Asymptotically efficient partial diallel crosses

Summary The asymptotic efficiency of partial diallel crosses is defined, and circulant plans having such a property are identified. In the absence of an optimal plan to suit his requirements, the breeder should opt for suggested plans to derive maximum information for given resources.     

Evaluation of circulant partial diallel crosses in maize

Summary The present study was conducted in maize (Zea mays L.) on crosses among 20 diverse parents. The materials were evaluated in four different environments for eight characters. Combining ability analysis was carried out following diallel and partial diallel crosses. The number of crosses per parent (s) varied from 3 to 19 and the results were studied to identify the critical value of s that would provide an adequate information with minimum resources. The S₅ partial diallel was as good as the S₁₉ for the detection of differences among general combining ability (GCA) effects. Even the S₃ gave adequate information in the case of characters with high heritability. However, partial diallel analysis was less efficient in detecting the differences due to specific combining ability (SCA) effects. These results varied with environments, and characters with low heritability were more prone to misinterpretation. GCA effects showed fluctuations in partial diallel analysis which were more pronounced in S₅ and S₃, particularly for characters with low heritability. The average standard error of difference between GCA effects increased with a decrease in s, with a steep slope for s < 7. The partial diallel analysis was more efficient for the estimation of the variance component of GCA than for SCA, as the estimate of SCA was biased upwards. Estimates of broad sense heritability obtained from the partial diallels agreed with the full diallel analysis better than the narrow sense estimates. Smaller partial diallels gave erratic estimates of heritability, particularly for the characters with low heritability.     

Optimal spending functions for asymmetric group sequential designs

We present optimized group sequential designs where testing of a single parameter theta is of interest. We require specification of a loss function and of a prior distribution for theta. For the examples presented, we pre-specify Type I and II error rates and minimize the expected sample size over the prior distribution for theta. Minimizing the square of sample size rather than the sample size is found to produce designs with slightly less aggressive interim stopping rules and smaller maximum sample sizes with essentially identical expected sample size. We compare optimal designs using Hwang-Shih-DeCani and Kim-DeMets spending functions to fully optimized designs not restricted by a spending function family. In the examples selected, we also examine when there might be substantial benefit gained by adding an interim analysis. Finally, we provide specific optimal asymmetric spending function designs that should be generally useful and simply applied when a design with minimal expected sample size is desired.     

Relative efficiency of North Carolina designs I and II and standard design III in three wheat crosses

Summary The efficiency of three analyses, namely, Designs I and II of Comstock and Robinson (1952) and standard Design III analysis of Kearsey and Jinks (1968), was compared in the F₂s of three wheat crosses (Norteno 67 x HD 1982, HD 1982 x Moti and Sonalika x Moti) for plant height, spikelets per spike and yield per plant. The three analyses showed a remarkable agreement in estimating the additive (D) component for all three characters in all three crosses. But, as regards the estimation of dominance ] (H) component, standard Design III analysis proved to be more efficient than the other two analyses in crosses 2 (HD 1982 x Moti) and 3 (Sonalika x Moti) for all three characters except spikelets per spike in cross 3.     

Optimal Split-plot Designs for a Mixed Model

Exact tests are given, for the usual hypotheses on split-plot models with random blocks and fixed treatment effects, considering different numbers of blocks for each level of whole-plot treatment and assuming normally distributed observations. U- and D-optimal designs are considered with respect to the tests of main effects and interactions as well as to estimation of parameters.     

Searching Optimal Designs in the Presence of Serially Correlated Errors

Based on simple updating formulaé, a computer algorithm for searching optimal designs when the errors are believed to be serially correlated in the one-dimensional situation is described. The performance of the designs found by the algorithm is compared with the optimal designs available in the literature.     

Using pooled exposure assessment to improve efficiency in case-control studies

Assays can be so expensive that interesting hypotheses become impractical to study epidemiologically. One need not, however, perform an assay for everyone providing a biological specimen. We propose pooling equal-volume aliquots from randomly grouped sets of cases and randomly grouped sets of controls, and then assaying the smaller number of pooled samples. If an effect modifier is of concern, the pooling can be done within strata defined by that variable. For covariates assessed on individuals (e.g., questionnaire data), set-based counterparts are calculated by adding the values for the individuals in each set. The pooling set then becomes the unit of statistical analysis. We show that, with appropriate specification of a set-based logistic model, standard software yields a valid estimated exposure odds ratio, provided the multiplicative formulation is correct. Pooling minimizes the depletion of irreplaceable biological specimens and can enable additional exposures to be studied economically. Statistical power suffers very little compared with the usual, individual-based analysis. In settings where high assay costs constrain the number of people an investigator can afford to study, specimen pooling can make it possible to study more people and hence improve the study's statistical power with no increase in cost.     

An Annealing Algorithm for Searching Optimal Block Designs

This paper is concerned with a computer algorithm for searching optimal block designs. The algorithm uses a technique called simulated annealing. Exchange and interchange steps are defined in a way similar to JONES and ECCLESTON (1980). Two examples are used to show the performance of the algorithm.