In human genetics, twin studies are widely underwent for investigation of the genetic influence on diseases. There are several measures that had been proposed to evaluate the similarity between two twins for dichotomous traits when the twins are sampled at random. These measures include the correlations, odds ratios, and casewise and pairwise concordances. When data are sampled through an ascertainment procedure, truncated data are formed. Under this circumstance, odds ratio cannot be defined and correlations cannot be correctly estimated. However, concordance measures for dichotomous traits can still be estimated using the likelihood method. On the other hand, though theoretically concordance measures can be extended to trichotomous traits, how to define them and to derive their estimators for ascertained trichotomous traits data have not been thoroughly discussed. In this study, we aim to address several relevant issues for ascertained trichotomous traits data. We define two new (casewise and pairwise) concordance measures for trichotomous traits and demonstrate how to apply a so-called 'self-contained subsets method (SCSM)' to estimation of twin concordances for ascertained data. We show that this method can obtain the same estimates as the likelihood method in an easier way and derive the asymptotic variances of the SCSM estimates under ascertainment. We establish the testing procedure for test of the equality of concordance measures between monozygotic twin pairs and dizygotic twin pairs, and illustrate the methods with a real data set and conduct Monte Carlo simulation to investigate its power performance.

This training model could help endoscopists improve the accuracy of measurement of polyps on colonoscopy in a short period. The durability of learning effect needs further investigation.

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We study differentially private mean estimation in a high-dimensional setting. Existing differential privacy techniques applied to large dimensions lead to computationally intractable problems or estimators with excessive privacy loss. Recent work in high-dimensional robust statistics has identified computationally tractable mean estimation algorithms with asymptotic dimension-independent error guarantees. We incorporate these results to develop a strict bound on the global sensitivity of the robust mean estimator. This yields a computationally tractable algorithm for differentially private mean estimation in high dimensions with dimensionindependent privacy loss. Finally, we show on synthetic data that our algorithm significantly outperforms classic differential privacy methods, overcoming barriers to high-dimensional differential privacy. * Equal contribution. Author order determined by a random coin flip of a virtual Canadian Loonie.Preprint. Under review.