Quantile dispersion graphs to compare the efficiencies of cluster randomized designs

The purpose of this article is to compare efficiencies of several cluster randomized designs using the method of quantile dispersion graphs (QDGs). A cluster randomized design is considered whenever subjects are randomized at a group level but analyzed at the individual level. A prior knowledge of the correlation existing between subjects within the same cluster is necessary to design these cluster randomized trials. Using the QDG approach, we are able to compare several cluster randomized designs without requiring any information on the intracluster correlation. For a given design, several quantiles of the power function, which are directly related to the effect size, are obtained for several effect sizes. The quantiles depend on the intracluster correlation present in the model. The dispersion of these quantiles over the space of the unknown intracluster correlation is determined, and then depicted by the QDGs. Two applications of the proposed methodology are presented.     

An efficient sequential design of clinical trials

We propose an efficient group sequential monitoring rule for clinical trials. At each interim analysis both efficacy and futility are evaluated through a specified loss structure together with the predicted power. The proposed design is robust to a wide range of priors, and achieves the specified power with a saving of sample size compared to existing adaptive designs. A method is also proposed to obtain a reduced-bias estimator of treatment difference for the proposed design. The new approaches hold great potential for efficiently selecting a more effective treatment in comparative trials. Operating characteristics are evaluated and compared with other group sequential designs in empirical studies. An example is provided to illustrate the application of the method.     

Comparison of conditional and unconditional confidence intervals for the double exponential distribution

Conditional confidence intervals for the location parameter of the double exponential distribution based on maximum likelihood estimators conditioned on a set of ancillary statistics and the corresponding unconditional confidence intervals based on the maximum likelihood estimators alone are compared in two ways. Monte Carlo techniques are used and the conditional approach appears to give slightly better results although agreement as n becomes larger is noted     

Testing parallelism of regression lines against ordered alternatives

For the problem of testing the equality of slopes of several regression lines against the alternative that the slopes are in increasing (decreasing) order of magnitude, two types of tests are proposed. These are the likelihood ratio test and a test that depends on suitable linear combination of one group statistics. Rank analogues of the two tests are also examined.     

An Adaptive Test for the Two-Sample Location Problem Based on U-Statistics

For the two-sample location problem with continuous data we consider a general class of tests, all members of it are based on U-statistics. The asymptotic efficacies are investigated in detail. We construct an adaptive test where all statistics involved are suitably chosen U-statistics. It is shown that the proposed adaptive test has good asymptotic and finite sample power properties.     

Use of the Correlation Coefficient with Normal Probability Plots

The use of the correlation coefficient is suggested as a technique for summarizing and objectively evaluating the information contained in probability plots. Goodness-of-fit tests are constructed using this technique for several commonly used plotting positions for the normal distribution. Empirical sampling methods are used to construct the null distribution for these tests, which are then compared on the basis of power against certain nonnormal alternatives. Commonly used regression tests of fit are also included in the comparisons. The results indicate that use of the plotting position p_i = (i - .375)/(n + .25) yields a competitive regression test of fit for normality.     

An Application of Matrix Power Series to Linear Models

In the system of two seemingly unrelated regressions, employing a matrix power series, we show that the two-stage estimator is better than the ordinary least square estimator (OLSE) in terms of the mean square error matrix (MSEM) criterion. The result enriches the existing literature and can be applied to many fields of applications related to economics and statistics.     

Testing of Suspected Observations in an Exponential Sample With Unknown Origin

The problem of multiple upper outliers in two-parameter exponential sample is considered. A test statistic is proposed to identify the outliers at the upper end of the sample. The null distribution of the test statistic is obtained and the critical values are found. The performance of the test is also compared with the earlier work.     

A comparison of some conditional and unconditional exact tests for 2x2 contingency tables

In 1935, R.A. Fisher published his well-known “exact” test for 2x2 contingency tables. This test is based on the conditional distribution of a cell entry when the rows and columns marginal totals are held fixed. Tocher (1950) and Lehmann (1959) showed that Fisher s test, when supplemented by randomization, is uniformly most powerful among all the unbiased tests UMPU). However, since all the practical tests for 2x2 tables are nonrandomized - and therefore biased the UMPU test is not necessarily more powerful than other tests of the same or lower size. Inthis work, the two-sided Fisher exact test and the UMPU test are compared with six nonrandomized unconditional exact tests with respect to their power. In both the two-binomial and double dichotomy models, the UMPU test is often less powerful than some of the unconditional tests of the same (or even lower) size. Thus, the assertion that the Tocher-Lehmann modification of Fisher's conditional test is the optimal test for 2x2 tables is unjustified.     

Locally best invariant test for outliers in a gamma type distribution

It is shown that the locally best invariant test for the existence of outliers for scale parameters of the gamma distribution is given by Bartholomew's test for exponentiality which is the ratio of the sum of squares of the data to the square of the sample mean. The optimality robustness, including null and nonnull robustness of the test is shown. A small simulation study to compare the power among the other eight competitive tests for testing exponentiality is performed. It is seen that the locally best invariant test is not always best but is reasonably good. It is slightly better than Cochran's test and suffers less from the limiting masking effect.