Testing noninferiority in three‐armed clinical trials based on likelihood ratio statistics

Clinical noninferiority trials with at least three groups have received much attention recently, perhaps due to the fact that regulatory agencies often require that a placebo group be evaluated along with a new experimental drug and an active control. The authors discuss likelihood ratio tests for binary endpoints and various noninferiority hypotheses. They find that, depending on the particular hypothesis, the test reduces asymptotically either to the intersection‐union test or to a test which follows asymptotically a mixture of generalized chi‐squared distributions. They investigate the performance of this asymptotic test and provide an exact modification. They show that this test considerably outperforms multiple testing methods such as the Bonferroni adjustment with respect to power. They illustrate their methods with a cancer study to compare antiemetic agents. Finally, they discuss the extension of the results to other settings, such as Gaussian endpoints.     

War demography: The impact of the 1808–09 War on the civilian population of Åland,Finland

A pre-industrial population crisis caused by a war is examined using Finnish historical records. During the War of Finland (1808–09) the Swedish military deployed on the Åland Islands helped spread infectious diseases among the civilian population. The result was a short but intense period of high mortality. This article focuses on the short-term demographic impact of this crisis. Changes in age-specific and sex-specific mortality, fertility, and nuptiality are explored. Mortality increase was notable in all age groups, although older and very young people were more severely affected. A catch-up period in fertility followed a significant decrease in the number of births. Nuptiality decreased only slightly during the war, but a marriage boom owing to frequent remarriages ensued. A projection, assuming that the crisis did not occur, indicates that Åland's population losses were never compensated.L'utilisation des actes d'état civil finlandais permet d'étudier une crise liée à la guerre dans une population pré-industrielle. Les militaires suédois, déployés sur les îles Åland pendant la guerre de 1808–1809, ont propagé dans la population civile des maladies contagieuses. Le résultat en a été une courte mais intense période de forte mortalité. Cet article est centré sur l'effet démographique à court terme de cette crise. Il explore les changements dans la mortalité selon l'âge et le sexe, la fécondité et la nuptialité. L'accroissement de la mortalité a été important dans tous les groupes d'âges, bien que les personnes très âgées et celles très jeunes aient été plus sévèrement frappées. Après une chute significative du nombre de naissances on voit apparaître une période de rattrapage de la fécondité. Quant à la nuptialité elle ne diminua que légèrement durant la guerre, qui fut suivie d'un fort accroissement des mariages dû à de nombreux remariages. Enfin une projection de la population, qui élimine l'effet de la crise, montre que les pertes d'Åland ne furent jamais compensées à l'avenir.     

Age and sex differentials in mortality during two nineteenth century population crises

The exceptionally detailed Finnish materials are used to examine age- and sex-specific mortality in different regions during the country's last famine, the Great Famine of the 1860s. This is compared with another mortality crisis, the 1808–09 War. The results show that in cases when multiple infectious diseases were responsible for elevated mortality, the increases for different age categories were, by and large, proportional to the levels prevailing during normal times. However, excess mortality showed more variability for children. Furthermore, age- and sex-specific social behaviour (specifically large-scale temporary migration) during the crisis period shaped the age patterns and sex differentials in mortality.     

Exact Tests of Significance in Higher Dimensional Tables

We describe methods used to provide an exact test of significance of the hypothesis that all factors are mutually independent of each other in 2³ and 2⁴ contingency tables. Several numerical examples demonstrate the advantages of exact tests over approximate significance levels. We give bounds on the number of tables needed to perform this exact significance test. In four or more dimensions the number of tables in this enumeration becomes astronomical with even modest sample sizes. Inverting the characteristic function of the exact distribution has proved useful in these situations.     

Multi-response permutation procedures for a priori classifications

An exact permutation test for analyzing and/or dredging multi-response data at the ordinal or higher levels is presented. The associated test statistic is based on the average distance (or any specified norm) between points within a priori disjoint subgroups of a finite population of points in an r-dimensional space (corresponding to r measured responses from each object in a finite population of objects). Alternative approximate tests based on the beta and normal distributions are provided. Two detailed examples utilizing actual social science data are considered, including comparisons of the approximate tests. An additional example describes the behavior of these tests under a variety of conditions, including extreme data configurations     

On Non-Normal Invariance Principles for Multi-Response Permutation Procedures

A non-normal invariance principle is established for a restricted class of univariate multi-response permutation procedures whose distance measure is the square of Euclidean distance. For observations from a distribution with finite second moment, the test statistic is found asymptotically to have a centered chi-squared distribution. Spectral expansions are used to determine the asymptotic distribution for more general distance measures d, and it is shown that if d(x, y) = |x — y|^u, u? 2, the asymptotic distribution is not invariant (i.e. it is dependent on the distribution of the observations).     

Robustness without rank order statistics

An alternative to conventional rank tests based on a Euclidean distance analysis space is described. Comparisons based on exact probability values among classical two-sample t-tests and the Wilcoxon–Mann–Whitney test illustrate the advantages of the Euclidean distance analysis space alternative.     

The spokane heart study: weibull regression and coronary artery disease

Coronary artery calcium is a marker of coronary artery disease and measures the progression of atherosclerosis. It is measured by electron beam computed tomography, and the measured amount of coronary artery calcium is highly skewed to the right and left censored. The distribution of coronary artery calcium appears to be Weibull. We propose a Weibull regression model and we analyze the data using these techniques. Our analysis is based on data from the Spokane Heart Study, which is a cohort of about a thousand subjects that are assessed every two years for coronary artery calcium and risk factors of coronary artery disease. The major focus of the heart study is to determine the natural history of atherosclerosis in its early phase, and we analyze the data as a cross-sectional study with 859 subjects. We would also like to highlight the use of Weibull regression techniques in situations like this, where we have extreme right skewed data. Our main emphasis will be on examining the effect of the traditional risk factors of age, gender, lipid profile (cholesterol and HDL), patient history of lipid abnormality, hypertension, and smoking, and other family history risks on coronary artery calcium. We found that the most important factors influencing the disease were age, sex, and patient history of smoking and lipid abnormality.     

Another response to professor neyman

This note is merely an additional response (cf. Mielke, 1978) to a number of statements recently made by Neyman (1977, 1980).