Weining Shen

Adaptive Bayesian multivariate density estimation with Dirichlet mixtures

We show that rate-adaptive multivariate density estimation can be performed using Bayesian methods based on Dirichlet mixtures of normal kernels with a prior distribution on the kernels covariance matrix parameter. We derive sufficient conditions on the prior specification that guarantee convergence to a true density at a rate that is minimax optimal for the smoothness class to which the true density belongs. No prior knowledge of smoothness is assumed. The sufficient conditions are shown to hold for the Dirichlet location mixture-of-normals prior with a Gaussian base measure and an inverse Wishart prior on the covariance matrix parameter. Locally Holder smoothness classes and their anisotropic extensions are considered. Our study involves several technical novelties, including sharp approximation of finitely differentiable multivariate densities by normal mixtures and a new sieve on the space of such densities. Copyright 2013, Oxford University Press.

Single-cell transcriptomics reconstructs fate conversion from fibroblast to cardiomyocyte

Direct lineage conversion offers a new strategy for tissue regeneration and disease modelling. Despite recent success in directly reprogramming fibroblasts into various cell types, the precise changes that occur as fibroblasts progressively convert to the target cell fates remain unclear. The inherent heterogeneity and asynchronous nature of the reprogramming process renders it difficult to study this process using bulk genomic techniques. Here we used single-cell RNA sequencing to overcome this limitation and analysed global transcriptome changes at early stages during the reprogramming of mouse fibroblasts into induced cardiomyocytes (iCMs). Using unsupervised dimensionality reduction and clustering algorithms, we identified molecularly distinct subpopulations of cells during reprogramming. We also constructed routes of iCM formation, and delineated the relationship between cell proliferation and iCM induction. Further analysis of global gene expression changes during reprogramming revealed unexpected downregulation of factors involved in mRNA processing and splicing. Detailed functional analysis of the top candidate splicing factor, Ptbp1, revealed that it is a critical barrier for the acquisition of cardiomyocyte-specific splicing patterns in fibroblasts. Concomitantly, Ptbp1 depletion promoted cardiac transcriptome acquisition and increased iCM reprogramming efficiency. Additional quantitative analysis of our dataset revealed a strong correlation between the expression of each reprogramming factor and the progress of individual cells through the reprogramming process, and led to the discovery of new surface markers for the enrichment of iCMs. In summary, our single-cell transcriptomics approaches enabled us to reconstruct the reprogramming trajectory and to uncover intermediate cell populations, gene pathways and regulators involved in iCM induction.

Adaptive Bayesian density regression for high-dimensional data

Density regression provides a flexible strategy for modeling the distribution of a response variable Y given predictors X = (X1 ,...,X p) by letting that the conditional density of Y given X as a completely unknown function and allowing its shape to change with the value of X. The number of predictors p may be very large, possibly much larger than the number of observations n, but the conditional density is assumed to depend only on a much smaller number of predictors, which are unknown. In addition to estimation, the goal is also to select the important predictors which actually affect the true conditional density. We consider a nonparametric Bayesian approach to density regression by constructing a random series prior based on tensor products of spline functions. The proposed prior also incorporates the issue of variable selection. We show that the posterior distribution of the conditional density contracts adaptively at the truth nearly at the optimal oracle rate, determined by the unknown sparsity and smoothness levels, even in the ultra highdimensional settings where p increases exponentially with n. The result is also extended to the anisotropic case where the degree of smoothness can vary in different directions, and both random and deterministic predictors are considered. We also propose a technique to calculate posterior moments of the conditional density function without requiring Markov chain Monte Carlo methods.

A direct method to evaluate the time-dependent predictive accuracy for biomarkers

Time-dependent receiver operating characteristic (ROC) curves and their area under the curve (AUC) are important measures to evaluate the prediction accuracy of biomarkers for time-to-event endpoints (e.g., time to disease progression or death). In this article, we propose a direct method to estimate AUC(t) as a function of time t using a flexible fractional polynomials model, without the middle step of modeling the time-dependent ROC. We develop a pseudo partial-likelihood procedure for parameter estimation and provide a test procedure to compare the predictive performance between biomarkers. We establish the asymptotic properties of the proposed estimator and test statistics. A major advantage of the proposed method is its ease to make inference and to compare the prediction accuracy across biomarkers, rendering our method particularly appealing for studies that require comparing and screening a large number of candidate biomarkers. We evaluate the finite-sample performance of the proposed method through simulation studies and illustrate our method in an application to AIDS Clinical Trials Group 175 data.

Bayesian sequential monitoring design for two-arm randomized clinical trials with noncompliance

In early-phase clinical trials, interim monitoring is commonly conducted based on the estimated intent-to-treat effect, which is subject to bias in the presence of noncompliance. To address this issue, we propose a Bayesian sequential monitoring trial design based on the estimation of the causal effect using a principal stratification approach. The proposed design simultaneously considers efficacy and toxicity outcomes and utilizes covariates to predict a patients potential compliance behavior and identify the causal effects. Based on accumulating data, we continuously update the posterior estimates of the causal treatment effects and adaptively make the go/no-go decision for the trial. Numerical results show that the proposed method has desirable operating characteristics and addresses the issue of noncompliance.

Model-free scoring system for risk prediction with application to hepatocellular carcinoma study

There is an increasing need to construct a risk-prediction scoring system for survival data and identify important risk factors (e.g., biomarkers) for patient screening and treatment recommendation. However, most existing methodologies either rely on strong model assumptions (e.g., proportional hazards) or only handle binary outcomes. In this article, we propose a flexible method that simultaneously selects important risk factors and identifies the optimal linear combination of risk factors by maximizing a pseudo-likelihood function based on the time-dependent area under the receiver operating characteristic curve. Our method is particularly useful for risk evaluation and recommendation of optimal subsequent treatments. We show that the proposed method has desirable theoretical properties, including asymptotic normality and the oracle property after variable selection. Numerical performance is evaluated on several simulation data sets and an application to hepatocellular carcinoma data.