Faculty Bibliography

Sparse additive modeling is a class of effective methods for performing high-dimensional nonparametric regression. This article develops a sparse additive model focused on estimation of treatment effect modification with simultaneous treatment effect-modifier selection. We propose a version of the sparse additive model uniquely constrained to estimate the interaction effects between treatment and pretreatment covariates, while leaving the main effects of the pretreatment covariates unspecified. The proposed regression model can effectively identify treatment effect-modifiers that exhibit possibly nonlinear interactions with the treatment variable that are relevant for making optimal treatment decisions. A set of simulation experiments and an application to a dataset from a randomized clinical trial are presented to demonstrate the method.

We consider a single-index regression model, uniquely constrained to estimate interactions between a set of pretreatment covariates and a treatment variable on their effects on a response variable, in the context of analyzing data from randomized clinical trials. We represent interaction effect terms of the model through a set of treatment-specific flexible link functions on a linear combination of the covariates (a single index), subject to the constraint that the expected value given the covariates equals zero, while leaving the main effects of the covariates unspecified. We show that the proposed semiparametric estimator is consistent for the interaction term of the model, and that the efficiency of the estimator can be improved with an augmentation procedure. The proposed single-index regression provides a flexible and interpretable modeling approach to optimizing individualized treatment rules based on patients' data measured at baseline, as illustrated by simulation examples and an application to data from a depression clinical trial. This article is protected by copyright. All rights reserved.

In a regression model for treatment outcome in a randomized clinical trial, a treatment effect modifier is a covariate that has an interaction with the treatment variable, implying that the treatment efficacies vary across values of such a covariate. In this paper, we present a method for determining a composite variable from a set of baseline covariates, that can have a nonlinear association with the treatment outcome, and acts as a composite treatment effect modifier. We introduce a parsimonious generalization of the single-index models that targets the effect of the interaction between the treatment conditions and the vector of covariates on the outcome, a single-index model with multiple-links (SIMML) that estimates a single linear combination of the covariates (i.e., a single-index), with treatment-specific nonparametric link functions. The approach emphasizes a focus on the treatment-by-covariates interaction effects on the treatment outcome that are relevant for making optimal treatment decisions. Asymptotic results for estimator are obtained under possible model misspecification. A treatment decision rule based on the derived single-index is defined, and it is compared to other methods for estimating optimal treatment decision rules. An application to a clinical trial for the treatment of depression is presented.

We consider a logistic regression model for a binary response where part of its covariates are subject-specific random intercepts and slopes from a large number of longitudinal covariates. These random effect covariates must be estimated from the observed data, and therefore, the model essentially involves errors in covariates. Because of high dimension and high correlation of the random effects, we employ longitudinal principal component analysis to reduce the total number of random effects to some manageable number of random effects. To deal with errors in covariates, we extend the conditional-score equation approach to this moderate dimensional logistic regression model with random effect covariates. To reliably solve the conditional-score equations in moderate/high dimension, we apply a majorization on the first derivative of the conditional-score functions and a penalized estimation by the smoothly clipped absolute deviation. The method was evaluated through a set of simulation studies and applied to a data set with longitudinal cortical thickness of 68 regions of interest to identify biomarkers that are related to dementia transition.

This tutorial introduces recent developments in precision medicine for estimating treatment decision rules. The objective of these developments is to advance personalised healthcare by identifying an optimal treatment option for each individual patient based on each patient's characteristics. The methods detailed in this tutorial define composite variables from the patient measures that can be viewed as 'biosignatures' for differential treatment response, which we have termed 'generated effect modifiers'. In contrast to most machine learning approaches to precision medicine, these biosignatures are derived from linear and non-linear regression models and thus have the advantage of easy visualisation and ready interpretation. The methods are illustrated using examples from randomised clinical trials.