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Motivated by the challenges in analyzing gut microbiome and metagenomic data, this work aims to tackle the issue of measurement errors in high-dimensional regression models that involve compositional covariates. This paper marks a pioneering effort in conducting statistical inference on high-dimensional compositional data affected by mismeasured or contaminated data. We introduce a calibration approach tailored for the linear log-contrast model. Under relatively lenient conditions regarding the sparsity level of the parameter, we have established the asymptotic normality of the estimator for inference. Numerical experiments and an application in microbiome study have demonstrated the efficacy of our high-dimensional calibration strategy in minimizing bias and achieving the expected coverage rates for confidence intervals. Moreover, the potential application of our proposed methodology extends well beyond compositional data, suggesting its adaptability for a wide range of research contexts.

Utilizing natural history data as external control plays an important role in the clinical development of rare diseases, since placebo groups in double-blind randomization trials may not be available due to ethical reasons and low disease prevalence. This article proposed an innovative approach for utilizing natural history data to support rare disease clinical development by constructing reference centile charts. Due to the deterioration nature of certain rare diseases, the distributions of clinical endpoints can be age-dependent and have an absorbing state of zero, which can result in censored natural history data. Existing methods of reference centile charts can not be directly used in the censored natural history data. Therefore, we propose a new calibrated zero-inflated kernel quantile (ZIKQ) estimation to construct reference centile charts from censored natural history data. Using the application to Duchenne Muscular Dystrophy drug development, we demonstrate that the reference centile charts using the ZIKQ method can be implemented to evaluate treatment efficacy and facilitate a more targeted patient enrollment in rare disease clinical development.

Transcriptome-wide association studies (TWAS) are powerful tools for identifying putative causal genes by integrating genome-wide association studies and gene expression data. However, most TWAS methods focus on linear associations between genes and traits, ignoring the complex nonlinear relationships that exist in biological systems. To address this limitation, we propose a novel quantile transcriptomics framework, QTWAS, that takes into account the nonlinear and heterogeneous nature of gene-trait associations. Our approach integrates a quantile-based gene expression model into the TWAS model, which allows for the discovery of nonlinear and heterogeneous gene-trait associations. By conducting comprehensive simulations and examining various psychiatric and neurodegenerative traits, we demonstrate that the proposed model outperforms traditional techniques in identifying gene-trait associations. Additionally, QTWAS can uncover important insights into nonlinear relationships between gene expression levels and phenotypes, complementing traditional TWAS approaches. We further show applications to 100 continuous traits from the UK Biobank and 10 binary traits related to brain disorders.

In microbiome studies, it is of interest to use a sample from a population of microbes, such as the gut microbiota community, to estimate the population proportion of these taxa. However, due to biases introduced in sampling and preprocessing steps, these observed taxa abundances may not reflect true taxa abundance patterns in the ecosystem. Repeated measures, including longitudinal study designs, may be potential solutions to mitigate the discrepancy between observed abundances and true underlying abundances. Yet, widely observed zero-inflation and over-dispersion issues can distort downstream statistical analyses aiming to associate taxa abundances with covariates of interest. To this end, we propose a Zero-Inflated Poisson Gamma (ZIPG) framework to address the aforementioned challenges. From a perspective of measurement errors, we accommodate the discrepancy between observations and truths by decomposing the mean parameter in Poisson regression into a true abundance level and a multiplicative measurement of sampling variability from the microbial ecosystem. Then, we provide a flexible model by connecting both mean abundance and the variability to different covariates, and build valid statistical inference procedures for both parameter estimation and hypothesis testing. Through comprehensive simulation studies and real data applications, the proposed ZIPG method provides significant insights into distinguished differential variability and abundance.

Gene-based testing is a commonly employed strategy in many genetic association studies. Gene-trait associations can be complex due to underlying population heterogeneity, gene-environment interactions, and various other reasons. Existing gene-based tests, such as Burden and Sequence Kernel Association Tests (SKAT), are based on detecting differences in a single summary statistic, such as the mean or the variance, and may miss or underestimate higher-order associations that could be scientifically interesting. In this paper, we propose a new family of gene-level association tests which integrate quantile rank score processes to better accommodate complex associations. The resulting test statistics have multiple advantages: (1) they are almost as efficient as the best existing tests when the associations are homogeneous across quantile levels, and have improved efficiency for complex and heterogeneous associations, (2) they provide useful insights on risk stratification, (3) the test statistics are distribution-free, and could hence accommodate a wide range of underlying distributions, and (4) they are computationally efficient. We established the asymptotic properties of the proposed tests under the null and alternative hypothesis and conducted large scale simulation studies to investigate their finite sample performance. We applied the proposed tests to the Metabochip data to identify genetic associations with lipid traits and compared the results with those of the Burden and SKAT tests.

Standard logistic regression analysis of case-control data has low power to detect gene-environment interactions, but until recently it was the only method that could be used on complex polygenic data for which parametric distributional models are not feasible. Under the assumption of gene-environment independence in the underlying population, Stalder et al. (2017, Biometrika, 104, 801-812) developed a retrospective method that treats both genetic and environmental variables nonparametrically. However, the mathematical symmetry of genetic and environmental variables is overlooked. We propose an improvement to the method of Stalder et al. (2017) that increases the efficiency of the estimates with no additional assumptions and modest computational cost. This improvement is achieved by treating the genetic and environmental variables symmetrically to generate two sets of parameter estimates that are combined to generate a more efficient estimate. We employ a semiparametric framework to develop the asymptotic theory of the estimator, show its asymptotic efficiency gain, and evaluate its performance via simulation studies. The method is illustrated using data from a case-control study of breast cancer.

We consider the problem of high-dimensional classification between the two groups with unequal covariance matrices. Rather than estimating the full quadratic discriminant rule, we propose to perform simultaneous variable selection and linear dimension reduction on original data, with the subsequent application of quadratic discriminant analysis on the reduced space. In contrast to quadratic discriminant analysis, the proposed framework doesn't require estimation of precision matrices and scales linearly with the number of measurements, making it especially attractive for the use on high-dimensional datasets. We support the methodology with theoretical guarantees on variable selection consistency, and empirical comparison with competing approaches. We apply the method to gene expression data of breast cancer patients, and confirm the crucial importance of ESR1 gene in differentiating estrogen receptor status.