On the use of the variogram in checking for independence in spatial data.

The variogram is a standard tool in the analysis of spatial data, and its shape provides useful information on the form of spatial correlation that may be present. However, it is also useful to be able to assess the evidence for the presence of any spatial correlation. A method of doing this, based on an assessment of whether the true function underlying the variogram is constant, is proposed. Nonparametric smoothing of the squared differences of the observed variables, on a suitably transformed scale, is used to estimate variogram shape. A statistic based on a ratio of quadratic forms is proposed and the test is constructed by investigating the distributional properties of this statistic under the assumption of an independent Gaussian process. The power of the test is investigated. Reference bands are proposed as a graphical follow-up. An example is discussed.

Integration of estrogen and progesterone receptors with pathological and molecular prognostic factors in breast cancer patients.

In this study we have examined biopsies from women with localized primary breast cancer to investigate the prognostic performance of estrogen receptors (ER) and progesterone receptors (PR) for estimating the metastatic probability of the patients, and to explore whether discrimination gets better by combining clinicopathological and other molecular parameters into a score. This prospective study involved 205 patients with a median follow-up of 5 y. Among the evaluated clinicopathological data were: patient's age; tumor size; axillary lymph node involvement; and tumor grade. The most representative tumor samples were derived to a single laboratory for immunohistochemical evaluation of the following molecular markers: ER, PR, proliferating cell nuclear antigen (PCNA), p53 protein product, erbB-2 (HER-2/neu) oncoprotein, and P170 glycoprotein (mdrl gen product). Distant metastases (study endpoint) appeared in 19.5% (40/205) of the patients, most of these patients presented a mixture of poor, regular and good prognostic factors. Disease-free survival analysis procedures (Kaplan-Meier method) identified tumor size, axillary lymph node involvement, tumor grade, receptor status, PCNA, p53, erbB-2 and P170 as useful prognostic factors. Proportional hazard regression analysis (Cox) identified in order of importance erbB-2, tumor size, receptors status, tumor grade and PCNA as useful prognostic factors. To facilitate the evaluation of the prognostic factors, a practical and simple score system was derived. A high pathological score identified 65% of the patients that developed distant metastases, while a high molecular score was obtained in 57% of patients with metastatic disease. There was a significant improvement in the diagnosis of probability of being with distant metastases when the pathological score was combined with the molecular score, 82% of the patients with distant metastases showed an elevated combined score. Validation of this scoring system will need further larger studies (validation set as opposed to the training set used in the present study). Due to the complexity of events in cancer, the evaluation of a combination of prognostic factors should be of value to clinicians to make a more objective estimate of the prognosis of individual breast cancer patients.