Journal of Data Science

Recent studies observed a surprising concept on model test error called the double descent phenomenon where the increasing model complexity decreases the test error first and then the error increases and decreases again. To observe this, we work on a two-layer neural network model with a ReLU activation function designed for binary classification under supervised learning. Our aim is to observe and investigate the mathematical theory behind the double descent behavior of model test error for varying model sizes. We quantify the model size by the ration of number of training samples to the dimension of the model. Due to the complexity of the empirical risk minimization procedure, we use the Convex Gaussian MinMax Theorem to find a suitable candidate for the global training loss.

When comparing two survival curves, three tests are widely used: the Cox proportional hazards test, the logrank test, and the Wilcoxon test. Despite their popularity in survival data analysis, there is no clear clinical interpretation especially when the proportional hazard assumption is not valid. Meanwhile, the restricted mean survival time (RMST) offers an intuitive and clinically meaningful interpretation. We compare these four tests with regards to statistical power under many configurations (e.g., proportional hazard, early benefit, delayed benefit, and crossing survivals) with data simulated from the Weibull distributions. We then use an example from a lung cancer trial to compare their required sample sizes. As expected, the CoxPH test is more powerful than others when the PH assumption is valid. The Wilcoxon test is often preferable when there is a decreasing trajectory in the event rate as time goes. The RMST test is much more powerful than others when a new treatment has early benefit. The recommended test(s) under each configuration are suggested in this article.

Extensive literature has been proposed for the analysis of correlated survival data. Subjects within a cluster share some common characteristics, e.g., genetic and environmental factors, so their time-to-event outcomes are correlated. The frailty model under proportional hazards assumption has been widely applied for the analysis of clustered survival outcomes. However, the prediction performance of this method can be less satisfactory when the risk factors have complicated effects, e.g., nonlinear and interactive. To deal with these issues, we propose a neural network frailty Cox model that replaces the linear risk function with the output of a feed-forward neural network. The estimation is based on quasi-likelihood using Laplace approximation. A simulation study suggests that the proposed method has the best performance compared with existing methods. The method is applied to the clustered time-to-failure prediction within the kidney transplantation facility using the national kidney transplant registry data from the U.S. Organ Procurement and Transplantation Network. All computer programs are available at https://github.com/rivenzhou/deep_learning_clustered.

In causal mediation analyses, of interest are the direct or indirect pathways from exposure to an outcome variable. For observation studies, massive baseline characteristics are collected as potential confounders to mitigate selection bias, possibly approaching or exceeding the sample size. Accordingly, flexible machine learning approaches are promising in filtering a subset of relevant confounders, along with estimation using the efficient influence function to avoid overfitting. Among various confounding selection strategies, two attract growing attention. One is the popular debiased, or double machine learning (DML), and another is the penalized partial correlation via fitting a Gaussian graphical network model between the confounders and the response variable. Nonetheless, for causal mediation analyses when encountering high-dimensional confounders, there is a gap in determining the best strategy for confounding selection. Therefore, we exemplify a motivating study on the human microbiome, where the dimensions of mediator and confounders approach or exceed the sample size to compare possible combinations of confounding selection methods. By deriving the multiply robust causal direct and indirect effects across various hypotheses, our comprehensive illustrations offer methodological implications on how the confounding selection impacts the final causal target parameter estimation while generating causality insights in demystifying the “gut-brain axis”. Our results highlighted the practicality and necessity of the discussed methods, which not only guide real-world applications for practitioners but also motivate future advancements for this crucial topic in the era of big data.

Cellular deconvolution is a key approach to deciphering the complex cellular makeup of tissues by inferring the composition of cell types from bulk data. Traditionally, deconvolution methods have focused on a single molecular modality, relying either on RNA sequencing (RNA-seq) to capture gene expression or on DNA methylation (DNAm) to reveal epigenetic profiles. While these single-modality approaches have provided important insights, they often lack the depth needed to fully understand the intricacies of cellular compositions, especially in complex tissues. To address these limitations, we introduce EMixed, a versatile framework designed for both single-modality and multi-omics cellular deconvolution. EMixed models raw RNA counts and DNAm counts or frequencies via allocation models that assign RNA transcripts and DNAm reads to cell types, and uses an expectation-maximization (EM) algorithm to estimate parameters. Benchmarking results demonstrate that EMixed significantly outperforms existing methods across both single-modality and multi-modality applications, underscoring the broad utility of this approach in enhancing our understanding of cellular heterogeneity.

Predicting the timing and occurrence of events is a major focus of data science applications, especially in the context of biomedical research. Performance for models estimating these outcomes, often referred to as time-to-event or survival outcomes, is frequently summarized using measures of discrimination, in particular time-dependent AUC and concordance. Many estimators for these quantities have been proposed which can be broadly categorized as either semi-parametric estimators or non-parametric estimators. In this paper, we review the mathematical construction of the two classes of estimators and compare their behavior. Importantly, we identify a previously unknown feature of the class of semi-parametric estimators that can result in vastly overoptimistic out-of-sample estimation of discriminative performance in common applied tasks. Although these semi-parametric estimators are popular in practice, the phenomenon we identify here suggests that this class of estimators may be inappropriate for use in model assessment and selection based on out-of-sample evaluation criteria. This is due to the semi-parametric estimators’ bias in favor of models that are overfit when using out-of-sample prediction criteria (e.g. cross-validation). Non-parametric estimators, which do not exhibit this behavior, are highly variable for local discrimination. We propose to address the high variability problem through penalized regression splines smoothing. The behavior of various estimators of time-dependent AUC and concordance are illustrated via a simulation study using two different mechanisms that produce overoptimistic out-of-sample estimates using semi-parametric estimators. Estimators are further compared using a case study using data from the National Health and Nutrition Examination Survey (NHANES) 2011–2014.

Loan behavior modeling is crucial in financial engineering. In particular, predicting loan prepayment based on large-scale historical time series data of massive customers is challenging. Existing approaches, such as logistic regression or nonparametric regression, could only model the direct relationship between the features and the prepayments. Motivated by extracting the hidden states of loan behavior, we propose the smoothing spline state space (QuadS) model based on a hidden Markov model with varying transition and emission matrices modeled by smoothing splines. In contrast to existing methods, our method benefits from capturing the loans’ unobserved state transitions, which not only increases prediction performances but also provides more interpretability. The overall model is learned by EM algorithm iterations, and within each iteration, smoothing splines are fitted with penalized least squares. Simulation studies demonstrate the effectiveness of the proposed method. Furthermore, a real-world case study using loan data from the Federal National Mortgage Association illustrates the practical applicability of our model. The QuadS model not only provides reliable predictions but also uncovers meaningful, hidden behavior patterns that can offer valuable insights for the financial industry.

Heart rate data collected from wearable devices – one type of time series data – could provide insights into activities, stress levels, and health. Yet, consecutive missing segments (i.e., gaps) that commonly occur due to improper device placement or device malfunction could distort the temporal patterns inherent in the data and undermine the validity of downstream analyses. This study proposes an innovative iterative procedure to fill gaps in time series data that capitalizes on the denoising capability of Singular Spectrum Analysis (SSA) and eliminates SSA’s requirement of pre-specifying the window length and number of groups. The results of simulations demonstrate that the performance of SSA-based gap-filling methods depends on the choice of window length, number of groups, and the percentage of missing values. In contrast, the proposed method consistently achieves the lowest rates of reconstruction error and gap-filling error across a variety of combinations of the factors manipulated in the simulations. The simulation findings also highlight that the commonly recommended long window length – half of the time series length – may not apply to time series with varying frequencies such as heart rate data. The initialization step of the proposed method that involves a large window length and the first four singular values in the iterative singular value decomposition process not only avoids convergence issues but also facilitates imputation accuracy in subsequent iterations. The proposed method provides the flexibility for researchers to conduct gap-filling solely or in combination with denoising on time series data and thus widens the applications.

In many medical comparative studies, subjects may provide either bilateral or unilateral data. While numerous testing procedures have been proposed for bilateral data that account for the intra-class correlation between paired organs of the same individual, few studies have thoroughly explored combined correlated bilateral and unilateral data. Ma and Wang (2021) introduced three test procedures based on the maximum likelihood estimation (MLE) algorithm for general g groups. In this article, we employ a model-based approach that treats the measurements from both eyes of each subject as repeated observations. We then compare this approach with Ma and Wang’s Score test procedure. Monte Carlo simulations demonstrate that the MLE-based Score test offers certain advantages under specific conditions. However, this model-based method lacks an explicit form for the test statistic, limiting its potential for further development of an exact test.

Piecewise linear-quadratic (PLQ) functions are a fundamental function class in convex optimization, especially within the Empirical Risk Minimization (ERM) framework, which employs various PLQ loss functions. This paper provides a workflow for decomposing a general convex PLQ loss into its ReLU-ReHU representation, along with a Python implementation designed to enhance the efficiency of presenting and solving ERM problems, particularly when integrated with ReHLine (a powerful solver for PLQ ERMs). Our proposed package, plqcom, accepts three representations of PLQ functions and offers user-friendly APIs for verifying their convexity and continuity. The Python package is available at https://github.com/keepwith/PLQComposite.