OBJECTIVES: To characterize the complex interplay between multiple clinical conditions in a time-to-event analysis framework using data from multiple hospitals, we developed two novel one-shot distributed algorithms for competing risk models (ODACoR). By applying our algorithms to the EHR data from eight national children's hospitals, we quantified the impacts of a wide range of risk factors on the risk of post-acute sequelae of SARS-COV-2 (PASC) among children and adolescents. MATERIALS AND METHODS: Our ODACoR algorithms are effectively executed due to their devised simplicity and communication efficiency. We evaluated our algorithms via extensive simulation studies as applications to quantification of the impacts of risk factors for PASC among children and adolescents using data from eight children's hospitals including the Children's Hospital of Philadelphia, Cincinnati Children's Hospital Medical Center, Children's Hospital of Colorado covering over 6.5 million pediatric patients. The accuracy of the estimation was assessed by comparing the results from our ODACoR algorithms with the estimators derived from the meta-analysis and the pooled data. RESULTS: The meta-analysis estimator showed a high relative bias (∼40%) when the clinical condition is relatively rare (∼0.5%), whereas ODACoR algorithms exhibited a substantially lower relative bias (∼0.2%). The estimated effects from our ODACoR algorithms were identical on par with the estimates from the pooled data, suggesting the high reliability of our federated learning algorithms. In contrast, the meta-analysis estimate failed to identify risk factors such as age, gender, chronic conditions history, and obesity, compared to the pooled data. DISCUSSION: Our proposed ODACoR algorithms are communication-efficient, highly accurate, and suitable to characterize the complex interplay between multiple clinical conditions. CONCLUSION: Our study demonstrates that our ODACoR algorithms are communication-efficient and can be widely applicable for analyzing multiple clinical conditions in a time-to-event analysis framework.

Covariate measurement error in nonparametric regression is a common problem in nutritional epidemiology and geostatistics, and other fields. Over the last two decades, this problem has received substantial attention in the frequentist literature. Bayesian approaches for handling measurement error have only been explored recently and are surprisingly successful, although there still is a lack of a proper theoretical justification regarding the asymptotic performance of the estimators. By specifying a Gaussian process prior on the regression function and a Dirichlet process Gaussian mixture prior on the unknown distribution of the unobserved covariates, we show that the posterior distribution of the regression function and the unknown covariate density attain optimal rates of contraction adaptively over a range of Holder classes, up to logarithmic terms. We also develop a novel surrogate prior for approximating the Gaussian process prior that leads to efficient computation and preserves the covariance structure, thereby facilitating easy prior elicitation. We demonstrate the empirical performance of our approach and compare it with competitors in a wide range of simulation experiments and a real data example.

Streaming data are dynamic in nature with frequent changes. To detect such changes, most methods measure the difference between the data distributions in a current time window and a reference window. Divergence metrics and density estimation are required to measure the difference between the data distributions. Our study shows that the Kullback-Leibler (KL) divergence, the most popular metric for comparing distributions, fails to detect certain changes due to its asymmetric property and its dependence on the variance of the data. We thus consider two metrics for detecting changes in univariate data streams: a symmetric KL-divergence and a divergence metric measuring the intersection area of two distributions. The experimental results show that these two metrics lead to more accurate results in change detection than baseline methods such as Change Finder and using conventional KL-divergence.

MOTIVATION: Gut microbiota can be classified at multiple taxonomy levels. Strategies to use changes in microbiota composition to effect health improvements require knowing at which taxonomy level interventions should be aimed. Identifying these important levels is difficult, however, because most statistical methods only consider when the microbiota are classified at one taxonomy level, not multiple. RESULTS: Using L1 and L2 regularizations, we developed a new variable selection method that identifies important features at multiple taxonomy levels. The regularization parameters are chosen by a new, data-adaptive, repeated cross-validation approach, which performed well. In simulation studies, our method outperformed competing methods: it more often selected significant variables, and had small false discovery rates and acceptable false-positive rates. Applying our method to gut microbiota data, we found which taxonomic levels were most altered by specific interventions or physiological status. AVAILABILITY: The new approach is implemented in an R package, which is freely available from the corresponding author. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Motivated by the problem of identifying correlations between genes or features of two related biological systems, we propose a model of feature selection in which only a subset of the predictors Xt are dependent on the multidimensional variate Y, and the remainder of the predictors constitute a “noise set” Xu independent of Y. Using Monte Carlo simulations, we investigated the relative performance of two methods: thresholding and singular-value decomposition, in combination with stochastic optimization to determine “empirical bounds” on the small-sample accuracy of an asymptotic approximation. We demonstrate utility of the thresholding and SVD feature selection methods to with respect to a recent infant intestinal gene expression and metagenomics dataset.

MOTIVATION: Protein abundance in quantitative proteomics is often based on observed spectral features derived from liquid chromatography mass spectrometry (LC-MS) or LC-MS/MS experiments. Peak intensities are largely non-normal in distribution. Furthermore, LC-MS-based proteomics data frequently have large proportions of missing peak intensities due to censoring mechanisms on low-abundance spectral features. Recognizing that the observed peak intensities detected with the LC-MS method are all positive, skewed and often left-censored, we propose using survival methodology to carry out differential expression analysis of proteins. Various standard statistical techniques including non-parametric tests such as the Kolmogorov-Smirnov and Wilcoxon-Mann-Whitney rank sum tests, and the parametric survival model and accelerated failure time-model with log-normal, log-logistic and Weibull distributions were used to detect any differentially expressed proteins. The statistical operating characteristics of each method are explored using both real and simulated datasets. RESULTS: Survival methods generally have greater statistical power than standard differential expression methods when the proportion of missing protein level data is 5% or more. In particular, the AFT models we consider consistently achieve greater statistical power than standard testing procedures, with the discrepancy widening with increasing missingness in the proportions. AVAILABILITY: The testing procedures discussed in this article can all be performed using readily available software such as R. The R codes are provided as supplemental materials. CONTACT: [email protected].

MOTIVATION: Estimation of misclassification error has received increasing attention in clinical diagnosis and bioinformatics studies, especially in small sample studies with microarray data. Current error estimation methods are not satisfactory because they either have large variability (such as leave-one-out cross-validation) or large bias (such as resubstitution and leave-one-out bootstrap). While small sample size remains one of the key features of costly clinical investigations or of microarray studies that have limited resources in funding, time and tissue materials, accurate and easy-to-implement error estimation methods for small samples are desirable and will be beneficial. RESULTS: A bootstrap cross-validation method is studied. It achieves accurate error estimation through a simple procedure with bootstrap resampling and only costs computer CPU time. Simulation studies and applications to microarray data demonstrate that it performs consistently better than its competitors. This method possesses several attractive properties: (1) it is implemented through a simple procedure; (2) it performs well for small samples with sample size, as small as 16; (3) it is not restricted to any particular classification rules and thus applies to many parametric or non-parametric methods.

MOTIVATION: The standard paradigm for a classifier design is to obtain a sample of feature-label pairs and then to apply a classification rule to derive a classifier from the sample data. Typically in laboratory situations the sample size is limited by cost, time or availability of sample material. Thus, an investigator may wish to consider a sequential approach in which there is a sufficient number of patients to train a classifier in order to make a sound decision for diagnosis while at the same time keeping the number of patients as small as possible to make the studies affordable. RESULTS: A sequential classification procedure is studied via the martingale central limit theorem. It updates the classification rule at each step and provides stopping criteria to ensure with a certain confidence that at stopping a future subject will have misclassification probability smaller than a predetermined threshold. Simulation studies and applications to microarray data analysis are provided. The procedure possesses several attractive properties: (1) it updates the classification rule sequentially and thus does not rely on distributions of primary measurements from other studies; (2) it assesses the stopping criteria at each sequential step and thus can substantially reduce cost via early stopping; and (3) it is not restricted to any particular classification rule and therefore applies to any parametric or non-parametric method, including feature selection or extraction. AVAILABILITY: R-code for the sequential stopping rule is available at http://stat.tamu.edu/~wfu/microarray/sequential/R-code.html

MOTIVATION: Ranking gene feature sets is a key issue for both phenotype classification, for instance, tumor classification in a DNA microarray experiment, and prediction in the context of genetic regulatory networks. Two broad methods are available to estimate the error (misclassification rate) of a classifier. Resubstitution fits a single classifier to the data, and applies this classifier in turn to each data observation. Cross-validation (in leave-one-out form) removes each observation in turn, constructs the classifier, and then computes whether this leave-one-out classifier correctly classifies the deleted observation. Resubstitution typically underestimates classifier error, severely so in many cases. Cross-validation has the advantage of producing an effectively unbiased error estimate, but the estimate is highly variable. In many applications it is not the misclassification rate per se that is of interest, but rather the construction of gene sets that have the potential to classify or predict. Hence, one needs to rank feature sets based on their performance. RESULTS: A model-based approach is used to compare the ranking performances of resubstitution and cross-validation for classification based on real-valued feature sets and for prediction in the context of probabilistic Boolean networks (PBNs). For classification, a Gaussian model is considered, along with classification via linear discriminant analysis and the 3-nearest-neighbor classification rule. Prediction is examined in the steady-distribution of a PBN. Three metrics are proposed to compare feature-set ranking based on error estimation with ranking based on the true error, which is known owing to the model-based approach. In all cases, resubstitution is competitive with cross-validation relative to ranking accuracy. This is in addition to the enormous savings in computation time afforded by resubstitution.