model used for analysis has fixed treatment effects. With many entries that are related by pedigree, analysis based on a model with random treatment effects becomes a competitive alternative. In simulations, we therefore study the properties of best linear unbiased predictions (BLUP) of genetic effects based on a nested treatment structure under these design options for a range of genetic parameters. It is concluded that BLUP provides efficient estimates of genetic effects and that resolvable incomplete block designs such as the α-design with restricted or unrestricted randomization can be recommended.     

Cytopathological evaluations combined RNA and protein analyses on defined cell regions using single frozen tissue block

The co-existence of multiple cell components in tissue samples is the main obstacle for precise molecular evaluation on defined cell types. Based on morphological examination, we developed an efficient approach for paralleled RNA and protein isolations from an identical histological region in frozen tissue section. The RNA and protein samples prepared were sufficient for RT-PCR and Western blot analyses, and the results obtained were well coincident each other as well as with the corresponding parameters revealed from immunohistochemical examinations. By this way, the sampling problem caused by cell-cross contamination can be largely avoided, committing the experimental data more specific to a denned cell type. These novel methods thus allow us to use single tissue block for a comprehensive study by integration of conventional cytological evaluations with nucleic acid and protein analyses.     

Small Sample Properties of Rank Tests for Incomplete Unbalanced Designs

A rank test is presented for analysis of incomplete unbalanced designs, i.e. for designs that may have been originally planned to be either balanced or unbalanced and where some observations may be missing at random. This test is a modification of the procedure of Benard and van El-teren (1953) based on a generalization of block weights proposed by Prentice (1979). It is compared with the tests of Haux, Schumacher, and Weckesser (1984) and Rai (1987). For incomplete or unbalanced designs with more than two treatments the quadratic forms proposed by these authors are proven to be invalid for small sample sizes, except for special cases. A necessary condition is given for test statistics to be valid also for small samples.     

Construction of resolvable spatial row-column designs

Resolvable row-column designs are widely used in field trials to control variation and improve the precision of treatment comparisons. Further gains can often be made by using a spatial model or a combination of spatial and incomplete blocking components. Martin, Eccleston, and Gleeson presented some general principles for the construction of robust spatial block designs which were addressed by spatial designs based on the linear variance (LV) model. In this article we define the two-dimensional form of the LV model and investigate extensions of the Martin et al. principles for the construction of resolvable spatial row-column designs. The computer construction of efficient spatial designs is discussed and some comparisons made with designs constructed assuming an autoregressive variance structure.     

Report on the Infinium 450k Methylation Array Analysis Workshop: April 20, 2012 UCL,London, UK

A new platform for DNA methylome analysis is Illumina''s Infinium HumanMethylation450. This technology is an extension of the previous HumanMethylation27 BeadChip and allows the methylation status of 12 samples per chip and 4 to 8 chips (total of 48 to 96 samples) to be assessed simultaneously for more than 480,000 cytosines across the genome. The platform incorporates two different probe types using different assay designs (InfiniumI and InfiniumII). Although this has allowed the assessment of more CpG sites, it has also introduced technical variation between the two probe types, which has complicated the analysis process. Many groups are working on normalization methods and analysis pipelines while many others are struggling to make sense of their new data sets. This motivated the organization of a meeting held at University College London that focused solely on the analysis methods and problems related to this new platform. The meeting was attended by 125 computational and bench scientists from 11 countries. There were 10 speakers, a small poster session and a discussion session.     

Report on the Infinium 450k Methylation Array Analysis Workshop

A new platform for DNA methylome analysis is Illumina's Infinium HumanMethylation450. This technology is an extension of the previous HumanMethylation27 BeadChip and allows the methylation status of 12 samples per chip and 4 to 8 chips (total of 48 to 96 samples) to be assessed simultaneously for more than 480,000 cytosines across the genome. The platform incorporates two different probe types using different assay designs (InfiniumI and InfiniumII). Although this has allowed the assessment of more CpG sites, it has also introduced technical variation between the two probe types, which has complicated the analysis process. Many groups are working on normalization methods and analysis pipelines while many others are struggling to make sense of their new data sets. This motivated the organization of a meeting held at University College London that focused solely on the analysis methods and problems related to this new platform. The meeting was attended by 125 computational and bench scientists from 11 countries. There were 10 speakers, a small poster session and a discussion session.     

Data-dependent permutation techniques for the analysis of ecological data

Two distribution-free permutation techniques are described for the analysis of ecological data. These methods are completely data dependent and provide analyses for the commonly-encountered completely-randomized and randomized-block designs in a multivariate framework. Euclidean distance forms the basis of both techniques, providing consistency with the observed distribution of data in many ecological studies.Abbreviations MRPP= Multiresponse permutation procedure - MRBP= Ibid, randomized block analog     

On the Construction of Balanced and Partially Balanced Ternary Design

A method of constructing balanced and partially balanced ternary designs from balanced and partially balanced incomplete block designs, respectively, and two methods of constructing partially balanced ternary designs from association schemes are obtained. Two new and efficient balanced ternary designs having K < V and R ≦ 20 are obtained by the first method.     

Construction of Partially Balanced Incomplete Block Designs with Nested Rows and Columns

A number of methods of construction of partially balanced incomplete block designs with nested rows and columns are developed and new balanced incomplete block designs with nested rows and columns are obtained as a by-product.     

Advantage of single-trial models for response to selection in wheat breeding multi-environment trials

An investigation was conducted to evaluate the impact of experimental designs and spatial analyses (single-trial models) of the response to selection for grain yield in the northern grains region of Australia (Queensland and northern New South Wales). Two sets of multi-environment experiments were considered. One set, based on 33 trials conducted from 1994 to 1996, was used to represent the testing system of the wheat breeding program and is referred to as the multi-environment trial (MET). The second set, based on 47 trials conducted from 1986 to 1993, sampled a more diverse set of years and management regimes and was used to represent the target population of environments (TPE). There were 18 genotypes in common between the MET and TPE sets of trials. From indirect selection theory, the phenotypic correlation coefficient between the MET and TPE single-trial adjusted genotype means [r _p(MT)] was used to determine the effect of the single-trial model on the expected indirect response to selection for grain yield in the TPE based on selection in the MET. Five single-trial models were considered: randomised complete block (RCB), incomplete block (IB), spatial analysis (SS), spatial analysis with a measurement error (SSM) and a combination of spatial analysis and experimental design information to identify the preferred (PF) model. Bootstrap-resampling methodology was used to construct multiple MET data sets, ranging in size from 2 to 20 environments per MET sample. The size and environmental composition of the MET and the single-trial model influenced the r _p(MT). On average, the PF model resulted in a higher r _p(MT) than the IB, SS and SSM models, which were in turn superior to the RCB model for MET sizes based on fewer than ten environments. For METs based on ten or more environments, the r _p(MT) was similar for all single-trial models.Communicated by H.C. Becker     

A distribution model for heritability.

A regression model to predict quantiles of narrow sense individual and family mean heritabilities is developed and used to predict confidence intervals either directly or via a generalized beta distribution model. Extensive simulations of balanced sib analysis trials in randomized complete block designs and normal distributed environmental and additive genetic effects confirmed that heritabilities follow a beta distribution even in cases with up to 10% of the data missing at random. The new model is both more accurate and more precise than commonly used alternatives based on "exact" chi 2 distributions and Satterthwaites approximations to the degrees of freedom. Estimates of the expected heritability and a Taylor approximation of the standard error of the heritability are needed as input to the quantile model. Applications of the presented models for estimating confidence intervals and as an aid in the design of experiments are provided.     

Utilization of chlorhexidine gluconate to evaluate a nonhuman primate skin-degerming model

We have developed a nonhuman skin-degerming model to predict the in vivo effectiveness of topical antimicrobial formulations. The model incorporates a balanced, randomized, complete block design and uses the hands of anesthetized cynomolgus monkeys as treatment sites to measure product effectiveness. Two different 4% chlorhexidine gluconate formulations were evaluated in the primate model and then retested in a human skin-degerming model of identical design. Statistical analysis of the data revealed no significant differences between the two models with regard to the response exhibited by each to the test formulations.     

Flexible design for following up positive findings

As more population-based studies suggest associations between genetic variants and disease risk, there is a need to improve the design of follow-up studies (stage II) in independent samples to confirm evidence of association observed at the initial stage (stage I). We propose to use flexible designs developed for randomized clinical trials in the calculation of sample size for follow-up studies. We apply a bootstrap procedure to correct the effect of regression to the mean, also called "winner's curse," resulting from choosing to follow up the markers with the strongest associations. We show how the results from stage I can improve sample size calculations for stage II adaptively. Despite the adaptive use of stage I data, the proposed method maintains the nominal global type I error for final analyses on the basis of either pure replication with the stage II data only or a joint analysis using information from both stages. Simulation studies show that sample-size calculations accounting for the impact of regression to the mean with the bootstrap procedure are more appropriate than is the conventional method. We also find that, in the context of flexible design, the joint analysis is generally more powerful than the replication analysis.