Modeling variability in treatment effects for cluster randomized controlled trials using by-variable smooth functions in a generalized additive mixed model.

Variability in treatment effects is common in intervention studies using cluster randomized controlled trial (C-RCT) designs. Such variability is often examined in multilevel modeling (MLM) to understand how treatment effects (TRT) differ based on the level of a covariate (COV), called TRT × COV. In detecting TRT × COV effects using MLM, relationships between covariates and outcomes are assumed to vary across clusters linearly. However, this linearity assumption may not hold in all applications and an incorrect assumption may lead to biased statistical inference about TRT × COV effects. In this study, we present generalized additive mixed model (GAMM) specifications in which cluster-specific functional relationships between covariates and outcomes can be modeled using by-variable smooth functions. In addition, the implementation for GAMM specifications is explained using the mgcv R package (Wood, 2021). The usefulness of the GAMM specifications is illustrated using intervention data from a C-RCT. Results of simulation studies showed that parameters and by-variable smooth functions were recovered well in various multilevel designs and the misspecification of the relationship between covariates and outcomes led to biased estimates of TRT × COV effects. Furthermore, this study evaluated the extent to which the GAMM can be treated as an alternative model to MLM in the presence of a linear relationship.

Sparse Bayesian modeling of hierarchical independent component analysis: Reliable estimation of individual differences in brain networks.

Independent component analysis (ICA) is one of the leading approaches for studying brain functional networks. There is increasing interest in neuroscience studies to investigate individual differences in brain networks and their association with demographic characteristics and clinical outcomes. In this work, we develop a sparse Bayesian group hierarchical ICA model that offers significant improvements over existing ICA techniques for identifying covariate effects on the brain network. Specifically, we model the population-level ICA source signals for brain networks using a Dirichlet process mixture. To reliably capture individual differences on brain networks, we propose sparse estimation of the covariate effects in the hierarchical ICA model via a horseshoe prior. Through extensive simulation studies, we show that our approach performs considerably better in detecting covariate effects in comparison with the leading group ICA methods. We then perform an ICA decomposition of a between-subject meditation study. Our method is able to identify significant effects related to meditative practice in brain regions that are consistent with previous research into the default mode network, whereas other group ICA approaches find few to no effects.

The power prior with multiple historical controls for the linear regression model.

Combining historical control data with current control data may reduce the necessary study size of a clinical trial. However, this only applies when the historical control data are similar enough to the current control data. Several Bayesian approaches for incorporating historical data in a dynamic way have been proposed, such as the meta-analytic-predictive (MAP) prior and the modified power prior (MPP). Here we discuss the generalization of the MPP approach for multiple historical control groups for the linear regression model. This approach is useful when the controls differ more than in a random way, but become again (approximately) exchangeable conditional on covariates. The proposed approach builds on the approach previously developed for binary outcomes by some of the current authors. Two MPP approaches have been developed with multiple controls. The first approach assumes independent powers, while in the second approach the powers have a hierarchical structure. We conducted several simulation studies to investigate the frequentist characteristics of borrowing methods and analyze a real-life data set. When there is between-study variation in the slopes of the model or in the covariate distributions, the MPP approach achieves approximately nominal type I error rates and greater power than the MAP prior, provided that the covariates are included in the model. When the intercepts vary, the MPP yields a slightly inflated type I error rate, whereas the MAP does not. We conclude that our approach is a worthy competitor to the MAP approach for the linear regression case.

Promotion time cure rate model with nonparametric form of covariate effects.

Survival data with a cured portion are commonly seen in clinical trials. Motivated from a biological interpretation of cancer metastasis, promotion time cure model is a popular alternative to the mixture cure rate model for analyzing such data. The existing promotion cure models all assume a restrictive parametric form of covariate effects, which can be incorrectly specified especially at the exploratory stage. In this paper, we propose a nonparametric approach to modeling the covariate effects under the framework of promotion time cure model. The covariate effect function is estimated by smoothing splines via the optimization of a penalized profile likelihood. Point-wise interval estimates are also derived from the Bayesian interpretation of the penalized profile likelihood. Asymptotic convergence rates are established for the proposed estimates. Simulations show excellent performance of the proposed nonparametric method, which is then applied to a melanoma study.

HIGH DIMENSIONAL CENSORED QUANTILE REGRESSION.

Censored quantile regression (CQR) has emerged as a useful regression tool for survival analysis. Some commonly used CQR methods can be characterized by stochastic integral-based estimating equations in a sequential manner across quantile levels. In this paper, we analyze CQR in a high dimensional setting where the regression functions over a continuum of quantile levels are of interest. We propose a two-step penalization procedure, which accommodates stochastic integral based estimating equations and address the challenges due to the recursive nature of the procedure. We establish the uniform convergence rates for the proposed estimators, and investigate the properties on weak convergence and variable selection. We conduct numerical studies to confirm our theoretical findings and illustrate the practical utility of our proposals.

Mixed effects models for recurrent events data with partially observed time-varying covariates: Ecological momentary assessment of smoking.

Cigarette smoking is a prototypical example of a recurrent event. The pattern of recurrent smoking events may depend on time-varying covariates including mood and environmental variables. Fixed effects and frailty models for recurrent events data assume that smokers have a common association with time-varying covariates. We develop a mixed effects version of a recurrent events model that may be used to describe variation among smokers in how they respond to those covariates, potentially leading to the development of individual-based smoking cessation therapies. Our method extends the modified EM algorithm of Steele (1996) for generalized mixed models to recurrent events data with partially observed time-varying covariates. It is offered as an alternative to the method of Rizopoulos, Verbeke, and Lesaffre (2009) who extended Steele's (1996) algorithm to a joint-model for the recurrent events data and time-varying covariates. Our approach does not require a model for the time-varying covariates, but instead assumes that the time-varying covariates are sampled according to a Poisson point process with known intensity. Our methods are well suited to data collected using Ecological Momentary Assessment (EMA), a method of data collection widely used in the behavioral sciences to collect data on emotional state and recurrent events in the every-day environments of study subjects using electronic devices such as Personal Digital Assistants (PDA) or smart phones.

Marginal mean models for zero-inflated count data.

Zero-inflated regression models have emerged as a popular tool within the parametric framework to characterize count data with excess zeros. Despite their increasing popularity, much of the literature on real applications of these models has centered around the latent class formulation where the mean response of the so-called at-risk or susceptible population and the susceptibility probability are both related to covariates. While this formulation in some instances provides an interesting representation of the data, it often fails to produce easily interpretable covariate effects on the overall mean response. In this article, we propose two approaches that circumvent this limitation. The first approach consists of estimating the effect of covariates on the overall mean from the assumed latent class models, while the second approach formulates a model that directly relates the overall mean to covariates. Our results are illustrated by extensive numerical simulations and an application to an oral health study on low income African-American children, where the overall mean model is used to evaluate the effect of sugar consumption on caries indices.

Point pattern analysis with spatially varying covariate effects, applied to the study of cerebrovascular deaths.

This article proposes a modeling approach for handling spatial heterogeneity present in the study of the geographical pattern of deaths due to cerebrovascular disease.The framework involvesa point pattern analysis with components exhibiting spatial variation. Preliminary studies indicate that mortality of this disease and the effect of relevant covariates do not exhibit uniform geographic distribution. Our model extends a previously proposed model in the literature that uses spatial and non-spatial variables by allowing for spatial variation of the effect of non-spatial covariates. A number of relative risk indicators are derived by comparing different covariate levels, different geographic locations, or both. The methodology is applied to the study of the geographical death pattern of cerebrovascular deaths in the city of Rio de Janeiro. The results compare well against existing alternatives, including fixed covariate effects. Our model is able to capture and highlight important data information that would not be noticed otherwise, providing information that is required for appropriate health decision-making.

GLOBALLY ADAPTIVE QUANTILE REGRESSION WITH ULTRA-HIGH DIMENSIONAL DATA.

Quantile regression has become a valuable tool to analyze heterogeneous covaraite-response associations that are often encountered in practice. The development of quantile regression methodology for high dimensional covariates primarily focuses on examination of model sparsity at a single or multiple quantile levels, which are typically prespecified ad hoc by the users. The resulting models may be sensitive to the specific choices of the quantile levels, leading to difficulties in interpretation and erosion of confidence in the results. In this article, we propose a new penalization framework for quantile regression in the high dimensional setting. We employ adaptive L1 penalties, and more importantly, propose a uniform selector of the tuning parameter for a set of quantile levels to avoid some of the potential problems with model selection at individual quantile levels. Our proposed approach achieves consistent shrinkage of regression quantile estimates across a continuous range of quantiles levels, enhancing the flexibility and robustness of the existing penalized quantile regression methods. Our theoretical results include the oracle rate of uniform convergence and weak convergence of the parameter estimators. We also use numerical studies to confirm our theoretical findings and illustrate the practical utility of our proposal.

A Penalization Method for Estimating Heterogeneous Covariate Effects in Cancer Genomic Data.

In high-throughput profiling studies, extensive efforts have been devoted to searching for the biomarkers associated with the development and progression of complex diseases. The heterogeneity of covariate effects associated with the outcomes across subjects has been noted in the literature. In this paper, we consider a scenario where the effects of covariates change smoothly across subjects, which are ordered by a known auxiliary variable. To this end, we develop a penalization-based approach, which applies a penalization technique to simultaneously select important covariates and estimate their unique effects on the outcome variables of each subject. We demonstrate that, under the appropriate conditions, our method shows selection and estimation consistency. Additional simulations demonstrate its superiority compared to several competing methods. Furthermore, applying the proposed approach to two The Cancer Genome Atlas datasets leads to better prediction performance and higher selection stability.

Time-dependent population PK models of single-agent atezolizumab in patients with cancer.

PURPOSE: The time-varying clearance (CL) of the PD-L1 inhibitor atezolizumab was assessed on a population of 1519 cancer patients (primarily with non-small-cell lung cancer or metastatic urothelial carcinoma) from three clinical studies. METHODS: The first step was to identify the baseline covariates affecting atezolizumab CL without including time-varying components (stationary covariate model). Two time-varying models were then investigated: (1) a model allowing baseline covariates to vary over time (time-varying covariate model), (2) a model with empirical time-varying Emax CL function. RESULTS: The final stationary covariate model included main effects of body weight, albumin levels, tumor size, anti-drug antibodies (ADA) and gender on atezolizumab CL. Both time-varying models resulted in a clear improvement of the data fit and visual predictive checks over the stationary model. The time-varying covariate model provided the best fit of the data. In this model, the main driver for change in CL over time was variations in albumin level with an increase in serum albumin (improvement in a patient's status) mirroring a decrease in CL. Time-varying ADAs had a small impact (9% increase in CL). None of the covariates impacted atezolizumab CL by more than ± 30% from median. The estimated maximum decrease in CL with time was 22% with the Emax model. CONCLUSION: The overall impact of covariates on atezolizumab CL did not warrant any change in atezolizumab dosing recommendations. The results support the hypothesis that variation in atezolizumab CL over time is associated with patients' disease status, as shown with other checkpoint inhibitors.

HINT: A hierarchical independent component analysis toolbox for investigating brain functional networks using neuroimaging data.

BACKGROUND: Independent component analysis (ICA) is a popular tool for investigating brain organization in neuroscience research. In fMRI studies, an important goal is to study how brain networks are modulated by subjects' clinical and demographic variables. Existing ICA methods and toolboxes don't incorporate subjects' covariates effects in ICA estimation of brain networks, which potentially leads to loss in accuracy and statistical power in detecting brain network differences between subjects' groups. NEW METHOD: We introduce a Matlab toolbox, HINT (Hierarchical INdependent component analysis Toolbox), that provides a hierarchical covariate-adjusted ICA (hc-ICA) for modeling and testing covariate effects and generates model-based estimates of brain networks on both the population- and individual-level. HINT provides a user-friendly Matlab GUI that allows users to easily load images, specify covariate effects, monitor model estimation via an EM algorithm, specify hypothesis tests, and visualize results. HINT also has a command line interface which allows users to conveniently run and reproduce the analysis with a script. COMPARISON TO EXISTING METHODS: HINT implements a new multi-level probabilistic ICA model for group ICA. It provides a statistically principled ICA modeling framework for investigating covariate effects on brain networks. HINT can also generate and visualize model-based network estimates for user-specified subject groups, which greatly facilitates group comparisons. RESULTS: We demonstrate the steps and functionality of HINT with an fMRI example data to estimate treatment effects on brain networks while controlling for other covariates. Results demonstrate estimated brain networks and model-based comparisons between the treatment and control groups. In comparisons using synthetic fMRI data, HINT shows desirable statistical power in detecting group differences in networks especially in small sample sizes, while maintaining a low false positive rate. HINT also demonstrates similar or increased accuracy in reconstructing both population- and individual-level source signal maps as compared to some state-of-the-art group ICA methods. CONCLUSION: HINT can provide a useful tool for both statistical and neuroscience researchers to evaluate and test differences in brain networks between subject groups.

Consistent model identification of varying coefficient quantile regression with BIC tuning parameter selection.

Quantile regression provides a flexible platform for evaluating covariate effects on different segments of the conditional distribution of response. As the effects of covariates may change with quantile level, contemporaneously examining a spectrum of quantiles is expected to have a better capacity to identify variables with either partial or full effects on the response distribution, as compared to focusing on a single quantile. Under this motivation, we study a general adaptively weighted LASSO penalization strategy in the quantile regression setting, where a continuum of quantile index is considered and coefficients are allowed to vary with quantile index. We establish the oracle properties of the resulting estimator of coefficient function. Furthermore, we formally investigate a BIC-type uniform tuning parameter selector and show that it can ensure consistent model selection. Our numerical studies confirm the theoretical findings and illustrate an application of the new variable selection procedure.

Two-Part and Related Regression Models for Longitudinal Data.

Statistical models that involve a two-part mixture distribution are applicable in a variety of situations. Frequently, the two parts are a model for the binary response variable and a model for the outcome variable that is conditioned on the binary response. Two common examples are zero-inflated or hurdle models for count data and two-part models for semicontinuous data. Recently, there has been particular interest in the use of these models for the analysis of repeated measures of an outcome variable over time. The aim of this review is to consider motivations for the use of such models in this context and to highlight the central issues that arise with their use. We examine two-part models for semicontinuous and zero-heavy count data, and we also consider models for count data with a two-part random effects distribution.

Different Approaches to Covariate Inclusion in the Mixture Rasch Model.

The present study investigates different approaches to adding covariates and the impact in fitting mixture item response theory models. Mixture item response theory models serve as an important methodology for tackling several psychometric issues in test development, including the detection of latent differential item functioning. A Monte Carlo simulation study is conducted in which data generated according to a two-class mixture Rasch model with both dichotomous and continuous covariates are fitted to several mixture Rasch models with misspecified covariates to examine the effects of covariate inclusion on model parameter estimation. In addition, both complete response data and incomplete response data with different types of missingness are considered in the present study in order to simulate practical assessment settings. Parameter estimation is carried out within a Bayesian framework vis-à-vis Markov chain Monte Carlo algorithms.

Generalizing Quantile Regression for Counting Processes with Applications to Recurrent Events.

In survival analysis, quantile regression has become a useful approach to account for covariate effects on the distribution of an event time of interest. In this paper, we discuss how quantile regression can be extended to model counting processes, and thus lead to a broader regression framework for survival data. We specifically investigate the proposed modeling of counting processes for recurrent events data. We show that the new recurrent events model retains the desirable features of quantile regression such as easy interpretation and good model flexibility, while accommodating various observation schemes encountered in observational studies. We develop a general theoretical and inferential framework for the new counting process model, which unifies with an existing method for censored quantile regression. As another useful contribution of this work, we propose a sample-based covariance estimation procedure, which provides a useful complement to the prevailing bootstrapping approach. We demonstrate the utility of our proposals via simulation studies and an application to a dataset from the US Cystic Fibrosis Foundation Patient Registry (CFFPR).

Pharmacokinetic-pharmacodynamic modeling of fostamatinib efficacy on ACR20 to support dose selection in patients with rheumatoid arthritis (RA).

R788 (fostamatinib) is an oral prodrug that is rapidly converted into a relatively selective spleen tyrosine kinase (SYK) inhibitor R406, evaluated for the treatment of rheumatoid arthritis (RA). This analysis aimed at developing a pharmacodynamic model for efficacy using pooled ACR20 data from two phase II studies in patients with rheumatoid arthritis (TASKi1 and TASKi2), describing the effect of fostamatinib as a function of fostamatinib exposure (dose, R406 plasma concentration) and other explanatory variables. The exposure-response relationship of fostamatinib was implemented into a continuous time Markov model describing the time course of transition probabilities between the three possible states of ACR20 non-responder, responder, and dropout at each visit. The probability of transition to the ACR20 response state was linearly (at the rate constant level) related to average R406 plasma concentrations and the onset of this drug effect was fast. Further, increases of fostamatinib dose resulted in increased dropout and subsequent loss of efficacy. This analysis provided an increased understanding of the exposure-response relationship, and provided support for fostamatinib 100 mg BID an appropriate dose regimen for further clinical evaluation.

Shrinkage Estimation of Varying Covariate Effects Based On Quantile Regression.

Varying covariate effects often manifest meaningful heterogeneity in covariate-response associations. In this paper, we adopt a quantile regression model that assumes linearity at a continuous range of quantile levels as a tool to explore such data dynamics. The consideration of potential non-constancy of covariate effects necessitates a new perspective for variable selection, which, under the assumed quantile regression model, is to retain variables that have effects on all quantiles of interest as well as those that influence only part of quantiles considered. Current work on l1-penalized quantile regression either does not concern varying covariate effects or may not produce consistent variable selection in the presence of covariates with partial effects, a practical scenario of interest. In this work, we propose a shrinkage approach by adopting a novel uniform adaptive LASSO penalty. The new approach enjoys easy implementation without requiring smoothing. Moreover, it can consistently identify the true model (uniformly across quantiles) and achieve the oracle estimation efficiency. We further extend the proposed shrinkage method to the case where responses are subject to random right censoring. Numerical studies confirm the theoretical results and support the utility of our proposals.