An efficient likelihood-free Bayesian inference method based on sequential neural posterior estimation

Sequential neural posterior estimation (SNPE) techniques have been recently proposed for dealing with simulation-based models with intractable likelihoods. Unlike approximate Bayesian computation, SNPE techniques learn the posterior from sequential simulation using neural network-based conditional density estimators by minimizing a specific loss function. The SNPE method proposed by Lueckmann et al. (2017) used a calibration kernel to boost the sample weights around the observed data, resulting in a concentrated loss function. However, the use of calibration kernels may increase the variances of both the empirical loss and its gradient, making the training inefficient. To improve the stability of SNPE, this paper proposes to use an adaptive calibration kernel and several variance reduction techniques. The proposed method greatly speeds up the process of training, and provides a better approximation of the posterior than the original SNPE method and some existing competitors as confirmed by numerical experiments.Comment: 30 pages, 7 figure

Survival Analysis with High-Dimensional Omics Data Using a Threshold Gradient Descent Regularization-Based Neural Network Approach

Analysis of data with a censored survival response and high-dimensional omics measurements is now common. Most of the existing analyses are based on specific (semi)parametric models, in particular the Cox model. Such analyses may be limited by not having sufficient flexibility, for example, in accommodating nonlinearity. For categorical and continuous responses, neural networks (NNs) have provided a highly competitive alternative. Comparatively, NNs for censored survival data remain limited. Omics measurements are usually high-dimensional, and only a small subset is expected to be survival-associated. As such, regularized estimation and selection are needed. In the existing NN studies, this is usually achieved via penalization. In this article, we propose adopting the threshold gradient descent regularization (TGDR) technique, which has competitive performance (for example, when compared to penalization) and unique advantages in regression analysis, but has not been adopted with NNs. The TGDR-based NN has a highly sensible formulation and an architecture different from the unregularized and penalization-based ones. Simulations show its satisfactory performance. Its practical effectiveness is further established via the analysis of two cancer omics datasets. Overall, this study can provide a practical and useful new way in the NN paradigm for survival analysis with high-dimensional omics measurements

Robust Outcome Weighted Learning for Optimal Individualized Treatment Rules

10.1080/10543406.2019.1633657Journal of Biopharmaceutical Statistics294606-62

A moment-based test for the homogeneity in mixture natural exponential family with quadratic variance functions

In this paper, we propose a simple moment-based procedure for testing homogeneity in the natural exponential family with quadratic variance functions. In the literature, solutions to this problem normally involve establishing identifiability of parameters first, then testing the hypotheses whether the data come from a single distribution or a mixture of distributions. Our procedure directly tests the hypotheses without the need to establish parameter estimability. Simulation studies demonstrate that the power of our test is comparable to the supplementary score test and the separate score test proposed by Wu and Gupta [Wu, Y., Gupta, A.K., 2003. Local score tests in mixture exponential family. J. Statist. Plann. Inference 116, 421-435], and the normalized score test proposed by Shoukri and Lathrop [Shoukri, M., Lathrop, G.M., 1993. Statistical testing of genetic linkage under heterogeneity. Biometrics 49, 151-161]. In these simulation studies, the methods by the others are specific to cases with a known null distribution, and our methods can also be applied to cases with unknown null distribution. Our test procedure is demonstrated on two real data sets.

Clustering on hierarchical heterogeneous data with prior pairwise relationships

Abstract Background Clustering is a fundamental problem in statistics and has broad applications in various areas. Traditional clustering methods treat features equally and ignore the potential structure brought by the characteristic difference of features. Especially in cancer diagnosis and treatment, several types of biological features are collected and analyzed together. Treating these features equally fails to identify the heterogeneity of both data structure and cancer itself, which leads to incompleteness and inefficacy of current anti-cancer therapies. Objectives In this paper, we propose a clustering framework based on hierarchical heterogeneous data with prior pairwise relationships. The proposed clustering method fully characterizes the difference of features and identifies potential hierarchical structure by rough and refined clusters. Results The refined clustering further divides the clusters obtained by the rough clustering into different subtypes. Thus it provides a deeper insight of cancer that can not be detected by existing clustering methods. The proposed method is also flexible with prior information, additional pairwise relationships of samples can be incorporated to help to improve clustering performance. Finally, well-grounded statistical consistency properties of our proposed method are rigorously established, including the accurate estimation of parameters and determination of clustering structures. Conclusions Our proposed method achieves better clustering performance than other methods in simulation studies, and the clustering accuracy increases with prior information incorporated. Meaningful biological findings are obtained in the analysis of lung adenocarcinoma with clinical imaging data and omics data, showing that hierarchical structure produced by rough and refined clustering is necessary and reasonable