Summary. Multitiered experiments are characterized by involving multiple randomizations, in a sense that we make explicit. We compare and contrast six types of multiple randomizations, using a wide range of examples, and discuss their use in designing experiments. We outline a system of describing the randomizations in terms of sets of objects, their associated tiers and the factor nesting, using randomization diagrams, which give a convenient and readily assimilated summary of an experiment's randomization. We also indicate how to formulate a randomization-based mixed model for the analysis of data from such experiments.

Aberrant glycosylation is a pathological alteration that is widespread in colon cancer, and usually accompanies the onset and progression of the disease. To date, the molecular mechanisms underlying aberrant glycosylation remain largely unknown. In this study, we identify somatic and germ-line mutations in the gene encoding for polypeptide N-acetylgalactosaminyltransferase 12 (GALNT12) in individuals with colon cancer. Biochemical analyses demonstrate that each of the 8 GALNT12 mutations identified inactivates the normal function of the GALNT enzyme in initiating mucin type O-linked protein glycosylation. Two of these inactivating GALNT12 mutations were identified as acquired somatic mutations in a set of 30 microsatellite stable colon tumors. Relative to background gene mutation rates, finding these somatic GALNT12 mutations was statistically significant at P < 0.001. Six additional inactivating GALNT12 mutations were detected as germ-line changes carried by patients with colon cancer; however, no inactivating variants were detected among cancer-free controls (P ‫؍‬ 0.005). Notably, in 3 of the 6 individuals harboring inactivating germ-line GALNT12 mutations, both a colon cancer and a second independent epithelial cancer had developed. These findings suggest that genetic defects in the O-glycosylation pathway in part underlie aberrant glycosylation in colon cancers, and they contribute to the development of a subset of these malignancies.cancer ͉ GALNT ͉ glycosylation

Standard factorial designs may sometimes be inadequate for experiments that aim to estimate a generalized linear model, for example, for describing a binary response in terms of several variables. A method is proposed for finding exact designs for such experiments which uses a criterion that allows for uncertainty in the link function, the linear predictor or the model parameters, together with a design search. Designs are assessed and compared by simulation of the distribution of efficiencies relative to locally optimal designs over a space of possible models. Exact designs are investigated for two applications and their advantages over factorial and central composite designs are demonstrated.

Colorectal cancer is the second most leading cause of cancer death among adult Americans. Two autosomal dominant hereditary forms of the disease, familial adenomatous polyposis and hereditary nonpolyposis colorectal cancer, together account for perhaps 5% of all cases. However, in Ϸ20% of additional colon cancer cases, the affected individuals report a family history of colon cancer in a first-degree relative. Similar familial clusters of colon cancer and early-onset colon adenomas have also been reported. To determine whether such familial aggregations arise by chance or reflect a hereditary colon cancer susceptibility, we conducted a whole genome scan to test for genetic linkage in 53 kindreds in which two or more siblings were affected by age 65 or younger with colon cancer or with advanced colon adenomas that were >1 cm in size or that showed high-grade dysplasia. In this cohort we found genetic linkage of disease (P ‫؍‬ 0.00045) to chromosomal region 9q22.2-31.2 in a pattern consistent with autosomal dominant disease alleles. These data suggest that a single locus can contribute to disease susceptibility in a subset of patients with nonsyndromic forms of familial colorectal neoplasia.colorectal cancer ͉ colon adenomas ͉ genetic linkage ͉ familial cancers C olorectal cancer is the second most leading cause of cancer death among adult Americans (1). Strongly penetrant autosomal dominant hereditary forms of the disease, familial adenomatous polyposis (FAP) and hereditary nonpolyposis colorectal cancer (HNPCC), together account for perhaps 5% of all cases (2-4). However, in Ϸ20% of additional colon cancer cases the affected individuals report a family history of colon cancer in a first-degree relative, and a genetic basis for these familial disease clusters has also been hypothesized (5).Colorectal cancers themselves develop from precursor colon adenomas (3). Thus, the inherited FAP syndrome, which is caused by inactivating mutations in the adenomatous polyposis coli (APC) gene, is marked by development of a profusion of hundreds of colon adenomas that then confer a near 100% risk of colon cancer development by an average age of 40 (2, 3). A subtler adenoma and cancer phenotype is associated with an APC I1307K polymorphism present in the Ashkenazi Jewish population (2). The APC I1307K variant DNA sequence demonstrates enhanced vulnerability to development of inactivating somatic APC mutations, resulting in a slightly less than 2-fold increased risk of colon adenoma and cancer development (2). The existence of additional disease genes associated with increased risk of developing colon adenomas and cancers is suggested by observations of an Ϸ3-fold increased risk of colon cancer among first-degree relatives of individuals who develop colon adenomas before age 60 (6), and by one study that suggested that 19% of persons in the general population might carry autosomal dominant disease alleles conferring susceptibility for colon adenoma or cancer development (7). However, more recent endoscopic-based studies have sug...