No abstract

The findings of this survey indicated a high level of untreated caries among children in Taiwan.

In molecular biology, the issue of quantifying the similarity between two biological sequences is very important. Past research has shown that word-based search tools are computationally efficient and can find some new functional similarities or dissimilarities invisible to other algorithms like FASTA. Recently, under the independent model of base composition, Wu, Burke, and Davison (1997, Biometrics 53, 1431 1439) characterized a family of word-based dissimilarity measures that defined distance between two sequences by simultaneously comparing the frequencies of all subsequences of n adjacent letters (i.e., n-words) in the two sequences. Specifically, they introduced the use of Mahalanobis distance and standardized Euclidean distance into the study of DNA sequence dissimilarity. They showed that both distances had better sensitivity and selectivity than the commonly used Euclidean distance. The purpose of this article is to extend Mahalanobis and standardized Euclidean distances to Markov chain models of base composition. In addition, a new dissimilarity measure based on Kullback-Leibler discrepancy between frequencies of all n-words in the two sequences is introduced. Applications to real data demonstrate that Kullback-Leibler discrepancy gives a better performance than Euclidean distance. Moreover, under a Markov chain model of order kQ for base composition, where kQ is the estimated order based on the query sequence, standardized Euclidean distance performs very well. Under such a model, it performs as well as Mahalanobis distance and better than Kullback-Leibler discrepancy and Euclidean distance. Since standardized Euclidean distance is drastically faster to compute than Mahalanobis distance, in a usual workstation/PC computing environment, the use of standardized Euclidean distance under the Markov chain model of order kQ of base composition is generally recommended. However, if the user is very concerned with computational efficiency, then the use of Kullback-Leibler discrepancy, which can be computed as fast as Euclidean distance, is recommended. This can significantly enhance the current technology in comparing large datasets of DNA sequences.

The algorithm SK-LD, estimate beta and simulation software are implemented in MATLAB code, and are available at http://www.stat.ncku.edu.tw/tjwu

SUMMARYThis paper presents a logistic regression procedure for the analysis of mixture data. The design of the mixture experiment is based on the simplex-lattice designs where the components represent the proportions of a mixture. i.e. each component is expressed as a fraction of the mixture with the sum equal to one. The Scheffe (1958) and Cox (1971) polynomial andBecker (1968) non-polynomial forms are used to model relationships between the expected response and individual components of the mixture. In a three components mixture it was shown that if one component is completely linear with the remaining two components, then the proper representation of such a system is the Becker non-polynomial model. An experimental data set designed to study the interrelating effects of calories from dietary fat, carbohydrate and fibre on tumour incidence is used to illustrate the analysis and the additive effect of the fibre component. Each mixture (diet) of fat. carbohydrate and fibre was administered to provide the same total caloric consumption.