As a typical tool to explore prognosis factors of patients suffering from a disease such as cancer, some approaches based on the proportional hazards model (Cox, 1972) have been well-known in survival analysis. However, if the approaches based on the proportional hazards model are applied to survival data of a sample in which cured individuals are included without any device or adjustment of the models, reification of the analysis results may be depart from practical meanings. Therefore, when cured individuals are included in a sample, we discuss extension of Boag's model taking account of covariates on the proportional hazards model. The extension becomes an adjustment of the proportional hazards model. An inference procedure based on the adjustment is examined in a semi-parametric procedure. We propose its semi-parametric inference procedure, an approximate approach via the EM algorithm and some estimation methods of the survival function. Adequacy and usefulness of these proposals are indicated through numerical investigations, and possibilities that some useful views can be obtained are indicated in some case studies.
Key words: Cure rate, Marginal likelihood, Partial likelihood, EM algorithm, Exact and approximate estimateIn this paper, we introduce two optimal linear discriminant functions (OLDF) using the integer programming (IP) and LP. Those are called IP-OLDF and LP-linear discriminant function. In order to evaluate these new methods with the Fisher's linear discriminant function (Fisher's method) and the quadratic discriminant function (Quadratic's methods), we had already applied these methods to the Iris data and the medical data in order to decide whether or not CPD (Cephalo Pelvic Disproportion). In this research, above results are confirmed by the 115 data sets of the 2-dimensional normal random data. We generate 2-dimensional array having 400 rows by 2 columns. The normal random numbers generated by N (0,2) are stored in the first column (variable x), N (0,1) are stored in the second column (variable y) also. This array is considered as a data such as 400 cases having 2 variables. Each 100 cases are used for the internal samples such as (G1, G2), and another 100 cases are used for the external samples such as (G3, G4) that correspond with (G1, G2). G1 and G3 are rotated from 0 degree to 90 degree such as 0, 30,45,60 and 90 degrees. G2 and G4 are added 23 sets of integers values such as (1,1). So, 115 data sets are made by the original array as the internal samples and the external samples for the discriminant analysis. IP-OLDF, LP-OLDF, Fisher's method and Quadratic's method are applied for these data sets and the miss-classify numbers of each method are analyzed by many statistical methods such as the elementary statistics, the Box-Whisker plot and the principal component analysis etc. At last, the regression model evaluates these miss-classify numbers. Those of LP, Fisher and Quadratic discriminant functions are regression by IP-OLDF. We get good regression models as follows: For the internal samples, the order of four methods is IP-OLDF < Quadratic's method < Fisher's method < LP-method. For the external samples, the order of four methods is Quadratic's method < IP-OLDF < Fisher's method < LP-method. These results are as same as t-test for the difference in the means.
The purpose of the present paper is to construct the group sequential procedure for testing sequentially the superiority and the inferiority between two treatments when a response is bivariate normal. It is based on the use of likelihood ratio method of our composite hypotheses in order to derive the statistic in the group sequential test. After the statistic is obtained, we construct the repeated confidence boundaries at each stage and the power of test by the recursive formulae of numerical integrations extended to two random variables. Then we investigate how the boundaries and the power of test are influenced by correlation coefficients through the simulations.
Key words: Repeated group significance test, Bivariate normal observations, Composite hypotheses, Likelihood ratio methodThe future planning Working Group (organized in 1997) offered the Society that we should have an Online Symposium on the Internet. According to this offer, the WG for Online event was organized and planned how to hold it. We set up the Web pages, some of which has facilities to read, write a comment directly in the pages. We asked 3 professors as ``secret'' panelers and offered to give us a kick-off comment along with our theme ``Education on Statistics''. We uploaded these comments on the Web and the participants replied to the comment and made comment-trees. In August, we asked the panelers to give a related comment against comments on the Web. Finally, we concluded this event in the 13rd Symposium of the Society, revealing all panelers. In the event, we succeeded in holding some kinds of discussions on the Web. There are, however, still a few problem with this approach.
Key words: Computer Network, World Wide Web, Education on Statistics