Consequences of dichotomization

Dichotomization is the transformation of a continuous outcome (response) to a binary outcome. This approach, while somewhat common, is harmful from the viewpoint of statistical estimation and hypothesis testing. We show that this leads to loss of information, which can be large. For normally distributed data, this loss in terms of Fisher's information is at least 1-2/pi (or 36%). In other words, 100 continuous observations are statistically equivalent to 158 dichotomized observations. The amount of information lost depends greatly on the prior choice of cut points, with the optimal cut point depending upon the unknown parameters. The loss of information leads to loss of power or conversely a sample size increase to maintain power. Only in certain cases, for instance, in estimating a value of the cumulative distribution function and when the assumed model is very different from the true model, can the use of dichotomized outcomes be considered a reasonable approach.     

Some extremal problems in designing discriminating experiments

This paper is devoted to some properties of local T-optimaj. designs fox discriminating between two rival regression models. It is demonstrated that the problem of searching for an optimal design is closely connected with the problem of searching for a Tchebycheff extremal basis. The question raised concerns the number of supporting points in an optimal design.     

Convex design theory 1

Bayesian fixed sample size estimation and sequential estimation of the parameters of the two parameter uniform distribution are discussed.     

Deriving Approximations in a Random Effects Model for Multicenter Clinical Trials with Binary Response

The design and analysis of multicenter trials based on a random effects model is well developed for a continuous response, but is less well developed for a binary response. Here we describe a random effects model for a binary response for two treatments and show how maximum likelihood estimates for the unknown treatment difference can be derived using a novel approximation to the likelihood. The suggested approximation is easy to use and seems to be better suited to the problem than the Laplace approximation and the approximation based on adaptive Gaussian quadratures. We also derive an approximation for the Fisher information matrix of the treatment parameters. The results extend those previously reviewed by Agresti and Hartzel (2000 Agresti , A. , Hartzel , J. ( 2000 ). Strategies for comparing treatments on a binary response with multi-centre data . Statist. Med. 19 : 1115 – 1139 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]).