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Tianxi Cai

Publications and source records attributed to Tianxi Cai.

At least 91 records · Page 5Linked to original sources

Expert-Supervised Reinforcement Learning for Offline Policy Learning and Evaluation

Offline Reinforcement Learning (RL) is a promising approach for learning optimal policies in environments where direct exploration is expensive or unfeasible. However, the adoption of such policies in practice is often challenging, as they are hard to interpret within the application context, and lack measures of uncertainty for the learned policy value and its decisions. To overcome these issues, we propose an Expert-Supervised RL (ESRL) framework which uses uncertainty quantification for offline policy learning. In particular, we have three contributions: 1) the method can learn safe and optimal policies through hypothesis testing, 2) ESRL allows for different levels of risk averse implementations tailored to the application context, and finally, 3) we propose a way to interpret ESRL's policy at every state through posterior distributions, and use this framework to compute off-policy value function posteriors. We provide theoretical guarantees for our estimators and regret bounds consistent with Posterior Sampling for RL (PSRL). Sample efficiency of ESRL is independent of the chosen risk aversion threshold and quality of the behavior policy.

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Estimating Average Treatment Effects with a Double-Index Propensity Score

We consider estimating average treatment effects (ATE) of a binary treatment in observational data when data-driven variable selection is needed to select relevant covariates from a moderately large number of available covariates $\mathbf{X}$. To leverage covariates among $\mathbf{X}$ predictive of the outcome for efficiency gain while using regularization to fit a parametric propensity score (PS) model, we consider a dimension reduction of $\mathbf{X}$ based on fitting both working PS and outcome models using adaptive LASSO. A novel PS estimator, the Double-index Propensity Score (DiPS), is proposed, in which the treatment status is smoothed over the linear predictors for $\mathbf{X}$ from both the initial working models. The ATE is estimated by using the DiPS in a normalized inverse probability weighting (IPW) estimator, which is found to maintain double-robustness and also local semiparametric efficiency with a fixed number of covariates $p$. Under misspecification of working models, the smoothing step leads to gains in efficiency and robustness over traditional doubly-robust estimators. These results are extended to the case where $p$ diverges with sample size and working models are sparse. Simulations show the benefits of the approach in finite samples. We illustrate the method by estimating the ATE of statins on colorectal cancer risk in an electronic medical record (EMR) study and the effect of smoking on C-reactive protein (CRP) in the Framingham Offspring Study.

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Robust and Efficient Semi-Supervised Estimation of Average Treatment Effects with Application to Electronic Health Records Data

We consider the problem of estimating the average treatment effect (ATE) in a semi-supervised learning setting, where a very small proportion of the entire set of observations are labeled with the true outcome but features predictive of the outcome are available among all observations. This problem arises, for example, when estimating treatment effects in electronic health records (EHR) data because gold-standard outcomes are often not directly observable from the records but are observed for a limited number of patients through small-scale manual chart review. We develop an imputation-based approach for estimating the ATE that is robust to misspecification of the imputation model. This effectively allows information from the predictive features to be safely leveraged to improve efficiency in estimating the ATE. The estimator is additionally doubly-robust in that it is consistent under correct specification of either an initial propensity score model or a baseline outcome model. It is also locally semiparametric efficient under an ideal semi-supervised model where the distribution of the unlabeled data is known. Simulations exhibit the efficiency and robustness of the proposed method compared to existing approaches in finite samples.We illustrate the method by comparing rates of treatment response to two biologic agents for treatment inflammatory bowel disease using EHR data from Partner's Healthcare.

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Individual Data Protected Integrative Regression Analysis of High-dimensional Heterogeneous Data

Evidence-based decision making often relies on meta-analyzing multiple studies, which enables more precise estimation and investigation of generalizability. Integrative analysis of multiple heterogeneous studies is, however, highly challenging in the ultra high dimensional setting. The challenge is even more pronounced when the individual level data cannot be shared across studies, known as DataSHIELD constraint (Wolfson et al., 2010). Under sparse regression models that are assumed to be similar yet not identical across studies, we propose in this paper a novel integrative estimation procedure for data-Shielding High-dimensional Integrative Regression (SHIR). SHIR protects individual data through summary-statistics-based integrating procedure, accommodates between study heterogeneity in both the covariate distribution and model parameters, and attains consistent variable selection. Theoretically, SHIR is statistically more efficient than the existing distributed approaches that integrate debiased LASSO estimators from the local sites. Furthermore, the estimation error incurred by aggregating derived data is negligible compared to the statistical minimax rate and SHIR is shown to be asymptotically equivalent in estimation to the ideal estimator obtained by sharing all data. The finite-sample performance of our method is studied and compared with existing approaches via extensive simulation settings. We further illustrate the utility of SHIR to derive phenotyping algorithms for coronary artery disease using electronic health records data from multiple chronic disease cohorts.

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Optimal Statistical Inference for Individualized Treatment Effects in High-dimensional Models

The ability to predict individualized treatment effects (ITEs) based on a given patient's profile is essential for personalized medicine. We propose a hypothesis testing approach to choosing between two potential treatments for a given individual in the framework of high-dimensional linear models. The methodological novelty lies in the construction of a debiased estimator of the ITE and establishment of its asymptotic normality uniformly for an arbitrary future high-dimensional observation, while the existing methods can only handle certain specific forms of observations. We introduce a testing procedure with the type-I error controlled and establish its asymptotic power. The proposed method can be extended to making inference for general linear contrasts, including both the average treatment effect and outcome prediction. We introduce the optimality framework for hypothesis testing from both the minimaxity and adaptivity perspectives and establish the optimality of the proposed procedure. An extension to high-dimensional approximate linear models is also considered. The finite sample performance of the procedure is demonstrated in simulation studies and further illustrated through an analysis of electronic health records data from patients with rheumatoid arthritis.

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Integrative High Dimensional Multiple Testing with Heterogeneity under Data Sharing Constraints

Identifying informative predictors in a high dimensional regression model is a critical step for association analysis and predictive modeling. Signal detection in the high dimensional setting often fails due to the limited sample size. One approach to improve power is through meta-analyzing multiple studies on the same scientific question. However, integrative analysis of high dimensional data from multiple studies is challenging in the presence of between study heterogeneity. The challenge is even more pronounced with additional data sharing constraints under which only summary data but not individual level data can be shared across different sites. In this paper, we propose a novel data shielding integrative large-scale testing (DSILT) approach to signal detection by allowing between study heterogeneity and not requiring sharing of individual level data. Assuming the underlying high dimensional regression models of the data differ across studies yet share similar support, the DSILT approach incorporates proper integrative estimation and debiasing procedures to construct test statistics for the overall effects of specific covariates. We also develop a multiple testing procedure to identify significant effects while controlling for false discovery rate (FDR) and false discovery proportion (FDP). Theoretical comparisons of the DSILT procedure with the ideal individual--level meta--analysis (ILMA) approach and other distributed inference methods are investigated. Simulation studies demonstrate that the DSILT procedure performs well in both false discovery control and attaining power. The proposed method is applied to a real example on detecting interaction effect of the genetic variants for statins and obesity on the risk for Type 2 Diabetes.

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Spherical Regression under Mismatch Corruption with Application to Automated Knowledge Translation

Motivated by a series of applications in data integration, language translation, bioinformatics, and computer vision, we consider spherical regression with two sets of unit-length vectors when the data are corrupted by a small fraction of mismatch in the response-predictor pairs. We propose a three-step algorithm in which we initialize the parameters by solving an orthogonal Procrustes problem to estimate a translation matrix $\mathbb{W}$ ignoring the mismatch. We then estimate a mapping matrix aiming to correct the mismatch using hard-thresholding to induce sparsity, while incorporating potential group information. We eventually obtain a refined estimate for $\mathbb{W}$ by removing the estimated mismatched pairs. We derive the error bound for the initial estimate of $\mathbb{W}$ in both fixed and high-dimensional setting. We demonstrate that the refined estimate of $\mathbb{W}$ achieves an error rate that is as good as if no mismatch is present. We show that our mapping recovery method not only correctly distinguishes one-to-one and one-to-many correspondences, but also consistently identifies the matched pairs and estimates the weight vector for combined correspondence. We examine the finite sample performance of the proposed method via extensive simulation studies, and with application to the unsupervised translation of medical codes using electronic health records data.

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Clinical Concept Embeddings Learned from Massive Sources of Multimodal Medical Data

Word embeddings are a popular approach to unsupervised learning of word relationships that are widely used in natural language processing. In this article, we present a new set of embeddings for medical concepts learned using an extremely large collection of multimodal medical data. Leaning on recent theoretical insights, we demonstrate how an insurance claims database of 60 million members, a collection of 20 million clinical notes, and 1.7 million full text biomedical journal articles can be combined to embed concepts into a common space, resulting in the largest ever set of embeddings for 108,477 medical concepts. To evaluate our approach, we present a new benchmark methodology based on statistical power specifically designed to test embeddings of medical concepts. Our approach, called cui2vec, attains state-of-the-art performance relative to previous methods in most instances. Finally, we provide a downloadable set of pre-trained embeddings for other researchers to use, as well as an online tool for interactive exploration of the cui2vec embeddings

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NILE: Fast Natural Language Processing for Electronic Health Records

Objective: Narrative text in Electronic health records (EHR) contain rich information for medical and data science studies. This paper introduces the design and performance of Narrative Information Linear Extraction (NILE), a natural language processing (NLP) package for EHR analysis that we share with the medical informatics community. Methods: NILE uses a modified prefix-tree search algorithm for named entity recognition, which can detect prefix and suffix sharing. The semantic analyses are implemented as rule-based finite state machines. Analyses include negation, location, modification, family history, and ignoring. Result: The processing speed of NILE is hundreds to thousands times faster than existing NLP software for medical text. The accuracy of presence analysis of NILE is on par with the best performing models on the 2010 i2b2/VA NLP challenge data. Conclusion: The speed, accuracy, and being able to operate via API make NILE a valuable addition to the NLP software for medical informatics and data science.

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Surrogate Aided Unsupervised Recovery of Sparse Signals in Single Index Models for Binary Outcomes

We consider the recovery of regression coefficients, denoted by $\boldsymbolβ_0$, for a single index model (SIM) relating a binary outcome $Y$ to a set of possibly high dimensional covariates $\boldsymbol{X}$, based on a large but 'unlabeled' dataset $\mathcal{U}$, with $Y$ never observed. On $\mathcal{U}$, we fully observe $\boldsymbol{X}$ and additionally, a surrogate $S$ which, while not being strongly predictive of $Y$ throughout the entirety of its support, can forecast it with high accuracy when it assumes extreme values. Such datasets arise naturally in modern studies involving large databases such as electronic medical records (EMR) where $Y$, unlike $(\boldsymbol{X}, S)$, is difficult and/or expensive to obtain. In EMR studies, an example of $Y$ and $S$ would be the true disease phenotype and the count of the associated diagnostic codes respectively. Assuming another SIM for $S$ given $\boldsymbol{X}$, we show that under sparsity assumptions, we can recover $\boldsymbolβ_0$ proportionally by simply fitting a least squares LASSO estimator to the subset of the observed data on $(\boldsymbol{X}, S)$ restricted to the extreme sets of $S$, with $Y$ imputed using the surrogacy of $S$. We obtain sharp finite sample performance bounds for our estimator, including deterministic deviation bounds and probabilistic guarantees. We demonstrate the effectiveness of our approach through multiple simulation studies, as well as by application to real data from an EMR study conducted at the Partners HealthCare Systems.

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Multi-view Banded Spectral Clustering with Application to ICD9 Clustering

Despite recent development in methodology, community detection remains a challenging problem. Existing literature largely focuses on the standard setting where a network is learned using an observed adjacency matrix from a single data source. Constructing a shared network from multiple data sources is more challenging due to the heterogeneity across populations. Additionally, no existing method leverages the prior distance knowledge available in many domains to help the discovery of the network structure. To bridge this gap, in this paper we propose a novel spectral clustering method that optimally combines multiple data sources while leveraging the prior distance knowledge. The proposed method combines a banding step guided by the distance knowledge with a subsequent weighting step to maximize consensus across multiple sources. Its statistical performance is thoroughly studied under a multi-view stochastic block model. We also provide a simple yet optimal rule of choosing weights in practice. The efficacy and robustness of the method is fully demonstrated through extensive simulations. Finally, we apply the method to cluster the International classification of diseases, ninth revision (ICD9), codes and yield a very insightful clustering structure by integrating information from a large claim database and two healthcare systems.

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A Fast Divide-and-Conquer Sparse Cox Regression

We propose a computationally and statistically efficient divide-and-conquer (DAC) algorithm to fit sparse Cox regression to massive datasets where the sample size $n_0$ is exceedingly large and the covariate dimension $p$ is not small but $n_0\gg p$. The proposed algorithm achieves computational efficiency through a one-step linear approximation followed by a least square approximation to the partial likelihood (PL). These sequences of linearization enable us to maximize the PL with only a small subset and perform penalized estimation via a fast approximation to the PL. The algorithm is applicable for the analysis of both time-independent and time-dependent survival data. Simulations suggest that the proposed DAC algorithm substantially outperforms the full sample-based estimators and the existing DAC algorithm with respect to the computational speed, while it achieves similar statistical efficiency as the full sample-based estimators. The proposed algorithm was applied to an extraordinarily large time-independent survival dataset and an extraordinarily large time-dependent survival dataset for the prediction of heart failure-specific readmission within 30 days among Medicare heart failure patients.

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Variance Components Genetic Association Test for Zero-inflated Count Outcomes

Commonly in biomedical research, studies collect data in which an outcome measure contains informative excess zeros; for example when observing the burden of neuritic plaques in brain pathology studies, those who show none contribute to our understanding of neurodegenerative disease. The outcome may be characterized by a mixture distribution with one component being the `structural zero' and the other component being a Poisson distribution. We propose a novel variance components score test of genetic association between a set of genetic markers and a zero-inflated count outcome from a mixture distribution. This test shares advantageous properties with SNP-set tests which have been previously devised for standard continuous or binary outcomes, such as the Sequence Kernel Association Test (SKAT). In particular, our method has superior statistical power compared to competing methods, especially when there is correlation within the group of markers, and when the SNPs are associated with both the mixing proportion and the rate of the Poisson distribution. We apply the method to Alzheimer's data from the Rush University Religious Orders Study and Memory and Aging Project (ROSMAP), where as proof of principle we find highly significant associations with the APOE gene, in both the `structural zero' and `count' parameters, when applied to a zero-inflated neuritic plaques count outcome.

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Semi-Supervised Approaches to Efficient Evaluation of Model Prediction Performance

In many modern machine learning applications, the outcome is expensive or time-consuming to collect while the predictor information is easy to obtain. Semi-supervised learning (SSL) aims at utilizing large amounts of `unlabeled' data along with small amounts of `labeled' data to improve the efficiency of a classical supervised approach. Though numerous SSL classification and prediction procedures have been proposed in recent years, no methods currently exist to evaluate the prediction performance of a working regression model. In the context of developing phenotyping algorithms derived from electronic medical records (EMR), we present an efficient two-step estimation procedure for evaluating a binary classifier based on various prediction performance measures in the semi-supervised (SS) setting. In step I, the labeled data is used to obtain a non-parametrically calibrated estimate of the conditional risk function. In step II, SS estimates of the prediction accuracy parameters are constructed based on the estimated conditional risk function and the unlabeled data. We demonstrate that under mild regularity conditions the proposed estimators are consistent and asymptotically normal. Importantly, the asymptotic variance of the SS estimators is always smaller than that of the supervised counterparts under correct model specification. We also correct for potential overfitting bias in the SS estimators in finite sample with cross-validation and develop a perturbation resampling procedure to approximate their distributions. Our proposals are evaluated through extensive simulation studies and illustrated with two real EMR studies aiming to develop phenotyping algorithms for rheumatoid arthritis and multiple sclerosis.

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Efficient and Adaptive Linear Regression in Semi-Supervised Settings

We consider the linear regression problem under semi-supervised settings wherein the available data typically consists of: (i) a small or moderate sized 'labeled' data, and (ii) a much larger sized 'unlabeled' data. Such data arises naturally from settings where the outcome, unlike the covariates, is expensive to obtain, a frequent scenario in modern studies involving large databases like electronic medical records (EMR). Supervised estimators like the ordinary least squares (OLS) estimator utilize only the labeled data. It is often of interest to investigate if and when the unlabeled data can be exploited to improve estimation of the regression parameter in the adopted linear model. In this paper, we propose a class of 'Efficient and Adaptive Semi-Supervised Estimators' (EASE) to improve estimation efficiency. The EASE are two-step estimators adaptive to model mis-specification, leading to improved (optimal in some cases) efficiency under model mis-specification, and equal (optimal) efficiency under a linear model. This adaptive property, often unaddressed in the existing literature, is crucial for advocating 'safe' use of the unlabeled data. The construction of EASE primarily involves a flexible 'semi-non-parametric' imputation, including a smoothing step that works well even when the number of covariates is not small; and a follow up 'refitting' step along with a cross-validation (CV) strategy both of which have useful practical as well as theoretical implications towards addressing two important issues: under-smoothing and over-fitting. We establish asymptotic results including consistency, asymptotic normality and the adaptive properties of EASE. We also provide influence function expansions and a 'double' CV strategy for inference. The results are further validated through extensive simulations, followed by application to an EMR study on auto-immunity.

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Functional principal variance component testing for a genetic association study of HIV progression

HIV-1C is the most prevalent subtype of HIV-1 and accounts for over half of HIV-1 infections worldwide. Host genetic influence of HIV infection has been previously studied in HIV-1B, but little attention has been paid to the more prevalent subtype C. To understand the role of host genetics in HIV-1C disease progression, we perform a study to assess the association between longitudinally collected measures of disease and more than 100,000 genetic markers located on chromosome 6. The most common approach to analyzing longitudinal data in this context is linear mixed effects models, which may be overly simplistic in this case. On the other hand, existing non-parametric methods may suffer from low power due to high degrees of freedom (DF) and may be computationally infeasible at the large scale. We propose a functional principal variance component (FPVC) testing framework which captures the nonlinearity in the CD4 and viral load with potentially low DF and is fast enough to carry out thousands or millions of times. The FPVC testing unfolds in two stages. In the first stage, we summarize the markers of disease progression according to their major patterns of variation via functional principal components analysis (FPCA). In the second stage, we employ a simple working model and variance component testing to examine the association between the summaries of disease progression and a set of single nucleotide polymorphisms. We supplement this analysis with simulation results which indicate that FPVC testing can offer large power gains over the standard linear mixed effects model.

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Evaluating Surrogate Marker Information using Censored Data

Given the long follow-up periods that are often required for treatment or intervention studies, the potential to use surrogate markers to decrease the required follow-up time is a very attractive goal. However, previous studies have shown that using inadequate markers or making inappropriate assumptions about the relationship between the primary outcome and surrogate marker can lead to inaccurate conclusions regarding the treatment effect. Currently available methods for identifying and validating surrogate markers tend to rely on restrictive model assumptions and/or focus on uncensored outcomes. The ability to use such methods in practice when the primary outcome of interest is a time-to-event outcome is difficult due to censoring and missing surrogate information among those who experience the primary outcome before surrogate marker measurement. In this paper, we propose a novel definition of the proportion of treatment effect explained by surrogate information collected up to a specified time in the setting of a time-to-event primary outcome. Our proposed approach accommodates a setting where individuals may experience the primary outcome before the surrogate marker is measured. We propose a robust nonparametric procedure to estimate the defined quantity using censored data and use a perturbation-resampling procedure for variance estimation. Simulation studies demonstrate that the proposed procedures perform well in finite samples. We illustrate the proposed procedures by investigating two potential surrogate markers for diabetes using data from the Diabetes Prevention Program.

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L1-Regularized Least Squares for Support Recovery of High Dimensional Single Index Models with Gaussian Designs

It is known that for a certain class of single index models (SIMs) $Y = f(\boldsymbol{X}_{p \times 1}^\intercal\boldsymbolβ_0, \varepsilon)$, support recovery is impossible when $\boldsymbol{X} \sim \mathcal{N}(0, \mathbb{I}_{p \times p})$ and a model complexity adjusted sample size is below a critical threshold. Recently, optimal algorithms based on Sliced Inverse Regression (SIR) were suggested. These algorithms work provably under the assumption that the design $\boldsymbol{X}$ comes from an i.i.d. Gaussian distribution. In the present paper we analyze algorithms based on covariance screening and least squares with $L_1$ penalization (i.e. LASSO) and demonstrate that they can also enjoy optimal (up to a scalar) rescaled sample size in terms of support recovery, albeit under slightly different assumptions on $f$ and $\varepsilon$ compared to the SIR based algorithms. Furthermore, we show more generally, that LASSO succeeds in recovering the signed support of $\boldsymbolβ_0$ if $\boldsymbol{X} \sim \mathcal{N}(0, \boldsymbolΣ)$, and the covariance $\boldsymbolΣ$ satisfies the irrepresentable condition. Our work extends existing results on the support recovery of LASSO for the linear model, to a more general class of SIMs.

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