Hyune-Ju Kim

The identification of changes in the recent trend is an important issue in the analysis of cancer mortality and incidence data. We apply a joinpoint regression model to describe such continuous changes and use the grid-search method to fit the regression function with unknown joinpoints assuming constant variance and uncorrelated errors. We find the number of significant joinpoints by performing several permutation tests, each of which has a correct significance level asymptotically. Each p-value is found using Monte Carlo methods, and the overall asymptotic significance level is maintained through a Bonferroni correction. These tests are extended to the situation with non-constant variance to handle rates with Poisson variation and possibly autocorrelated errors. The performance of these tests are studied via simulations and the tests are applied to U.S. prostate cancer incidence and mortality rates.

We consider likelihood ratio tests to detect a change-point in simple linear regression (a) when the alternative specifies that only the intercept changes and (b) when the alternative permits the intercept and the slope to change. Approximations for the significance level are obtained under reasonably general assumptions about the empirical distribution of the independent variable. The approximations are compared with simulations in order to assess their accuracy. For the model in which only the intercept is allowed to change, a confidence region for the change-point and an approximate joint confidence region for the change-point, the difference in intercepts, and the slope are obtained by inversion of the appropriate likelihood ratio tests.

With progression of tumor growth, rats demonstrate anorexia and reduced food intake, a function of meal number and meal size. Tumor necrosis factor-alpha (TNF-alpha), a recognized anorectic agent, reacts with two different receptors (type I: 55 kDa; type II: 75 kDa). We used a dimeric, pegylated 55-kDa TNF receptor construct to test its effects on food intake, meal number, and meal size, which were continuously measured with a rat eater meter in 16 Fischer 344 male rats injected with 10(6) viable methylcholanthrene cells. When anorexia developed, rats received a subcutaneous injection of either 0.25 mg/kg body wt of soluble TNF receptor construct (study) or vehicle (tumor-bearing control). Before TNF inhibitor injection, no differences were observed in food intake, meal number, or meal size between the two groups. After the TNF inhibitor injection, study vs. control rats significantly improved food intake as a result of an increase in meal number and meal size. Rats also showed a significant improvement in body weight. These data suggest that TNF-alpha, in addition to other cytokines, contributes to the anorexia of tumor growth, probably mediated via the hypothalamus.

In this paper, we propose methods to cluster groups of two-dimensional data whose mean functions are piecewise linear into several clusters with common characteristics such as the same slopes. To fit segmented line regression models with common features for each possible cluster, we use a restricted least squares method. In implementing the restricted least squares method, we estimate the maximum number of segments in each cluster by using both the permutation test method and the Bayes information criterion method and then propose to use the Bayes information criterion to determine the number of clusters. For a more effective implementation of the clustering algorithm, we propose a measure of the minimum distance worth detecting and illustrate its use in two examples. We summarize simulation results to study properties of the proposed methods and also prove the consistency of the cluster grouping estimated with a given number of clusters. The presentation and examples in this paper focus on the segmented line regression model with the ordered values of the independent variable, which has been the model of interest in cancer trend analysis, but the proposed method can be applied to a general model with design points either ordered or unordered.