Stratified analysis of correlated binary outcome data: a comparison of model dependent and robust tests of significance

Model dependent and robust test statistics constructed using a generalized estimating equations extension of logistic regression applicable to the analysis of correlated binary outcome data are shown to have relatively simple algebraic expressions in stratified analyses where all variables are measured at the cluster level These expressions are used to demonstrate the close relationship to standard procedures which assume that subjects responses are independent, to prove that the asymptotic validity of model dependent test statistics is assured if the average correlation between cluster members is constant, and that this assumption can be relaxed when there are the same number of subjects in each cluster.     

Multivariate tests comparing binomial probabilities, with application to safety studies for drugs

Summary.  In magazine advertisements for new drugs, it is common to see summary tables that compare the relative frequency of several side-effects for the drug and for a placebo, based on results from placebo-controlled clinical trials. The paper summarizes ways to conduct a global test of equality of the population proportions for the drug and the vector of population proportions for the placebo. For multivariate normal responses, the Hotelling T ²-test is a well-known method for testing equality of a vector of means for two independent samples. The tests in the paper are analogues of this test for vectors of binary responses. The likelihood ratio tests can be computationally intensive or have poor asymptotic performance. Simple quadratic forms comparing the two vectors provide alternative tests. Much better performance results from using a score-type version with a null-estimated covariance matrix than from the sample covariance matrix that applies with an ordinary Wald test. For either type of statistic, asymptotic inference is often inadequate, so we also present alternative, exact permutation tests. Follow-up inferences are also discussed, and our methods are applied to safety data from a phase II clinical trial.     

Uniformly best estimation in linear regression when prior information is fuzzy

Modeling prior information as a fuzzy set and using Zadeh’s extension principle, a general approach is presented how to rate linear affine estimators in linear regression. This general approach is applied to fuzzy prior information sets given by ellipsoidal α-cuts. Here, in an important and meaningful subclass, a uniformly best linear affine estimator can be determined explicitly. Surprisingly, such a uniformly best linear affine estimator is optimal with respect to a corresponding relative squared error approach. Two illustrative special cases are discussed, where a generalized least squares estimator on the one hand and a general ridge or Kuks–Olman estimator on the other hand turn out to be uniformly best.