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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.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARY A fast Fisher scoring algorithm for maximum likelihood estimation in unbalanced mixed models with nested random effects is described. The algorithm uses explicit formulae for the inverse and the determinant of the covariance matrix, given by LaMotte (1972), and avoids inversion of large matrices. Description of the algorithm concentrates on computational aspects for large sets of data. Some key words: Fisher scoring algorithm; Maximum likelihood estimation; Nested random effects; Variance component. This content downloaded from 185.44.78.115 on Tue

It is widely reported that women drink less and have a lower prevalence of drink problems than men, but the gender differences in the relationship between level of drinking and drink problems have rarely been investigated quantitatively. This paper reports results from the Medical Research Council National Survey of Health and Development (the 1946 British Cohort) when the subjects were 43 years old. Using 7-day recall for alcohol consumption and CAGE scores of 2, 3 or 4 for drink problems, it was found that the prevalence of drink problems increased with level of alcohol consumption. Women were more likely than men to report drink problems at the same level of alcohol consumption. However, this gender difference was largely accounted for by individual differences in weight of body water. Beer accounted for the excess of men's drinking over women's and the proportion of alcohol consumed as beer was inversely related to drink problems. Eighty per cent of women and 52% of men who had drink problems in the past year reported drinking less than an average of 3 U (women) or 4 U (men) a day in the past week. As drinking levels in women begin to approach those in men, rates of drink problems in women are likely to overtake those in men because of women's greater physiological sensitivity to the effects of alcohol.

SUMMARY A fast Fisher scoring algorithm for maximum likelihood estimation in unbalanced mixed models with nested random effects is described. The algorithm uses explicit formulae for the inverse and the determinant of the covariance matrix, given by LaMotte (1972), and avoids inversion of large matrices. Description of the algorithm concentrates on computational aspects for large sets of data.

factor analysis, Fisher scoring algorithm, maximum likelihood, multilevel analysis,

No abstract

A common perception about many commercially available medical treatments is that they are effective for every patient having the relevant indication and that developers have provided the regulatory authorities with evidence of such a property. We show that the standard of evidence is much lower and that the standard is appropriate only when the treatment effects are almost constant. We discuss the implications on the design and analysis of clinical trials if the standards were made to correspond with the common perception. We conclude that the evidence of positive mean treatment effect should be accompanied by evidence of limited dispersion of the effects and by a sensitivity analysis that explores the impact of the selection bias in recruitment.