There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Linear models

Piecewise polynomials or splines extend the advantages of polynomials to include greater flexibility, local effects of parameter changes and the possibility of imposing useful constraints on estimated functions. Among these constraints is monotonicity, which can be an important property in many curve estimation problems. This paper shows the virtues of monotone splines through a number of statistical applications, including response variable transformation in nonlinear regression, transformation of variables in multiple regression, principal components and canonical correlation, and the use of monotone splines to model a dose-response function and to perform item analysis. Computational and inferential issues are discussed and illustrated.

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Monotone Regression Splines in Action

The British Thoracic Society first published management guidelines for community acquired pneumonia in children in 2002 and covered available evidence to early 2000. These updated guidelines represent a review of new evidence since then and consensus clinical opinion where evidence was not found. This document incorporates material from the 2002 guidelines and supersedes the previous guideline document.

https://thorax.bmj.com/content/thoraxjnl/66/Suppl_2/ii1.full.pdf

British Thoracic Society guidelines for the management of community acquired pneumonia in children: update 2011

The purpose of the present paper is to give a simplified method of finding the density function and the moments of linear function of order statistics from uniform distribution This is done by using a relationship between a B-spline and the linear function of uniform order statistics Two examples are presented to illustrate this method Some applications of the results are also considered

Linear functions of uniform order statistics and b-splines

OBJECTIVE: The objective of this study was to study the risk factors, management protocols, and the outcome of vulvar cancer cases over a period of 10 years in a tertiary care hospital. METHODOLOGY: It is a retrospective cohort study. The hospital records of 41 patients with histologically proven vulvar cancer were studied from the Department of Obstetrics and Gynaecology and the Department of Radiotherapy (RT). The presence of risk factors, stage of disease, treatment modalities used, and disease outcomes in terms of survival were studied. The data collected were analyzed and compared with the published literature. RESULTS: The mean age for the diagnosis of vulvar cancer was 52 years and the peak incidence was seen in the age group of 50–70 years. Incidence was significantly more in multiparous ( P = 0.001) and postmenopausal women ( P = 0.007). An average of 4.1 cases were seen per year. Nearly, 97.56% of the cases were squamous cell carcinomas. Twenty cases belonged to the early stage of the disease (Stage I and II) whereas 21 cases had advanced disease (Stage III and IV). Nearly, 48.78% of the cases were primarily treated with surgery, 26.83% with RT, 7.3% with chemotherapy, and 17.07% with combined chemoradiation. Seventy-eight percent of the surgically treated cases had a mean survival of 5 years. Mean survival of 1 year was recorded in advanced disease cases. Limitation of the study was poor follow-up after treatment. CONCLUSION: Incidence of vulvar cancer is significantly high in multiparous and postmenopausal women. Conservative surgical treatment is the best option in the early stage of the disease (Stage I and II) and gives high survival rates whereas advanced disease treated with chemoradiation has a poor survival.

A cohort study of vulvar cancer over a period of 10 years and review of literature.

Angiogenesis plays an important role in cervical cancer progression. Currently among several factors known to promote angiogenesis, vascular endothelial growth factor (VEGF) is most important. To evaluate the effect of treatment on VEGF levels and their correlation with other predictive factors, pre-and post treatment levels of VEGF were estimated in cervical cancer patients. 110 cases of frank cancer and 50 controls were enrolled for the present study: 18 in Stage I, 32 in Stage II, 48 in Stage III, and 12 in Stage IV. Serum VEGF levels were estimated by ELISA in patients on the day of recruitment and post treatment follow-up at a fixed time interval of 6-8 weeks. VEGF levels were highly significant among patients as compared to controls (p = 0.001). The pre-treatment VEGF levels among different stages of the disease were marginally insignificant (p = 0.07). However, they were significantly different for (i) various grades (p < 0.001), (ii) tumor size (p = 0.026), and (iii) smoking habits (p = 0.018). Post treatment levels were highly significant, as compared to pre-treatment values (p = 0.001). The pre-treatment and post-treatment VEGF levels were associated with (i) disease stage (p = 0.002), (ii) grade (p = 0.001), and (iii) tumor size (p = 0.001). In conclusion, VEGF is a potent angiogenic factor and can be considered as an effective prognostic marker in cervical cancer.

Correlation of serum vascular endothelial growth factor with clinicopathological parameters in cervical cancer.

In many community-based surveys, multi-level sampling is inherent in the design. In the design of these studies, especially to calculate the appropriate sample size, investigators need good estimates of intra-class correlation coefficient (ICC), along with the cluster size, to adjust for variation inflation due to clustering at each level. The present study used data on the assessment of clinical vitamin A deficiency and intake of vitamin A-rich food in children in a district in India. For the survey, 16 households were sampled from 200 villages nested within eight randomly-selected blocks of the district. ICCs and components of variances were estimated from a three-level hierarchical random effects analysis of variance model. Estimates of ICCs and variance components were obtained at village and block levels. Between-cluster variation was evident at each level of clustering. In these estimates, ICCs were inversely related to cluster size, but the design effect could be substantial for large clusters. At the block level, most ICC estimates were below 0.07. At the village level, many ICC estimates ranged from 0.014 to 0.45. These estimates may provide useful information for the design of epidemiological studies in which the sampled (or allocated) units range in size from households to large administrative zones.

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Intra-class correlation estimates for assessment of vitamin A intake in children.

Background: Clinical diagnosis of neurocysticercosis (NC) is established by CT scan and MRI. However, absolute diagnosis is not possible in a fair number of cases, and serological assays are used as adjunct. Besides, CT scan and MR imaging are resource-intensive tests and not practical for screening in endemic areas. Aim: To provide a low-cost, efficient, and reproducible assay for the detection of antibodies against cysticerci. Hence we have attempted to standardize and evaluate the diagnostic utility of the cysticercus fasciolaris antigen in a Dot ELISA assay for diagnosis of NC. Setting and Design: Tertiary hospital-based, case-control series. Materials and Methods: Confirmed cases of NC diagnosed by presence of ring lesions in CT scan or MR imaging with presence of scolex were taken as positive controls (n = 50). Negative controls (n = 50) included subjects with normal CT scan studies (n = 30) and diseased controls with ring lesions in CT scan confirmed to be neurotuberculosis (n = 20). Dot ELISA was standardized and validated with commercially available ELISA (UBI, USA) using sera from the study groups. Statistical Analysis: Chi-square test was used to compare the immunodiagnostic performance of the two tests. P value less than .05 ( P Results: The Dot ELISA had a sensitivity of 88% and specificity of 74% with a positive predictive value of 77.19% and negative predictive value of 81.06%. Likelihood ratios for a positive and a negative test were 3.4 and 0.2. The sensitivity and specificity of commercial ELISA were 92% and 84% respectively. Difference between the performances of the two tests was not significant statistically. Conclusions: Dot ELISA has sensitivity and specificity comparable to ELISA for the diagnosis of NC. The test is simpler, not requiring expertise and instrumentation. Further validation of the test as a screening tool is required.

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Girdhar G. Agarwal

Papers

Linear functions of uniform order statistics and b-splines

A cohort study of vulvar cancer over a period of 10 years and review of literature.

Correlation of serum vascular endothelial growth factor with clinicopathological parameters in cervical cancer.

Intra-class correlation estimates for assessment of vitamin A intake in children.

Utility of cysticercus fasciolaris antigen in Dot ELISA for the diagnosis of neurocysticercosis.