The principles of linkage disequilibrium mapping of dichotomous diseases can be well applied to the mapping of quantitative-trait loci through the method of selective genotyping. In 1999, M. Slatkin considered a truncation selection (TS) approach. We propose in this report an extended TS approach and an extreme-rank-selection (ERS) approach. The properties of these selection approaches are studied analytically. By using a simulation study, we demonstrate that both the extended TS approach and the ERS approach provide remarkable improvements over Slatkin's original TS approach.

A general parametric estimation method which makes use of the coverage probabilities or spacings is proposed. Under some regularity conditions, it is shown that such estimators are asymptotically normal. This method generalizes the maximum spacing method of estimation that has been discussed in the literature. Furthermore, it is shown that the maximum spacing estimator is asymptotically most e cient within the subclass of spacings-based estimators under consideration.

Every January for more than 40 years, the American Cancer Society (ACS) has estimated the total number of cancer deaths that are expected to occur in the United States and individual states in the upcoming year. In a collaborative effort to improve the accuracy of the predictions, investigators from the National Cancer Institute and the ACS have developed and tested a new prediction method. The new method was used to create the mortality predictions for the first time in Cancer Statistics, 2004 and Cancer Facts & Figures 2004. The authors present a conceptual overview of the previous ACS method and the new state-space method (SSM), and they review the results of rigorous testing to determine which method provides more accurate predictions of the observed number of cancer deaths from the years 1997 to 1999. The accuracy of the methods was compared using squared deviations (the square of the predicted minus observed values) for each of the cancer sites for which predictions are published as well as for all cancer sites combined. At the national level, the squared deviations were not consistently lower for every cancer site for either method, but the average squared deviations (averaged across cancer sites, years, and sex) was substantially lower for the SSM than for the ACS method. During the period 1997 to 1999, the ACS estimates of deaths were usually greater than the observed numbers for all cancer sites combined and for several major individual cancer sites, probably because the ACS method was less sensitive to recent changes in cancer mortality rates (and associated counts) that occurred for several major cancer sites in the early and mid 1990s. The improved accuracy of the new method was particularly evident for prostate cancer, for which mortality rates changed dramatically in the late 1980s and early 1990s. At the state level, the accuracy of the two methods was comparable. Based on these results, the ACS has elected to use the new method for the annual prediction of the number of cancer deaths at the national and state levels. (CA Cancer J Clin 2004;54:30 -40.) © American Cancer Society, 2004.

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