When a ranking of institutions such as medical centers or universities is based on an indicator provided with a standard error, confidence intervals should be calculated to assess the quality of these ranks. We consider the problem of constructing simultaneous confidence intervals (CIs) for the ranks of centers based on an observed sample. We present a novel method based on Tukey's honest significant difference test (HSD) which is the first method to produce valid simultaneous CIs for ranks. Moreover, we introduce a new variant of Tukey's HSD based on the sequential rejection principle. The new algorithm ensures familywise error control, and produces simultaneous confidence intervals for the ranks uniformly shorter than those provided by Tukey's HSD for the same level of significance. We illustrate the method through both simulations and real data analysis from 64 hospitals in the Netherlands. Software for our new methods is available online in package ICRanks downloadable from CRAN. Supplementary materials include supplementary R code for the simulations and proofs of the propositions presented in this paper.
Summary We present a new general method for constrained likelihood ratio testing which, when few constraints are violated, improves upon the existing approach in the literature that compares the likelihood ratio with the quantile of a mixture of chi-squared distributions; the improvement is in terms of both simplicity and power. The proposed method compares the constrained likelihood ratio statistic against the quantile of only one chi-squared random variable with data-dependent degrees of freedom. The new test is shown to have a valid exact significance level $\alpha$. It also has more power than the classical approach against alternatives for which the number of violations is not large. We provide more details for testing a simple order $\mu_1\leqslant\cdots\leqslant\mu_p$ against all alternatives using the proposed approach and give clear guidelines as to when the new method would be advantageous. A simulation study suggests that for testing a simple order, the new approach is more powerful in many scenarios than the existing method that uses a mixture of chi-squared variables. We illustrate the results of our adaptive procedure using real data on the liquidity preference hypothesis.
Introduction/Aims Duchenne and Becker muscular dystrophies (DMD and BMD, respectively) are characterized by fat replacement of different skeletal muscles in a specific temporal order. Given the structural role of dystrophin in skeletal muscle mechanics, muscle architecture could be important in the progressive pathophysiology of muscle degeneration. Therefore, the aim of this study was to assess the role of muscle architecture in the progression of fat replacement in DMD and BMD. Methods We assessed the association between literature‐based leg muscle architectural characteristics and muscle fat fraction from 22 DMD and 24 BMD patients. Dixon‐based magnetic resonance imaging estimates of fat fractions at baseline and 12 (only DMD) and 24 months were related to fiber length and physiological cross‐sectional area (PCSA) using age‐controlled linear mixed modeling. Results DMD and BMD muscles with long fibers and BMD muscles with large PCSAs were associated with increased fat fraction. The effect of fiber length was stronger in muscles with larger PCSA. Discussion Muscle architecture may explain the pathophysiology of muscle degeneration in dystrophinopathies, in which proximal muscles with a larger mass (fiber length × PCSA) are more susceptible, confirming the clinical observation of a temporal proximal‐to‐distal progression. These results give more insight into the mechanical role in the pathophysiology of muscular dystrophies. Ultimately, this new information can be used to help support the selection of current and the development of future therapies.
We propose a structure of a semiparametric two-component mixture model when one component is parametric and the other is defined through linear constraints on its distribution function. Estimation of a two-component mixture model with an unknown component is very difficult when no particular assumption is made on the structure of the unknown component. A symmetry assumption was used in the literature to simplify the estimation. Such method has the advantage of producing consistent and asymptotically normal estimators, and identifiability of the semiparametric mixture model becomes tractable. Still, existing methods which estimate a semiparametric mixture model have their limits when the parametric component has unknown parameters or the proportion of the parametric part is either very high or very low. We propose in this paper a method to incorporate a prior linear information about the distribution of the unknown component in order to better estimate the model when existing estimation methods fail. The new method is based on ϕ−divergences and has an original form since the minimization is carried over both arguments of the divergence. The resulting estimators are proved to be consistent and asymptotically normal under standard assumptions. We show that using the Pearson's χ 2 divergence our algorithm has a linear complexity when the constraints are moment-type. Simulations on univariate and multivariate mixtures demonstrate the viability and the interest of our novel approach.
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