Relative contrast estimation and inference for treatment recommendation

When there are resource constraints, it may be necessary to rank individualized treatment benefits to facilitate the prioritization of assigning different treatments. Most existing literature on individualized treatment rules targets absolute conditional treatment effect differences as a metric for the benefit. However, there can be settings where relative differences may better represent such benefit. In this paper, we consider modeling such relative differences formed as scale-invariant contrasts between the conditional treatment effects. By showing that all scale-invariant contrasts are monotonic transformations of each other, we posit a single index model for a particular relative contrast. We then characterize semiparametric estimating equations, including the efficient score, to estimate index parameters. To achieve semiparametric efficiency, we propose a two-step approach that minimizes a doubly robust loss function for initial estimation and then performs a one-step efficiency augmentation procedure. Careful theoretical and numerical studies are provided to show the superiority of our proposed approach.

Semiparametric distributed lag quantile regression for modeling time-dependent exposure mixtures

Studying time-dependent exposure mixtures has gained increasing attentions in environmental health research. When a scalar outcome is of interest, distributed lag (DL) models have been employed to characterize the exposures effects distributed over time on the mean of final outcome. However, there is a methodological gap on investigating time-dependent exposure mixtures with different quantiles of outcome. In this paper, we introduce semiparametric partial-linear single-index (PLSI) DL quantile regression, which can describe the DL effects of time-dependent exposure mixtures on different quantiles of outcome and identify susceptible periods of exposures. We consider two time-dependent exposure settings: discrete and functional, when exposures are measured in a small number of time points and at dense time grids, respectively. Spline techniques are used to approximate the nonparametric DL function and single-index link function, and a profile estimation algorithm is proposed. Through extensive simulations, we demonstrate the performance and value of our proposed models and inference procedures. We further apply the proposed methods to study the effects of maternal exposures to ambient air pollutants of fine particulate and nitrogen dioxide on birth weight in New York University Children's Health and Environment Study (NYU CHES).

Semiparametric function-on-function quantile regression model with dynamic single-index interactions

In this paper we propose a new semiparametric function-on-function quantile regression model with time-dynamic single-index interactions. Our model is very flexible in taking into account of the nonlinear time-dynamic interaction effects of the multivariate longitudinal/functional covariates on the longitudinal response, that most existing quantile regression models for longitudinal data are special cases of our proposed model. We propose to approximate the bivariate nonparametric coefficient functions by tensor product B-splines, and employ a check loss minimization approach to estimate the bivariate coefficient functions and the index parameter vector. Under some mild conditions, we establish the asymptotic normality of the estimated single-index coefficients using projection orthogonalization technique, and obtain the convergence rates of the estimated bivariate coefficient functions. Furthermore, we propose a score test to examine whether there exist interaction effects between the covariates. The finite sample performance of the proposed method is illustrated by Monte Carlo simulations and an empirical data analysis.

A fusion learning method to subgroup analysis of Alzheimer's disease

Uncovering the heterogeneity in the disease progression of Alzheimer's is a key factor to disease understanding and treatment development, so that interventions can be tailored to target the subgroups that will benefit most from the treatment, which is an important goal of precision medicine. However, in practice, one top methodological challenge hindering the heterogeneity investigation is that the true subgroup membership of each individual is often unknown. In this article, we aim to identify latent subgroups of individuals who share a common disorder progress over time, to predict latent subgroup memberships, and to estimate and infer the heterogeneous trajectories among the subgroups. To achieve these goals, we apply a concave fusion learning method to conduct subgroup analysis for longitudinal trajectories of the Alzheimer's disease data. The heterogeneous trajectories are represented by subject-specific unknown functions which are approximated by B-splines. The concave fusion method can simultaneously estimate the spline coefficients and merge them together for the subjects belonging to the same subgroup to automatically identify subgroups and recover the heterogeneous trajectories. The resulting estimator of the disease trajectory of each subgroup is supported by an asymptotic distribution. It provides a sound theoretical basis for further conducting statistical inference in subgroup analysis.