Estimation and model selection in generalized additive partial linear models for correlated data with diverging number of covariates

We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases statistical power for correlated data through incorporating the correlation information. A unique feature of the proposed method is its capability of handling model selection in cases where it is difficult to specify the likelihood function. We derive the quadratic inference function-based estimators for the linear coefficients and the nonparametric functions when the dimension of covariates diverges, and establish asymptotic normality for the linear coefficient estimators and the rates of convergence for the nonparametric functions estimators for both finite and high-dimensional cases. The proposed method and theoretical development are quite challenging since the numbers of linear covariates and nonlinear components both increase as the sample size increases. We also propose a doubly penalized procedure for variable selection which can simultaneously identify nonzero linear and nonparametric components, and which has an asymptotic oracle property. Extensive Monte Carlo studies have been conducted and show that the proposed procedure works effectively even with moderate sample sizes. A pharmacokinetics study on renal cancer data is illustrated using the proposed method.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1194 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Stage-Aware Learning for Dynamic Treatments

Recent advances in dynamic treatment regimes (DTRs) provide powerful optimal treatment searching algorithms, which are tailored to individuals' specific needs and able to maximize their expected clinical benefits. However, existing algorithms could suffer from insufficient sample size under optimal treatments, especially for chronic diseases involving long stages of decision-making. To address these challenges, we propose a novel individualized learning method which estimates the DTR with a focus on prioritizing alignment between the observed treatment trajectory and the one obtained by the optimal regime across decision stages. By relaxing the restriction that the observed trajectory must be fully aligned with the optimal treatments, our approach substantially improves the sample efficiency and stability of inverse probability weighted based methods. In particular, the proposed learning scheme builds a more general framework which includes the popular outcome weighted learning framework as a special case of ours. Moreover, we introduce the notion of stage importance scores along with an attention mechanism to explicitly account for heterogeneity among decision stages. We establish the theoretical properties of the proposed approach, including the Fisher consistency and finite-sample performance bound. Empirically, we evaluate the proposed method in extensive simulated environments and a real case study for COVID-19 pandemic