arXiv subjects

Nicholas C. Henderson

Publications and source records attributed to Nicholas C. Henderson.

14 recordsLinked to original sources

arXiv2026

Robust Updating of a Risk Prediction Model by Integrating External Ranking Information

Utilizing established risk factors and prognostic models can often improve the construction of a newer risk model that uses novel biomarkers in a smaller, internal study. However, directly borrowing information from an established prognostic model is often unsuitable due to differences in study populations, patient outcomes measured, and other specific features of the internal study design. To better enable the use of established prognostic information when constructing a novel risk model, we propose an estimation approach centered around the idea that the risk rankings rather than the risk scores from an established prognostic model are often more transportable to the internal study context. To leverage external ranking information, our approach introduces the ranking parameters associated with the regression coefficients of an internal risk model and estimates the internal risk model parameters by penalizing a ranking-based discrepancy measure between the ranking parameters and the rankings implied by the established prognostic model. Our method does not require the external prognostic model to have a specific form, but only requires one to compute risk score rankings from an external model. Simulation studies demonstrate that our method leads to competitive predictive performance and performs particularly well when the true internal and external prognostic models have high rank correlation but large discrepancies between their underlying risk scores. We demonstrate the use of our approach through the development of a prognostic model for advanced prostate cancer patients who were treated with an immune checkpoint inhibitor

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arXiv2025

Targeted Parameter Estimation for Robust Empirical Bayes Ranking

Ordering the expected outcomes across a collection of clusters after performing a covariate adjustment commonly arises in many applied settings, such as healthcare provider evaluation. Regression parameters in such covariate adjustment models are frequently estimated by maximum likelihood or through other criteria that do not directly evaluate the quality of the rankings resulting from using a particular set of parameter estimates. In this article, we propose both a novel empirical Bayes ranking procedure and an associated estimation approach for finding the regression parameters of the covariate adjustment model. By building our ranking approach around estimating approximate percentiles of the covariate-adjusted cluster-level means, we are able to develop manageable expressions for the expected ranking squared-error loss associated with any choice of the covariate-adjustment model parameters, and we harness this to generate a novel unbiased estimator for this expected loss. Minimization of this unbiased estimator directly leads to a novel ranking procedure that is often more robust than conventional empirical Bayes ranking methods. Through a series of simulation studies, we show that our approach consistently delivers improved ranking squared-error performance relative to competing methods, such as posterior expected ranks and ranking the components of the best linear unbiased predictor. Estimating rankings using our method is illustrated with an example from a longitudinal study evaluating test scores across a large group of schools.

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arXiv2025

Accelerating Proximal Gradient-type Algorithms using Damped Anderson Acceleration with Restarts and Nesterov Initialization

Despite their frequent slow convergence, proximal gradient schemes are widely used in large-scale optimization tasks due to their tremendous stability, scalability, and ease of computation. In this paper, we develop and investigate a general two-phase scheme for accelerating the convergence of proximal gradient algorithms. By using Nesterov's momentum method in an initialization phase, our procedure delivers fast initial descent that is robust to the choice of starting value. Once iterates are much closer to the solution after the first phase, we utilize a variation of Anderson acceleration to deliver more rapid local convergence in the second phase. Drawing upon restarting schemes developed for Nesterov acceleration, we can readily identify points where it is advantageous to switch from the first to the second phase, which enables use of the procedure without requiring one to specify the number of iterations used in each phase. For the second phase, we adapt and extend a version of Anderson acceleration with algorithm restarts, and we introduce a subsetted version of this procedure that improves performance in problems with substantial sparsity. Through simulation studies involving four representative optimization problems, we show that our proposed algorithm can generate substantial improvements over competing acceleration methods.

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arXiv2025

Quantifying uncertainty of individualized treatment effects in right-censored survival data: A comparison of Bayesian additive regression trees and causal survival forest

Estimation of individualized treatment effects (ITE), also known as conditional average treatment effects (CATE), is an active area of methodology development. However, much less attention has been paid to the quantification of uncertainty of ITE/CATE estimates in right-censored survival data. Here we undertake an extensive simulation study to examine the coverage of interval estimates from two popular estimation algorithms, Bayesian additive regression trees (BART) and causal survival forest (CSF). We conducted simulation designs from 3 different settings: first, in a setting where BART was developed for an accelerated failure time model; second, where CSF was developed; and finally, a ``neutral'' simulation taken from a setting where neither BART nor CSF was developed. BART outperformed CSF in all three simulation settings. Both the BART and CSF algorithms involve multiple hyperparameters, and BART credible intervals had better coverage than the CSF confidence intervals under the default values, as well as under optimized values, of these hyperparameters.

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arXiv2025

Evaluating and Testing for Actionable Treatment Effect Heterogeneity

Developing tools for estimating heterogeneous treatment effects (HTE) and individualized treatment effects has been an area of active research in recent years. While these tools have proven to be useful in many contexts, a concern when deploying such methods is the degree to which incorporating HTE into a prediction model provides an advantage over predictive methods which do not allow for variation in treatment effect across individuals. To address this concern, we propose a procedure which evaluates the extent to which an HTE model provides a predictive advantage. Specifically, our procedure targets the gain in predictive performance from using a flexible predictive model incorporating HTE versus an alternative model which is similar to the HTE-utilizing model except that it is constrained to not allow variation in treatment effect. By drawing upon recent work in using nested cross-validation techniques for prediction error inference, we generate confidence intervals for this measure of gain in predictive performance which allows one to directly calculate the level at which one is confident of a substantial HTE-modeling gain in prediction -- a quantity which we refer to as the h-value. Our procedure is generic and can be directly used to assess the benefit of modeling HTE for any method that incorporates treatment effect variation.

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arXiv2024

Generalized Bayesian Additive Regression Trees for Restricted Mean Survival Time Inference

Prediction methods for time-to-event outcomes often utilize survival models that rely on strong assumptions about noninformative censoring or on how individual-level covariates and survival functions are related. When the main interest is in predicting individual-level restricted mean survival times (RMST), reliance on such assumptions can lead to poor predictive performance if these assumptions are not satisfied. We propose a generalized Bayes framework that avoids full probability modeling of all survival outcomes by using an RMST-targeted loss function that depends on a collection of inverse probability of censoring weights (IPCW). In our generalized Bayes formulation, we utilize a flexible additive tree regression model for the RMST function, and the posterior distribution of interest is obtained through model-averaging IPCW-conditional loss function-based pseudo-Bayesian posteriors. Because informative censoring can be captured by the IPCW-dependent loss function, our approach only requires one to specify a model for the censoring distribution, thereby obviating the need for complex joint modeling to handle informative censoring. We evaluate the performance of our method through a series of simulations that compare it with several well-known survival machine learning methods, and we illustrate the application of our method using a multi-site cohort of breast cancer patients with clinical and genomic covariates.

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arXiv2023

Parameter-Expanded ECME Algorithms for Logistic and Penalized Logistic Regression

Parameter estimation in logistic regression is a well-studied problem with the Newton-Raphson method being one of the most prominent optimization techniques used in practice. A number of monotone optimization methods including minorization-maximization (MM) algorithms, expectation-maximization (EM) algorithms and related variational Bayes approaches offer a family of useful alternatives guaranteed to increase the logistic regression likelihood at every iteration. In this article, we propose a modified version of a logistic regression EM algorithm which can substantially improve computationally efficiency while preserving the monotonicity of EM and the simplicity of the EM parameter updates. By introducing an additional latent parameter and selecting this parameter to maximize the penalized observed-data log-likelihood at every iteration, our iterative algorithm can be interpreted as a parameter-expanded expectation-condition maximization either (ECME) algorithm, and we demonstrate how to use the parameter-expanded ECME with an arbitrary choice of weights and penalty function. In addition, we describe a generalized version of our parameter-expanded ECME algorithm that can be tailored to the challenges encountered in specific high-dimensional problems, and we study several interesting connections between this generalized algorithm and other well-known methods. Performance comparisons between our method, the EM algorithm, and several other optimization methods are presented using a series of simulation studies based upon both real and synthetic datasets.

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arXiv2022

Improved Small Domain Estimation via Compromise Regression Weights

Shrinkage estimates of small domain parameters typically utilize a combination of a noisy "direct" estimate that only uses data from a specific small domain and a more stable regression estimate. When the regression model is misspecified, estimation performance for the noisier domains can suffer due to substantial shrinkage towards a poorly estimated regression surface. In this paper, we introduce a new class of robust, empirically-driven regression weights that target estimation of the small domain means under potential misspecification of the global regression model. Our regression weights are a convex combination of the model-based weights associated with the best linear unbiased predictor (BLUP) and those associated with the observed best predictor (OBP). The compromise parameter in this convex combination is found by minimizing a novel, unbiased estimate of the mean-squared prediction error for the small domain means, and we label the associated small domain estimates the "compromise best predictor", or CBP. Using a data-adaptive mixture for the regression weights enables the CBP to possess the robustness of the OBP while retaining the main advantages of the EBLUP whenever the regression model is correct. We demonstrate the use of the CBP in an application estimating gait speed in older adults.

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arXiv2021

Nonparametric Analysis of Delayed Treatment Effects using Single-Crossing Constraints

Clinical trials involving novel immuno-oncology (IO) therapies frequently exhibit survival profiles which violate the proportional hazards assumption due to a delay in treatment effect, and in such settings, the survival curves in the two treatment arms may have a crossing before the two curves eventually separate. To flexibly model such scenarios, we describe a nonparametric approach for estimating the treatment arm-specific survival functions which constrains these two survival functions to cross at most once without making any additional assumptions about how the survival curves are related. A main advantage of our approach is that it provides an estimate of a crossing time if such a crossing exists, and moreover, our method generates interpretable measures of treatment benefit including crossing-conditional survival probabilities and crossing-conditional estimates of restricted residual mean life. We demonstrate the use and effectiveness of our approach with a large simulation study and an analysis of reconstructed outcomes from a recent combination-therapy trial.

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arXiv2018

Damped Anderson acceleration with restarts and monotonicity control for accelerating EM and EM-like algorithms

The expectation-maximization (EM) algorithm is a well-known iterative method for computing maximum likelihood estimates from incomplete data. Despite its numerous advantages, a main drawback of the EM algorithm is its frequently observed slow convergence which often hinders the application of EM algorithms in high-dimensional problems or in other complex settings.To address the need for more rapidly convergent EM algorithms, we describe a new class of acceleration schemes that build on the Anderson acceleration technique for speeding fixed-point iterations. Our approach is effective at greatly accelerating the convergence of EM algorithms and is automatically scalable to high dimensional settings. Through the introduction of periodic algorithm restarts and a damping factor, our acceleration scheme provides faster and more robust convergence when compared to un-modified Anderson acceleration while also improving global convergence. Crucially, our method works as an "off-the-shelf" method in that it may be directly used to accelerate any EM algorithm without relying on the use of any model-specific features or insights. Through a series of simulation studies involving five representative problems, we show that our algorithm is substantially faster than the existing state-of-art acceleration schemes.

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arXiv2018

Bayesian Bivariate Subgroup Analysis for Risk-Benefit Evaluation

Subgroup analysis is a frequently used tool for evaluating heterogeneity of treatment effect and heterogeneity in treatment harm across observed baseline patient characteristics. While treatment efficacy and adverse event measures are often reported separately for each subgroup, analyzing their within-subgroup joint distribution is critical for better informed patient decision-making. In this paper, we describe Bayesian models for performing a subgroup analysis to compare the joint occurrence of a primary endpoint and an adverse event between two treatment arms. Our approaches emphasize estimation of heterogeneity in this joint distribution across subgroups, and our approaches directly accommodate subgroups with small numbers of observed primary and adverse event combinations. In addition, we describe several ways in which our models may be used to generate interpretable summary measures of benefit-risk tradeoffs for each subgroup. The methods described here are illustrated throughout using a large cardiovascular trial (N = 9,361) investigating the efficacy of an intervention for reducing systolic blood pressure to a lower-than-usual target.

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arXiv2017

Individualized Treatment Effects with Censored Data via Fully Nonparametric Bayesian Accelerated Failure Time Models

Individuals often respond differently to identical treatments, and characterizing such variability in treatment response is an important aim in the practice of personalized medicine. In this article, we describe a non-parametric accelerated failure time model that can be used to analyze heterogeneous treatment effects (HTE) when patient outcomes are time-to-event. By utilizing Bayesian additive regression trees and a mean-constrained Dirichlet process mixture model, our approach offers a flexible model for the regression function while placing few restrictions on the baseline hazard. Our non-parametric method leads to natural estimates of individual treatment effect and has the flexibility to address many major goals of HTE assessment. Moreover, our method requires little user input in terms of tuning parameter selection or subgroup specification. We illustrate the merits of our proposed approach with a detailed analysis of two large clinical trials for the prevention and treatment of congestive heart failure using an angiotensin-converting enzyme inhibitor. The analysis revealed considerable evidence for the presence of HTE in both trials as demonstrated by substantial estimated variation in treatment effect and by high proportions of patients exhibiting strong evidence of having treatment effects which differ from the overall treatment effect.

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arXiv2015

Making the cut: improved ranking and selection for large-scale inference

Identifying leading measurement units from a large collection is a common inference task in various domains of large-scale inference. Testing approaches, which measure evidence against a null hypothesis rather than effect magnitude, tend to overpopulate lists of leading units with those associated with low measurement error. By contrast, local maximum likelihood (ML) approaches tend to favor units with high measurement error. Available Bayesian and empirical Bayesian approaches rely on specialized loss functions that result in similar deficiencies. We describe and evaluate a generic empirical Bayesian ranking procedure that populates the list of top units in a way that maximizes the expected overlap between the true and reported top lists for all list sizes. The procedure relates unit-specific posterior upper tail probabilities with their empirical distribution to yield a ranking variable. It discounts high-variance units less than popular non-ML methods and thus achieves improved operating characteristics in the models considered.

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arXiv2015

AR(1) Latent Class Models for Longitudinal Count Data

In a variety of applications involving longitudinal or repeated-measurements data, it is desired to uncover natural groupings or clusters which exist among study subjects. Motivated by the need to recover longitudinal trajectories of conduct problems in the field of developmental psychopathology, we propose a method to address this goal when the data in question are counts. We assume that the subject-specific observations are generated from a first-order autoregressive process which is appropriate for counts. A key advantage of our approach is that the marginal distribution of the response can be expressed in closed form, circumventing common computational issues associated with random effects models. To further improve computational efficiency, we propose a quasi-EM procedure for estimating the model parameters where, within each EM iteration, the maximization step is approximated by solving an appropriately chosen set of estimating equations. Additionally, we introduce a novel method to express the degree to which both the underlying data and the fitted model are able to correctly assign subjects to their (unknown) latent classes. We explore the effectiveness of our procedures through simulations based on a four-class model, placing a special emphasis on posterior classification. Finally, we analyze data and recover trajectories of conduct problems in an important nationally representative sample.

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