arXiv subjects

Michael R. Kosorok

Publications and source records attributed to Michael R. Kosorok.

At least 55 records · Page 3Linked to original sources

arXiv2020

Missing Data Imputation for Classification Problems

Imputation of missing data is a common application in various classification problems where the feature training matrix has missingness. A widely used solution to this imputation problem is based on the lazy learning technique, $k$-nearest neighbor (kNN) approach. However, most of the previous work on missing data does not take into account the presence of the class label in the classification problem. Also, existing kNN imputation methods use variants of Minkowski distance as a measure of distance, which does not work well with heterogeneous data. In this paper, we propose a novel iterative kNN imputation technique based on class weighted grey distance between the missing datum and all the training data. Grey distance works well in heterogeneous data with missing instances. The distance is weighted by Mutual Information (MI) which is a measure of feature relevance between the features and the class label. This ensures that the imputation of the training data is directed towards improving classification performance. This class weighted grey kNN imputation algorithm demonstrates improved performance when compared to other kNN imputation algorithms, as well as standard imputation algorithms such as MICE and missForest, in imputation and classification problems. These problems are based on simulated scenarios and UCI datasets with various rates of missingness.

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arXiv2020

Technical Background for "A Precision Medicine Approach to Develop and Internally Validate Optimal Exercise and Weight Loss Treatments for Overweight and Obese Adults with Knee Osteoarthritis"

We provide additional statistical background for the methodology developed in the clinical analysis of knee osteoarthritis in "A Precision Medicine Approach to Develop and Internally Validate Optimal Exercise and Weight Loss Treatments for Overweight and Obese Adults with Knee Osteoarthritis" (Jiang et al. 2020). Jiang et al. 2020 proposed a pipeline to learn optimal treatment rules with precision medicine models and compared them with zero-order models with a Z-test. The model performance was based on value functions, a scalar that predicts the future reward of each decision rule. The jackknife (i.e., leave-one-out cross validation) method was applied to estimate the value function and its variance of several outcomes in IDEA. IDEA is a randomized clinical trial studying three interventions (exercise (E), dietary weight loss (D), and D+E) on overweight and obese participants with knee osteoarthritis. In this report, we expand the discussion and justification with additional statistical background. We elaborate more on the background of precision medicine, the derivation of the jackknife estimator of value function and its estimated variance, the consistency property of jackknife estimator, as well as additional simulation results that reflect more of the performance of jackknife estimators. We recommend reading Jiang et al. 2020 for clinical application and interpretation of the optimal ITR of knee osteoarthritis as well as the overall understanding of the pipeline and recommend using this article to understand the underlying statistical derivation and methodology.

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arXiv2019

High dimensional precision medicine from patient-derived xenografts

The complexity of human cancer often results in significant heterogeneity in response to treatment. Precision medicine offers potential to improve patient outcomes by leveraging this heterogeneity. Individualized treatment rules (ITRs) formalize precision medicine as maps from the patient covariate space into the space of allowable treatments. The optimal ITR is that which maximizes the mean of a clinical outcome in a population of interest. Patient-derived xenograft (PDX) studies permit the evaluation of multiple treatments within a single tumor and thus are ideally suited for estimating optimal ITRs. PDX data are characterized by correlated outcomes, a high-dimensional feature space, and a large number of treatments. Existing methods for estimating optimal ITRs do not take advantage of the unique structure of PDX data or handle the associated challenges well. In this paper, we explore machine learning methods for estimating optimal ITRs from PDX data. We analyze data from a large PDX study to identify biomarkers that are informative for developing personalized treatment recommendations in multiple cancers. We estimate optimal ITRs using regression-based approaches such as Q-learning and direct search methods such as outcome weighted learning. Finally, we implement a superlearner approach to combine a set of estimated ITRs and show that the resulting ITR performs better than any of the input ITRs, mitigating uncertainty regarding user choice of any particular ITR estimation methodology. Our results indicate that PDX data are a valuable resource for developing individualized treatment strategies in oncology.

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arXiv2019

Balanced Policy Evaluation and Learning for Right Censored Data

Individualized treatment rules can lead to better health outcomes when patients have heterogeneous responses to treatment. Very few individualized treatment rule estimation methods are compatible with a multi-treatment observational study with right censored survival outcomes. In this paper we extend policy evaluation methods to the right censored data setting. Existing approaches either make restrictive assumptions about the structure of the data, or use inverse weighting methods that increase the variance of the estimator resulting in decreased performance. We propose a method which uses balanced policy evaluation combined with an imputation approach to remove right censoring. We show that the proposed imputation approach is compatible with a large number of existing survival models and can be used to extend any individualized treatment rule estimation method to the right censored data setting. We establish the rate at which the imputed values converge to the conditional expected survival times, as well as consistency guarantees and regret bounds for the combined balanced policy with imputation approach. In simulation studies, we demonstrate the improved performance of our approach compared to existing methods. We also apply our method to data from the University of North Carolina Center for AIDS Research HIV Clinical Cohort.

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arXiv2019

Sample Size Calculations for SMARTs

Sequential Multiple Assignment Randomized Trials (SMARTs) are considered the gold standard for estimation and evaluation of treatment regimes. SMARTs are typically sized to ensure sufficient power for a simple comparison, e.g., the comparison of two fixed treatment sequences. Estimation of an optimal treatment regime is conducted as part of a secondary and hypothesis-generating analysis with formal evaluation of the estimated optimal regime deferred to a follow-up trial. However, running a follow-up trial to evaluate an estimated optimal treatment regime is costly and time-consuming; furthermore, the estimated optimal regime that is to be evaluated in such a follow-up trial may be far from optimal if the original trial was underpowered for estimation of an optimal regime. We derive sample size procedures for a SMART that ensure: (i) sufficient power for comparing the optimal treatment regime with standard of care; and (ii) the estimated optimal regime is within a given tolerance of the true optimal regime with high-probability. We establish asymptotic validity of the proposed procedures and demonstrate their finite sample performance in a series of simulation experiments.

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arXiv2019

Genome analysis and pleiotropy assessment using causal networks with loss of function mutation and metabolomics

Background: Many genome-wide association studies have detected genomic regions associated with traits, yet understanding the functional causes of association often remains elusive. Utilizing systems approaches and focusing on intermediate molecular phenotypes might facilitate biologic understanding. Results: The availability of exome sequencing of two populations of African-Americans and European-Americans from the Atherosclerosis Risk in Communities study allowed us to investigate the effects of annotated loss-of-function (LoF) mutations on 122 serum metabolites. To assess the findings, we built metabolomic causal networks for each population separately and utilized structural equation modeling. We then validated our findings with a set of independent samples. By use of methods based on concepts of Mendelian randomization of genetic variants, we showed that some of the affected metabolites are risk predictors in the causal pathway of disease. For example, LoF mutations in the gene KIAA1755 were identified to elevate the levels of eicosapentaenoate (p-value=5E-14), an essential fatty acid clinically identified to increase essential hypertension. We showed that this gene is in the pathway to triglycerides, where both triglycerides and essential hypertension are risk factors of metabolomic disorder and heart attack. We also identified that the gene CLDN17, harboring loss-of-function mutations, had pleiotropic actions on metabolites from amino acid and lipid pathways. Conclusion: Using systems biology approaches for the analysis of metabolomics and genetic data, we integrated several biological processes, which lead to findings that may functionally connect genetic variants with complex diseases.

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arXiv2019

Efficient estimation of accelerated lifetime models under length-biased sampling

In prevalent cohort studies where subjects are recruited at a cross-section, the time to an event may be subject to length-biased sampling, with the observed data being either the forward recurrence time, or the backward recurrence time, or their sum. In the regression setting, it has been shown that the accelerated failure time model for the underlying event time is invariant under these observed data set-ups and can be fitted using standard methodology for accelerated failure time model estimation, ignoring the length-bias. However, the efficiency of these estimators is unclear, owing to the fact that the observed covariate distribution, which is also length-biased, may contain information about the regression parameter in the accelerated life model. We demonstrate that if the true covariate distribution is completely unspecified, then the naive estimator based on the conditional likelihood given the covariates is fully efficient.

math.ST↗

arXiv2019

Estimating Individualized Treatment Regimes from Crossover Designs

The field of precision medicine aims to tailor treatment based on patient-specific factors in a reproducible way. To this end, estimating an optimal individualized treatment regime (ITR) that recommends treatment decisions based on patient characteristics to maximize the mean of a pre-specified outcome is of particular interest. Several methods have been proposed for estimating an optimal ITR from clinical trial data in the parallel group setting where each subject is randomized to a single intervention. However, little work has been done in the area of estimating the optimal ITR from crossover study designs. Such designs naturally lend themselves to precision medicine, because they allow for observing the response to multiple treatments for each patient. In this paper, we introduce a method for estimating the optimal ITR using data from a 2x2 crossover study with or without carryover effects. The proposed method is similar to policy search methods such as outcome weighted learning; however, we take advantage of the crossover design by using the difference in responses under each treatment as the observed reward. We establish Fisher and global consistency, present numerical experiments, and analyze data from a feeding trial to demonstrate the improved performance of the proposed method compared to standard methods for a parallel study design.

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arXiv2018

Receiver Operating Characteristic Curves and Confidence Bands for Support Vector Machines

Many problems that appear in biomedical decision making, such as diagnosing disease and predicting response to treatment, can be expressed as binary classification problems. The costs of false positives and false negatives vary across application domains and receiver operating characteristic (ROC) curves provide a visual representation of this trade-off. Nonparametric estimators for the ROC curve, such as a weighted support vector machine (SVM), are desirable because they are robust to model misspecification. While weighted SVMs have great potential for estimating ROC curves, their theoretical properties were heretofore underdeveloped. We propose a method for constructing confidence bands for the SVM ROC curve and provide the theoretical justification for the SVM ROC curve by showing that the risk function of the estimated decision rule is uniformly consistent across the weight parameter. We demonstrate the proposed confidence band method and the superior sensitivity and specificity of the weighted SVM compared to commonly used methods in diagnostic medicine using simulation studies. We present two illustrative examples: diagnosis of hepatitis C and a predictive model for treatment response in breast cancer.

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arXiv2018

A proportional hazards model for interval-censored data subject to instantaneous failures

The proportional hazards (PH) model is arguably one of the most popular models used to analyze time to event data arising from clinical trials and longitudinal studies, among many others. In many such studies, the event time of interest is not directly observed but is known relative to periodic examination times; i.e., practitioners observe either current status or interval-censored data. The analysis of data of this structure is often fraught with many difficulties. Further exacerbating this issue, in some such studies the observed data also consists of instantaneous failures; i.e., the event times for several study units coincide exactly with the time at which the study begins. In light of these difficulties, this work focuses on developing a mixture model, under the PH assumptions, which can be used to analyze interval-censored data subject to instantaneous failures. To allow for modeling flexibility, two methods of estimating the unknown cumulative baseline hazard function are proposed; a fully parametric and a monotone spline representation are considered. Through a novel data augmentation procedure involving latent Poisson random variables, an expectation-maximization (EM) algorithm was developed to complete model fitting. The resulting EM algorithm is easy to implement and is computationally efficient. Moreover, through extensive simulation studies the proposed approach is shown to provide both reliable estimation and inference.

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arXiv2017

Augmented Outcome-weighted Learning for Optimal Treatment Regimes

Precision medicine is of considerable interest in clinical, academic and regulatory parties. The key to precision medicine is the optimal treatment regime. Recently, Zhou et al. (2017) developed residual weighted learning (RWL) to construct the optimal regime that directly optimize the clinical outcome. However, this method involves computationally intensive non-convex optimization, which cannot guarantee a global solution. Furthermore, this method does not possess fully semiparametrical efficiency. In this article, we propose augmented outcome-weighted learning (AOL). The method is built on a doubly robust augmented inverse probability weighted estimator, and hence constructs semiparametrically efficient regimes. Our proposed AOL is closely related to RWL. The weights are obtained from counterfactual residuals, where negative residuals are reflected to positive and accordingly their treatment assignments are switched to opposites. Convex loss functions are thus applied to guarantee a global solution and to reduce computations. We show that AOL is universally consistent, i.e., the estimated regime of AOL converges the Bayes regime when the sample size approaches infinity, without knowing any specifics of the distribution of the data. We also propose variable selection methods for linear and nonlinear regimes, respectively, to further improve performance. The performance of the proposed AOL methods is illustrated in simulation studies and in an analysis of the Nefazodone-CBASP clinical trial data.

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arXiv2017

Causal nearest neighbor rules for optimal treatment regimes

The estimation of optimal treatment regimes is of considerable interest to precision medicine. In this work, we propose a causal $k$-nearest neighbor method to estimate the optimal treatment regime. The method roots in the framework of causal inference, and estimates the causal treatment effects within the nearest neighborhood. Although the method is simple, it possesses nice theoretical properties. We show that the causal $k$-nearest neighbor regime is universally consistent. That is, the causal $k$-nearest neighbor regime will eventually learn the optimal treatment regime as the sample size increases. We also establish its convergence rate. However, the causal $k$-nearest neighbor regime may suffer from the curse of dimensionality, i.e. performance deteriorates as dimensionality increases. To alleviate this problem, we develop an adaptive causal $k$-nearest neighbor method to perform metric selection and variable selection simultaneously. The performance of the proposed methods is illustrated in simulation studies and in an analysis of a chronic depression clinical trial.

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arXiv2017

Estimating Dynamic Treatment Regimes in Mobile Health Using V-learning

The vision for precision medicine is to use individual patient characteristics to inform a personalized treatment plan that leads to the best healthcare possible for each patient. Mobile technologies have an important role to play in this vision as they offer a means to monitor a patient's health status in real-time and subsequently to deliver interventions if, when, and in the dose that they are needed. Dynamic treatment regimes formalize individualized treatment plans as sequences of decision rules, one per stage of clinical intervention, that map current patient information to a recommended treatment. However, existing methods for estimating optimal dynamic treatment regimes are designed for a small number of fixed decision points occurring on a coarse time-scale. We propose a new reinforcement learning method for estimating an optimal treatment regime that is applicable to data collected using mobile technologies in an outpatient setting. The proposed method accommodates an indefinite time horizon and minute-by-minute decision making that are common in mobile health applications. We show the proposed estimators are consistent and asymptotically normal under mild conditions. The proposed methods are applied to estimate an optimal dynamic treatment regime for controlling blood glucose levels in patients with type 1 diabetes.

stat.ML↗

arXiv2017

Double Sparsity Kernel Learning with Automatic Variable Selection and Data Extraction

Learning with Reproducing Kernel Hilbert Spaces (RKHS) has been widely used in many scientific disciplines. Because a RKHS can be very flexible, it is common to impose a regularization term in the optimization to prevent overfitting. Standard RKHS learning employs the squared norm penalty of the learning function. Despite its success, many challenges remain. In particular, one cannot directly use the squared norm penalty for variable selection or data extraction. Therefore, when there exists noise predictors, or the underlying function has a sparse representation in the dual space, the performance of standard RKHS learning can be suboptimal. In the literature,work has been proposed on how to perform variable selection in RKHS learning, and a data sparsity constraint was considered for data extraction. However, how to learn in a RKHS with both variable selection and data extraction simultaneously remains unclear. In this paper, we propose a unified RKHS learning method, namely, DOuble Sparsity Kernel (DOSK) learning, to overcome this challenge. An efficient algorithm is provided to solve the corresponding optimization problem. We prove that under certain conditions, our new method can asymptotically achieve variable selection consistency. Simulated and real data results demonstrate that DOSK is highly competitive among existing approaches for RKHS learning.

stat.ME↗

arXiv2017

Estimating Individualized Treatment Rules for Ordinal Treatments

Precision medicine is an emerging scientific topic for disease treatment and prevention that takes into account individual patient characteristics. It is an important direction for clinical research, and many statistical methods have been recently proposed. One of the primary goals of precision medicine is to obtain an optimal individual treatment rule (ITR), which can help make decisions on treatment selection according to each patient's specific characteristics. Recently, outcome weighted learning (OWL) has been proposed to estimate such an optimal ITR in a binary treatment setting by maximizing the expected clinical outcome. However, for ordinal treatment settings, such as individualized dose finding, it is unclear how to use OWL. In this paper, we propose a new technique for estimating ITR with ordinal treatments. In particular, we propose a data duplication technique with a piecewise convex loss function. We establish Fisher consistency for the resulting estimated ITR under certain conditions, and obtain the convergence and risk bound properties. Simulated examples and two applications to datasets from an irritable bowel problem and a type 2 diabetes mellitus observational study demonstrate the highly competitive performance of the proposed method compared to existing alternatives.

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arXiv2016

Robust Hybrid Learning for Estimating Personalized Dynamic Treatment Regimens

Dynamic treatment regimens (DTRs) are sequential decision rules tailored at each stage by potentially time-varying patient features and intermediate outcomes observed in previous stages. The complexity, patient heterogeneity and chronicity of many diseases and disorders call for learning optimal DTRs which best dynamically tailor treatment to each individual's response over time. Proliferation of personalized data (e.g., genetic and imaging data) provides opportunities for deep tailoring as well as new challenges for statistical methodology. In this work, we propose a robust hybrid approach referred as Augmented Multistage Outcome-Weighted Learning (AMOL) to integrate outcome-weighted learning and Q-learning to identify optimal DTRs from the Sequential Multiple Assignment Randomization Trials (SMARTs). We generalize outcome weighted learning (O-learning; Zhao et al.~2012) to allow for negative outcomes; we propose methods to reduce variability of weights in O-learning to achieve numeric stability and higher efficiency; finally, for multiple-stage SMART studies, we introduce doubly robust augmentation to machine learning based O-learning to improve efficiency by drawing information from regression model-based Q-learning at each stage. The proposed AMOL remains valid even if the Q-learning model is misspecified. We establish the theoretical properties of AMOL, including the consistency of the estimated rules and the rates of convergence to the optimal value function. The comparative advantage of AMOL over existing methods is demonstrated in extensive simulation studies and applications to two SMART data sets: a two-stage trial for attention deficit and hyperactive disorder (ADHD) and the STAR*D trial for major depressive disorder (MDD).

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arXiv2015

Asymptotics for change-point models under varying degrees of mis-specification

Change-point models are widely used by statisticians to model drastic changes in the pattern of observed data. Least squares/maximum likelihood based estimation of change-points leads to curious asymptotic phenomena. When the change-point model is correctly specified, such estimates generally converge at a fast rate ($n$) and are asymptotically described by minimizers of jump process. Under complete mis-specification by a smooth curve, i.e. when a change-point model is fitted to data described by a smooth curve, the rate of convergence slows down to $n^{1/3}$ and the limit distribution changes to that of the minimizer of a continuous Gaussian process. In this paper we provide a bridge between these two extreme scenarios by studying the limit behavior of change-point estimates under varying degrees of model mis-specification by smooth curves, which can be viewed as local alternatives. We find that the limiting regime depends on how quickly the alternatives approach a change-point model. We unravel a family of `intermediate' limits that can transition, at least qualitatively, to the limits in the two extreme scenarios.

math.ST↗

arXiv2015

Residual Weighted Learning for Estimating Individualized Treatment Rules

Personalized medicine has received increasing attention among statisticians, computer scientists, and clinical practitioners. A major component of personalized medicine is the estimation of individualized treatment rules (ITRs). Recently, Zhao et al. (2012) proposed outcome weighted learning (OWL) to construct ITRs that directly optimize the clinical outcome. Although OWL opens the door to introducing machine learning techniques to optimal treatment regimes, it still has some problems in performance. In this article, we propose a general framework, called Residual Weighted Learning (RWL), to improve finite sample performance. Unlike OWL which weights misclassification errors by clinical outcomes, RWL weights these errors by residuals of the outcome from a regression fit on clinical covariates excluding treatment assignment. We utilize the smoothed ramp loss function in RWL, and provide a difference of convex (d.c.) algorithm to solve the corresponding non-convex optimization problem. By estimating residuals with linear models or generalized linear models, RWL can effectively deal with different types of outcomes, such as continuous, binary and count outcomes. We also propose variable selection methods for linear and nonlinear rules, respectively, to further improve the performance. We show that the resulting estimator of the treatment rule is consistent. We further obtain a rate of convergence for the difference between the expected outcome using the estimated ITR and that of the optimal treatment rule. The performance of the proposed RWL methods is illustrated in simulation studies and in an analysis of cystic fibrosis clinical trial data.

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