The optimal method to make inferences about a linear combination of proportions

Asymptotic inferences about a linear combination of K independent binomial proportions are very frequent in applied research. Nevertheless, until quite recently research had been focused almost exclusively on cases of K≤2 (particularly on cases of one proportion and the difference of two proportions). This article focuses on cases of K>2, which have recently begun to receive more attention due to their great practical interest. In order to make this inference, there are several procedures which have not been compared: the score method (S0) and the method proposed by Martín Andrés et al. (W3) for adjusted Wald (which is a generalization of the method proposed by Price and Bonett) on the one hand and, on the other hand, the method of Zou et al. (N0) based on the Wilson confidence interval (which is a generalization of the Newcombe method). The article describes a new procedure (P0) based on the classic Peskun method, modifies the previous methods giving them continuity correction (methods S0c, W3c, N0c and P0c, respectively) and, finally, a simulation is made to compare the eight aforementioned procedures (which are selected from a total of 32 possible methods). The conclusion reached is that the S0c method is the best, although for very small samples (n i ≤ 10, ∀ i) the W3 method is better. The P0 method would be the optimal method if one needs a method which is almost never too liberal, but this entails using a method which is too conservative and which provides excessively wide CIs. The W3 and P0 methods have the additional advantage of being very easy to apply. A free programme which allows the application of the S0 and S0c methods (which are the most complex) can be obtained at http://www.ugr.es/local/bioest/Z_LINEAR_K.EXE

Simultaneous Confidence Intervals for Risk Ratios in the Many-to-One Comparisons of Proportions

For many-to-one comparisons of independent binomial proportions using their ratios, we propose the MOVER approach generalizing Fieller\u27s theorem to a ratio of proportions by obtaining variance estimates in the neighbourhood of confidence limits for each proportion. We review two existing methods of inverting Wald and score test statistics and compare their performance with the proposed MOVER approach with score limits and Jeffreys limits for single proportions. As an appropriate multiplicity adjustment incorporating correlations between risk ratios, a Dunnett critical value is computed assuming a common, constant correlation of 0.5 instead of plugging in sample correlation coefficients. The simulation results suggest that the MOVER approach has desirable operating characteristics comparable to those of the method of inverting score test statistics. The MOVER with Jeffreys limits yields the median joint coverage percentage closest to the nominal level but its intervals may be wider than the other intervals in some parameter settings

Handling Covariates in the Design of Clinical Trials

There has been a split in the statistics community about the need for taking covariates into account in the design phase of a clinical trial. There are many advocates of using stratification and covariate-adaptive randomization to promote balance on certain known covariates. However, balance does not always promote efficiency or ensure more patients are assigned to the better treatment. We describe these procedures, including model-based procedures, for incorporating covariates into the design of clinical trials, and give examples where balance, efficiency and ethical considerations may be in conflict. We advocate a new class of procedures, covariate-adjusted response-adaptive (CARA) randomization procedures that attempt to optimize both efficiency and ethical considerations, while maintaining randomization. We review all these procedures, present a few new simulation studies, and conclude with our philosophy.Comment: Published in at http://dx.doi.org/10.1214/08-STS269 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bounding Estimates of Wage Discrimination

The Blinder Oaxaca decomposition method for defining discrimination from the wage equations of two groups has had a wide degree of application. However, the implication of this measure can very dramatically depending on the definition of the non-discriminatory wage chosen for comparison. This paper uses a form of extreme bounds analysis to define the limits on the measure of discrimination that can be obtained from these decompositions. A simple application is presented to demonstrate the use of the bootstrap to define the distributions of the discrimination measure.Extreme Bounds Analysis, Discrimination, Bootstrap

Confidence Intervals for Comparison of the Squared Multiple Correlation Coefficients of Non-nested Models

Multiple linear regression analysis is used widely to evaluate how an outcome or responsevariable is related to a set of predictors. Once a final model is specified, the interpretation of predictors can be achieved by assessing the relative importance of predictors. A common approach to predictor importance is to compare the increase in squared multiple correlation for a given model when one predictor is added to the increase when another predictor is added to the same model. This thesis proposes asymmetric confidence-intervals for a difference between two correlated squared multiple correlation coefficients of non-nested models. These new proceduresare developed by recovering variance estimates needed for the difference from asymmetric confidence limits for single multiple correlation coefficients. Simulation resultsshow that the new procedure based on confidence limits obtained from the two-moment scaled central F approximation performs much better than the traditional Wald approach. Two examples are used to illustrate the methodology. The application of the procedure indominance analysis and commonality analysis is discussed