Sample Size Calculation and Blinded Sample Size Recalculation in Clinical Trials Where the Treatment Effect is Measured by the Relative Risk

In clinical trials with binary endpoints, the required sample size does not depend only on the specified type I error rate, the desired power and the treatment effect but also on the overall event rate which, however, is usually uncertain. The internal pilot study design has been proposed to overcome this difficulty. Here, nuisance parameters required for sample size calculation are re-estimated during the ongoing trial and the sample size is recalculated accordingly. We performed extensive simulation studies to investigate the characteristics of the internal pilot study design for two-group superiority trials where the treatment effect is captured by the relative risk. As the performance of the sample size recalculation procedure crucially depends on the accuracy of the applied sample size formula, we firstly explored the precision of three approximate sample size formulae proposed in the literature for this situation. It turned out that the unequal variance asymptotic normal formula outperforms the other two, especially in case of unbalanced sample size allocation. Using this formula for sample size recalculation in the internal pilot study design assures that the desired power is achieved even if the overall rate is mis-specified in the planning phase. The maximum inflation of the type I error rate observed for the internal pilot study design is small and lies below the maximum excess that occurred for the fixed sample size design.     

The social class of Catholics in Scotland

The social status of people brought up as Catholics in Scotland, as measured by their occupational class, is analysed by using cross-sectional survey data gathered in 1997. The main finding is that Catholics have probably risen in social status to a greater extent than non-Catholics. The experience of Scottish Catholics seems to be distinctive, because no such patterns are found for England, and indeed in this respect Scottish Catholics more closely resemble members of non-Christian religions in England than they do English Catholics. The most likely explanation is the particular role which state-funded Catholic schools have played in Scotland, especially the system of comprehensive secondary schools that was set up after 1965. However, the analysis is suggestive rather than definitive and needs to be replicated on cohort data with larger sample sizes.     

Rank tests in the two-sample scale problem with unequal and unknown locations

The two-sample scale problem is studied in the case of unequal and unknown location parameters. The method proposed is based on the idea of Moses (1963) and it is distribution-free. The two samples are separated into random subgroups of the same sizek. It is proposed to choosek=4 and to apply the Wilconxon test or the Savage test to the ranges or sample variances of the subgroups. The asymptotic power functions of the tests are compared. For small and moderate sample sizes simulations are carried out. Relations to some other procedures, especially to the method of Compagnone and Denker (1996) are briefly discussed.     

Calculating the power or sample size for the logistic and proportional hazards models

An algorithm is presented for calculating the power for the logistic and proportional hazards models in which some of the covariates are discrete and the remainders are multivariate normal. The mean and covariance matrix of the multivariate normal covariates may depend on the discrete covariates.

The algorithm, which finds the power of the Wald test, uses the result that the information matrix can be calculated using univariate numerical integration even when there are several continuous covariates. The algorithm is checked using simulation and in certain situations gives more accurate results than current methods which are based on simple formulae. The algorithm is used to explore properties of these models, in particular, the power gain from a prognostic covariate in the analysis of a clinical trial or observational study. The methods can be extended to determine power for other generalized linear models.     

Role of social welfare in European suicide prevention

Yur'yev A, Värnik A, Värnik P, Sisask M, Leppik L. Role of social welfare in European suicide prevention The aims of this study were to assess the relationship between suicide mortality and social expenditure in 26 European countries, explore attitudes towards welfare systems and their relationship with suicide mortality, and compare attitudes towards welfare provision in Eastern and Western Europe. The World Health Organization suicide data and Organisation for Economic Co‐operation and Development social expenditure data for 1980–2005 were used. Data on attitudes towards welfare systems were taken from the European Social Survey. Differences between mean scores for attitudes in Western and Eastern European countries were calculated. Correlations between social expenditure and suicide trends were negative in most countries for both genders. Inverse correlations between attitudes towards welfare provision and suicide mortality rates were demonstrated for males only. Differences in attitudes were found between Eastern and Western European countries; for example, confidence in the welfare system was found to be stronger in Western Europe. Higher social expenditure and greater confidence in welfare provision appear to have suicide‐preventive effects.     

New Goodness-of-Fit Tests Based on Sample Quantiles

In this article power divergences statistics based on sample quantiles are transformed in order to introduce new goodness-of-fit tests. Quantiles of the distribution of proposed statistics are calculated under uniformity, normality, and exponentiality. Several power comparisons are performed to show that the new tests are generally more powerful than the original ones.     

An Empirical Analysis of Backlog,Inventory, Production,and Price Adjustments: An Application of Recursive Systems of Log-Linear Models

This article presents an empirical analysis of firms' order backlogs, inventories, production, and price adjustments to unanticipated demand shocks. The data are obtained from quarterly INSEE Business Survey Tests on firms' realizations, expectations, and appraisals of some various economic variables. The analysis is based on the formulation and the estimation of a recursive system of conditional log-linear probability models.     

Using a mixture model for multiple imputation in the presence of outliers: the 'Healthy for life' project

Summary.  We consider the problem of obtaining population-based inference in the presence of missing data and outliers in the context of estimating the prevalence of obesity and body mass index measures from the 'Healthy for life' study. Identifying multiple outliers in a multivariate setting is problematic because of problems such as masking, in which groups of outliers inflate the covariance matrix in a fashion that prevents their identification when included, and swamping, in which outliers skew covariances in a fashion that makes non-outlying observations appear to be outliers. We develop a latent class model that assumes that each observation belongs to one of K unobserved latent classes, with each latent class having a distinct covariance matrix. We consider the latent class covariance matrix with the largest determinant to form an 'outlier class'. By separating the covariance matrix for the outliers from the covariance matrices for the remainder of the data, we avoid the problems of masking and swamping. As did Ghosh-Dastidar and Schafer, we use a multiple-imputation approach, which allows us simultaneously to conduct inference after removing cases that appear to be outliers and to promulgate uncertainty in the outlier status through the model inference. We extend the work of Ghosh-Dastidar and Schafer by embedding the outlier class in a larger mixture model, consider penalized likelihood and posterior predictive distributions to assess model choice and model fit, and develop the model in a fashion to account for the complex sample design. We also consider the repeated sampling properties of the multiple imputation removal of outliers.     

当代音系理论管窥

20世纪60年代,生成音系学诞生,开始了音系研究的崭新阶段。70年代以后,非线性音系理论提出,使得音系研究更为立体。80年代以来,各种观点和流派异彩纷呈,蔚为大观。当代音系理论的出现,极大地推动了语音系统的研究,丰富了语言理论的探索。