Faculty Bibliography

Hutson and Vexler (2018) demonstrate an example of aliasing with the beta and normal distribution. This letter presents another illustration of aliasing using the beta and normal distributions via an infinite mixture model, inspired by the problem of modeling placebo response.

Treatment response heterogeneity poses serious challenges for selecting treatment for many diseases. To better understand this heterogeneity and to help in determining the best patient-specific treatments for a given disease, many clinical trials are collecting large amounts of patient-level data prior to administering treatment in the hope that some of these data can be used to identify moderators of treatment effect. These data can range from simple scalar values to complex functional data such as curves or images. Combining these various types of baseline data to discover "biosignatures" of treatment response is crucial for advancing precision medicine. Motivated by the problem of selecting optimal treatment for subjects with depression based on clinical and neuroimaging data, we present an approach that both (1) identifies covariates associated with differential treatment effect and (2) estimates a treatment decision rule based on these covariates. We focus on settings where there is a potentially large collection of candidate biomarkers consisting of both scalar and functional data. The validity of the proposed approach is justified via extensive simulation experiments and illustrated using data from a placebo-controlled clinical trial investigating antidepressant treatment response in subjects with depression.

Statistical learning-extracting regularities in the environment-may underlie complex social behavior. 124 children, 56 with autism and 68 typically developing, ages 2-8 years, completed a novel visual statistical learning task on an iPad. Averaged together, children with autism demonstrated less learning on the task compared to typically developing children. However, multivariate classification analyses characterized individual behavior patterns, and demonstrated a subset of children with autism had similar learning patterns to typically developing children and that subset of children had less severe autism symptoms. Therefore, statistically averaging data resulted in missing critical heterogeneity. Variability in statistical learning may help to understand differences in autism symptoms across individuals and could be used to tailor and inform treatment decisions.

Smartphones offer a flexible tool to collect data about mental health, but less is known about their effectiveness as a method to assess variability in children's problem behaviors. Caregivers of children with autism completed daily questions about irritability, anxiety and mood delivered via smartphones across 8-weeks. Smartphone questions were consistent with subscales on standard caregiver questionnaires. Data collection from 7 to 10 days at the beginning and 7 to 10 days at the end of the study were sufficient to capture similar amounts of variance as daily data across 8-weeks. Other significant findings included effects of caregiver socioeconomic status and placebo-like effects from participation even though the study included no specific treatment. Nevertheless, single questions via smartphones collected over relatively brief periods reliably represent subdomains in standardized behavioral questionnaires, thereby decreasing burden on caregivers.

Latent class models are widely used to identify unobserved subgroups (i.e., latent classes) based upon one or more manifest variables. The probability of belonging to each subgroup is typically modeled as a function of a set of measured covariates. In this paper, we extend existing latent class models to incorporate matrix covariates. This research is motivated by a randomized placebo-controlled depression clinical trial. One study goal is to identify a subgroup of subjects who experience symptoms improvement early on during antidepressant treatment, which is considered to be an indication of a placebo rather than a true pharmacological response. We want to relate the likelihood of belonging to this subgroup of early responders to baseline electroencephalography (EEG) measurement that takes the form of a matrix. The proposed method is built upon a low rank Candecomp/Parafac (CP) decomposition of the target coefficient matrix through low-dimensional latent variables, which effectively reduces the model dimensionality. We adopt a Bayesian hierarchical modeling approach to estimate the latent variables, which allows a flexible way to incorporate prior knowledge about covariate effect heterogeneity and offers a data-driven method of regularization. Simulation studies suggest that the proposed method is robust against potentially misspecified rank in the CP decomposition. With the motivating example we show how the proposed method can be applied to extract valuable information from baseline EEG measurements that explains the likelihood of belonging to the early responder subgroup, helping to identify placebo responders and suggesting new targets for the study of placebo response.

Antidepressant medications are commonly used to treat depression, but only about 30% of patients reach remission with any single first-step antidepressant. If the first-step treatment fails, response and remission rates at subsequent steps are even more limited. The literature on biomarkers for treatment response is largely based on secondary analyses of studies designed to answer primary questions of efficacy, rather than on a planned systematic evaluation of biomarkers for treatment decision. The lack of evidence-based knowledge to guide treatment decisions for patients with depression has lead to the recognition that specially designed studies with the primary objective being to discover biosignatures for optimizing treatment decisions are necessary. Establishing Moderators and Biosignatures of Antidepressant Response in Clinical Care (EMBARC) is one such discovery study. Stage 1 of EMBARC is a randomized placebo controlled clinical trial of 8 week duration. A wide array of patient characteristics is collected at baseline, including assessments of brain structure, function and connectivity along with electrophysiological, biological, behavioral and clinical features. This paper reports on the data analytic strategy for discovering biosignatures for treatment response based on Stage 1 of EMBARC.

In a randomized clinical trial (RCT), it is often of interest not only to estimate the effect of various treatments on the outcome, but also to determine whether any patient characteristic has a different relationship with the outcome, depending on treatment. In regression models for the outcome, if there is a non-zero interaction between treatment and a predictor, that predictor is called an "effect modifier". Identification of such effect modifiers is crucial as we move towards precision medicine, that is, optimizing individual treatment assignment based on patient measurements assessed when presenting for treatment. In most settings, there will be several baseline predictor variables that could potentially modify the treatment effects. This article proposes optimal methods of constructing a composite variable (defined as a linear combination of pre-treatment patient characteristics) in order to generate an effect modifier in an RCT setting. Several criteria are considered for generating effect modifiers and their performance is studied via simulations. An example from a RCT is provided for illustration.

Understanding heterogeneity in phenotypical characteristics, symptoms manifestations and response to treatment of subjects with psychiatric illnesses is a continuing challenge in mental health research. A long-standing goal of medical studies is to identify groups of subjects characterized with a particular trait or quality and to distinguish them from other subjects in a clinically relevant way. This paper develops and illustrates a novel approach to this problem based on a method of optimal-partitioning (clustering) of functional data. The proposed method allows for the simultaneous clustering of different populations (e.g., symptoms of drug and placebo treated patients) in order to identify prototypical outcome profiles that are distinct from one or the other treatment and outcome profiles common to the different treatments. The clustering results are used to discover potential treatment effect modifiers (i.e., moderators), in particular, moderators of specific drug effects and placebo response. A depression clinical trial is used to illustrate the method.

A major focus of personalized medicine is on the development of individualized treatment rules. Good decision rules have the potential to significantly advance patient care and reduce the burden of a host of diseases. Statistical methods for developing such rules are progressing rapidly, but few methods have considered the use of pre-treatment functional data to guide in decision-making. Furthermore, those methods that do allow for the incorporation of functional pre-treatment covariates typically make strong assumptions about the relationships between the functional covariates and the response of interest. We propose two approaches for using functional data to select an optimal treatment that address some of the shortcomings of previously developed methods. Specifically, we combine the flexibility of functional additive regression models with Q-learning or A-learning in order to obtain treatment decision rules. Properties of the corresponding estimators are discussed. Our approaches are evaluated in several realistic settings using synthetic data and are applied to real data arising from a clinical trial comparing two treatments for major depressive disorder in which baseline imaging data are available for subjects who are subsequently treated.