arXiv subjects

Tianyu Pan

Publications and source records attributed to Tianyu Pan.

8 recordsLinked to original sources

arXiv2025

A Honest Cross-Validation Estimator for Prediction Performance

Cross-validation is a standard tool for obtaining a honest assessment of the performance of a prediction model. The commonly used version repeatedly splits data, trains the prediction model on the training set, evaluates the model performance on the test set, and averages the model performance across different data splits. A well-known criticism is that such cross-validation procedure does not directly estimate the performance of the particular model recommended for future use. In this paper, we propose a new method to estimate the performance of a model trained on a specific (random) training set. A naive estimator can be obtained by applying the model to a disjoint testing set. Surprisingly, cross-validation estimators computed from other random splits can be used to improve this naive estimator within a random-effects model framework. We develop two estimators -- a hierarchical Bayesian estimator and an empirical Bayes estimator -- that perform similarly to or better than both the conventional cross-validation estimator and the naive single-split estimator. Simulations and a real-data example demonstrate the superior performance of the proposed method.

stat.ML↗

arXiv2025

Conditional Inference for Secondary Outcomes Based on the Testing Result for the Primary Outcome in Clinical Trials

In clinical trials, inferences on clinical outcomes are often made conditional on specific selective processes. For instance, only when a treatment demonstrates a significant effect on the primary outcome, further analysis is conducted to investigate its efficacy on selected secondary outcomes. Similarly, inferences may also depend on whether a trial is terminated early at interim stage. While conventional approaches primarily aim to control the family-wise error rate through multiplicity adjustments, they do not necessarily ensure the desired statistical property of the inference result, when the analysis is conducted according to a selective process. For example, the conditional coverage level of a regular confidence interval under a selective processes can be very different from its nominal level even after adjustment for multiple testing. In this paper, we argue that the validity of the inference procedure conditional on selective process is important in many applications. In addition, we propose to construct confidence intervals with correct conditional coverage probability by accounting for related selective process. Specifically, our approach involves a pivotal quantity constructed by inversing the cumulative distribution function of a truncated normal distribution induced by the selective process. Theoretical justification and comprehensive simulations illustrate the effectiveness of this method in realistic settings. We also apply our method to analyze data from the SPRINT, resulting in more conservative but conditionally valid confidence intervals for the average treatment effect than those originally published.

stat.ME↗

arXiv2025

On the two-step hybrid design for augmenting randomized trials using real-world data

Hybrid clinical trials, that borrow real-world data (RWD), are gaining interest, especially for rare diseases. They assume RWD and randomized control arm be exchangeable, but violations can bias results, inflate type I error, or reduce power. A two-step hybrid design first tests exchangeability, reducing inappropriate borrowing but potentially inflating type I error (Yuan et al., 2019). We propose four methods to better control type I error. Approach 1 estimates the variance of test statistics, rejecting the null hypothesis based on large sample normal approximation. Approach 2 uses a numerical approach for exact critical value determination. Approach 3 splits type I error rates by equivalence test outcome. Approach 4 adjusts the critical value only when equivalence is established. Simulation studies using a hypothetical ALS scenario, evaluate type I error and power under various conditions, compared to the Bayesian power prior approach (Ibrahim et al., 2015). Our methods and the Bayesian power prior control type I error, whereas Yuan et al. (2019) increases it under exchangeability. If exchangeability doesn't hold, all methods fail to control type I error. Our methods show type I error inflation of 6%-8%, compared to 10% for Yuan et al. (2019) and 16% for the Bayesian power prior.

stat.ME↗

arXiv2024

A Bayesian Approach for Selecting Relevant External Data (BASE): Application to a study of Long-Term Outcomes in a Hemophilia Gene Therapy Trial

Gene therapies aim to address the root causes of diseases, particularly those stemming from rare genetic defects that can be life-threatening or severely debilitating. Although an increasing number of gene therapies have received regulatory approvals in recent years, understanding their long-term efficacy in trials with limited follow-up time remains challenging. To address this critical question, we propose a novel Bayesian framework designed to selectively integrate relevant external data with internal trial data to improve the inference of the durability of long-term efficacy. We proved that the proposed method has desired theoretical properties, such as identifying and favoring external subsets deemed relevant, where the relevance is defined as the similarity, induced by the marginal likelihood, between the generating mechanisms of the internal data and the selected external data. We also conducted comprehensive simulations to evaluate its performance under various scenarios. Furthermore, we apply this method to predict and infer the endogenous factor IX (FIX) levels of patients who receive Etranacogene dezaparvovec over the long-term. Our estimated long-term FIX levels, validated by recent trial data, indicate that Etranacogene dezaparvovec induces sustained FIX production. Together, the theoretical findings, simulation results, and successful application of this framework underscore its potential to address similar long-term effectiveness estimation and inference questions in real world applications.

stat.ME↗

arXiv2022

Precision education: A Bayesian nonparametric approach for handling item and examinee heterogeneity in assessment data

We propose a novel nonparametric Bayesian IRT model in this paper by introducing the clustering effect at question level and further assume heterogeneity at examinee level under each question cluster, characterized by the mixture of Binomial distributions. The main contribution of this work is threefold: (1) We demonstrate that the model is identifiable. (2) The clustering effect can be captured asymptotically and the parameters of interest that measure the proficiency of examinees in solving certain questions can be estimated at a root n rate (up to a log term). (3) We present a tractable sampling algorithm to obtain valid posterior samples from our proposed model. We evaluate our model via a series of simulations as well as apply it to an English assessment data. This data analysis example nicely illustrates how our model can be used by test makers to distinguish different types of students and aid in the design of future tests.

stat.ME↗

arXiv2020

Identifying latent groups in spatial panel data using a Markov random field constrained product partition model

Understanding the heterogeneity over spatial locations is an important problem that has been widely studied in many applications such as economics and environmental science. In this paper, we focus on regression models for spatial panel data analysis, where repeated measurements are collected over time at various spatial locations. We propose a novel class of nonparametric priors that combines Markov random field (MRF) with the product partition model (PPM), and show that the resulting prior, called by MRF-PPM, is capable of identifying the latent group structure among the spatial locations while efficiently utilizing the spatial dependence information. We derive a closed-form conditional distribution for the proposed prior and introduce a new way to compute the marginal likelihood that renders efficient Bayesian inference. We further study the theoretical properties of the proposed MRF-PPM prior and show a clustering consistency result for the posterior distribution. We demonstrate the excellent empirical performance of our method via extensive simulation studies and applications to a US precipitation data and a California median household income data study.

stat.ME↗

arXiv2020

Nonparametric Matrix Response Regression with Application to Brain Imaging Data Analysis

With the rapid growth of neuroimaging technologies, a great effort has been dedicated recently to investigate the dynamic changes in brain activity. Examples include time course calcium imaging and dynamic brain functional connectivity. In this paper, we propose a novel nonparametric matrix response regression model to characterize the nonlinear association between 2D image outcomes and predictors such as time and patient information. Our estimation procedure can be formulated as a nuclear norm regularization problem, which can capture the underlying low-rank structure of the dynamic 2D images. We present a computationally efficient algorithm, derive the asymptotic theory and show that the method outperforms other existing approaches in simulations. We then apply the proposed method to a calcium imaging study for estimating the change of fluorescent intensities of neurons, and an electroencephalography study for a comparison in the dynamic connectivity covariance matrices between alcoholic and control individuals. For both studies, the method leads to a substantial improvement in prediction error.

stat.ME↗

arXiv2020

Spatial homogeneity learning for spatially correlated functional data with application to COVID-19 Growth rate curves

We study the spatial heterogeneity effect on regional COVID-19 pandemic timing and severity by analyzing the COVID-19 growth rate curves in the United States. We propose a geographically detailed functional data grouping method equipped with a functional conditional autoregressive (CAR) prior to fully capture the spatial correlation in the pandemic curves. The spatial homogeneity pattern can then be detected by a geographically weighted Chinese restaurant process prior which allows both locally spatially contiguous groups and globally discontiguous groups. We design an efficient Markov chain Monte Carlo (MCMC) algorithm to simultaneously infer the posterior distributions of the number of groups and the grouping configuration of spatial functional data. The superior numerical performance of the proposed method over competing methods is demonstrated using simulated studies and an application to COVID-19 state-level and county-level data study in the United States.

stat.AP↗