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We illustrate that the magic rectangles and magic rectangle sets are essentially constant block-sum partially balanced incomplete block designs in disguise. Further, nearly constant block-sum partially balanced incomplete block-sum designs are defined and obtained for the special class when r = 1 , λ 1 = 1 and λ 2 = 0 . It is shown that these are the best designs minimizing the corrected sum of squares due to block-sums. A short catalog of these designs is provided. Thus, these constant or nearly constant block-sum partially balanced incomplete block designs can be constructed for any number of blocks and any block sizes except 2.

Pioneer of powerful tools for sifting data and optimizing device designs. Pioneer of powerful tools for sifting data and optimizing device designs. Black and white photograph of a young C.R. Rao writing at a desk

We show that the univariate Khattree–Bahuguna measure of skewness cannot exceed thereby reducing the range of feasible values stated by original authors by a factor of two. This substantially changes the interpretation of the magnitude of this measure especially for the highly skewed data. We also show that this bound cannot be improved further. A similar change in the upper bound occurs also for the two multivariate measures of skewness defined by Khattree and Bahuguna.

Radiation has been associated with increases in noncancerous diseases. An effect of low-dose radiation on the prevalence of clinically detected glaucoma has not been previously reported. We therefore investigated the prevalence of glaucoma in A-bomb survivors and its possible association with radiation dose. A total of 1,589 people who participated in the clinical examination program for A-bomb survivors at the Radiation Effects Research Foundation (RERF) between October 2006 and September 2008 and who had reconstructed radiation doses, were recruited into this cross-sectional screening study. The prevalence of glaucoma and its dose-response relationship to A-bomb radiation were measured. Each subject underwent an initial screening consisting of an interview and ophthalmological examination. Questionable cases with any indication of ocular disease, including glaucoma, were referred to local hospitals for more comprehensive evaluation. A diagnosis of glaucoma was made based on specific optic disc appearance, perimetric results and other ocular findings. Of 1,589 eligible people, we detected 284 (17.9%) cases of glaucoma overall, including 36 (2.3%) cases of primary open-angle glaucoma with intraocular pressure levels greater than 21 mmHg, 226 (14.2%) cases of normal-tension glaucoma and 25 (1.6%) cases of primary angle-closure glaucoma. Seven glaucoma risk factors were examined as potential confounders but only two needed to be included in the final model. Binary regression using a generalized estimating equation method, with adjustment for gender, age, city, cataract surgery or diabetes mellitus, revealed an odds ratio at 1 Gy of 1.31 (95% confidence interval 1.11–1.53, P = 0.001) in the case of normal-tension glaucoma, but no association for other types of glaucoma. The prevalence of normal-tension glaucoma may increase with A-bomb radiation dose, but uncertainties associated with nonparticipation (59% participation) suggest caution in the interpretation of these results until they are confirmed by other studies.

Background: The physical, psychological, social, and spiritual quality of life (QoL) may be affected by breast cancer diagnosis and treatment, with mixed findings for psychological quality of life and cognitive ability performance. The present study aimed to evaluate QoL in women over 1 year from biopsy for a breast abnormality. Methods: Self-reported measures of physical, psychological, social, and spiritual QoL were obtained after biopsy results but prior to treatment initiation (baseline), 4 and 12 months later. CogState computerized neuropsychological screening battery also provided an evaluation of psychological QoL. Three groups of women including those with benign biopsy results, those with malignancy treated with chemotherapy, and those with malignancy not treated with chemotherapy were compared at 4 and 12 months after adjusting for baseline to isolate the effects of treatment. Additional covariates included are age, level of education, and income. Results: Benign biopsy results group included 72 women, whereas malignancy was found in 87 women of whom 33 were treated with chemotherapy and 54 without chemotherapy. At the time of diagnosis, women with cancer had worse psychological and social QoL but better spiritual QoL than those with benign biopsy results. Only CogState monitoring accuracy was worse for women with cancer compared with the controls at the time of biopsy results. After adjusting for QoL at baseline, women treated for cancer had worse physical and social QoL at 4 and 12 months later. Psychological well-being was worse for women with cancer at 4th month but improved at 1 year. No differences in cognition were found at 4 and 12 months when adjusted for baseline cognition and covariates. Discussion: Breast cancer is a traumatic life event for women, affecting psychological and social QoL domains, yet increasing spiritual QoL. Later, cancer treatment worsens physical, psychological, and social QoL compared with those without cancer. Conclusions: These findings suggest that interventions to improve psychological QoL may be especially important at the time of cancer diagnosis, while interventions to improve physical well-being are the most needed during and following cancer treatment. Support to improve social QoL is needed from the time of diagnosis into post-treatment survivorship.

Numerous investigations have been carried out in the past for the first two moments of a distribution along with its skewness and kurtosis. The interrelationship between the empirical versions of these is hardly explored beyond that between the first two. We present a new characterization of the normal distribution based on the regression function of the sample third central moment on the sample mean. The correlation between the two is further explored yielding new insights. These investigations result in certain interesting inequalities pertaining to skewness and kurtosis that are distinct from the commonly known ones.

Most multiple imputation methods for multivariate missing data have been developed for normally distributed data. However, methods may not be suitable for nonnegative and/or highly skewed data. We propose an approach by using Expectation-Maximization (EM) method based on the assumption of multivariate Lomax distribution on non-negative skewed data. Extensive simulations show that this proposed method outperforms the regular normality-based EM and k-nearest-neighbor (kNN) imputation methods under the missing completely at random (MCAR) mechanism. An application on a real-world biomedical data is then provided.

Copulas have been used in various applications in biomedical sciences and finance. We suggest copulas as the generic all-purpose transformations which can enable one to apply various standard multivariate procedures more efficiently and with better statistical properties and results. More specifically, we consider the problem of transformation of any continuous data to multivariate normality using copulas as a device for defining the transformation. Such a transformation effectively enables us to model a variety of problems involving non-normal data using the classical multivariate statistical techniques. We evaluate and illustrate various applications including those in regression, multicollinearity, principal component analysis, factor analysis, partial least square modeling and structural equation modeling where analyses using the appropriate copula transformations result in substantial improvement in implementation, interpretation, prediction as well as in the corresponding models. A great many datasets available in the literature are analyzed which amply demonstrate the power of such an approach.