I-SPY2 is a long-running phase 2 platform trial that evaluates neoadjuvant treatments for locally advanced breast cancer to identify those with high efficacy that are likely to be successful in phase 3 trials, assigning patients to novel agents using response-adaptive randomization (RAR). Recently, I-SPY2 was reconfigured as a sequential multiple assignment randomized trial (SMART), with up to three stages of therapy. At the first stage, a patient is assigned to a tumor-subtype-specific therapy. If the patient fails to show a satisfactory response, the patient is assigned to a second subtype-specific therapy, and receives a third, rescue therapy if response is still not achieved. The I-SPY2 SMART thus supports identification of highly efficacious entire treatment regimes. The transition of I-SPY2 to a SMART required development of a RAR scheme that updates randomization probabilities at each stage, aligned with the goal of maximizing the number of patients who achieve a pathological complete response (pCR). We present our Bayesian RAR approach, which updates randomization probabilities based on the posterior probability that treatments are part of the optimal regime. Empirical studies demonstrate that it results in more patients having treatment experience consistent with highly efficacious regimes, improves overall within-trial pCR rates, and identifies optimal regimes post trial at rates similar to or exceeding those under simple, uniform, nonadaptive randomization.

In matched observational studies with continuous treatments, individuals with different treatment doses but the same or similar covariate values are paired for causal inference. While inexact covariate matching (i.e., covariate imbalance after matching) is common in practice, previous matched studies with continuous treatments have often overlooked this issue as long as post-matching covariate balance meets certain criteria. Through re-analyzing a matched observational study on the effect of social distancing on COVID-19 case counts, we show that this routine practice can introduce severe bias for causal inference. Motivated by this finding, we propose a general framework for mitigating bias due to inexact matching in matched observational studies with continuous treatments, covering the matching, estimation, and inference stages. In the matching stage, we propose a carefully designed caliper that incorporates both covariate and treatment dose information to improve matching for downstream treatment effect estimation and inference. For the estimation and inference, we introduce a bias-corrected Neyman estimator paired with a corresponding bias-corrected variance estimator. The effectiveness of our proposed framework is demonstrated through numerical studies and a re-analysis of the aforementioned observational study on the effect of social distancing on COVID-19 case counts. An open-source $\tt {R}$ package for implementing our framework has also been developed.

We thank the discussants for their insightful comments and suggestions. In this rejoinder, we underscore the role of the network specification under interference regardless of the chosen probabilistic regime, revisit the conceptual design-based coupled with exposure mapping framework we pursue in our paper, comment on the welcome extensions and modifications proposed by the discussants, and discuss the promise and perils of multiple networks.

Correlation networks are commonly used to infer associations between microbes and metabolites. The resulting $p$-values are then corrected for multiple comparisons using existing methods such as the Benjamini & Hochberg (BH) procedure to control the false discovery rate (FDR). However, most existing methods for FDR control assume the $p$-values are weakly dependent. Consequently, they can have low power in recovering microbe-metabolite association networks that exhibit important topological features, such as the presence of densely associated modules. We propose a novel inference procedure that is both powerful for detecting significant associations in the microbe-metabolite network and capable of controlling the FDR. Power enhancement is achieved by modeling latent structures in the form of a bipartite stochastic block model. We develop a variational expectation-maximization (EM) algorithm to estimate the model parameters and incorporate the learned graph in the testing procedure. In addition to FDR control, this procedure provides a clustering of microbes and metabolites into modules, which is useful for interpretation. We demonstrate the merit of the proposed method in simulations and an application to bacterial vaginosis.

Risk stratification is an invaluable tool for modern healthcare systems. By separating patients into subgroups with distinct disease severity and prognosis, it allows better clinical decision making due to targeted care thus ultimately fosters healthier patient populations. For example, the American Joint Committee on Cancer staging is an indispensible first step for any cancer care. Based on the stages, appropriate treatments are given to optimize clinical outcomes such as recurrence free survival or overall survival. Consequently, it enhances communication, engagement, and research focus. This paper presents a new algorithm entitled 'Ordering Poset Elements by Recursive Amalgamation' (OPERA) for patient stratification using many risk factors. Health risk factors frequently exhibit total or partial ordering and when considered jointly, they form a partially ordered set or a poset. Compared with the usual regression models, OPERA can explore high order interactions similar to the well-known tree method. On the other hand, by explicitly exploring the poset structure, OPERA allows flexible staging patterns and faster pruning for better performance. OPERA is evaluated in extensive simulation studies and cancer staging data to demonstrate its ability in performing risk stratification using ordered risk factors.

Hidden Markov models (HMMs) are widely used to characterize latent state transition patterns in substance use. However, traditional HMM frameworks are incompetent when dealing with the complexities introduced by high-dimensional risk factors and varying time intervals, particularly in determining the number of hidden states and selecting variables for state transition parameters. To tackle the analytical challenges in the Population Assessment of Tobacco and Health (PATH) Study, a nationally representative longitudinal cohort study on tobacco use, we propose a continuous-time HMM framework with a regularization algorithm to identify multi-dimensional risk factors underlying complex poly-tobacco use transitions. We develop an elastic-net regularization on the transition covariates to identify informative covariates and improve model estimation accuracy. The inclusion of key covariates enables accurate determination of the number of hidden states. We incorporate survey weights and information on strata and clustering throughout the modeling framework. We demonstrate the validity of our approach in determining state numbers, identifying informative covariates, and estimating model parameters through a series of simulations. Application of the proposed approach to PATH data analysis revealed several demographic, behavioral, and psychosocial factors that contribute to the differential risks of transition between tobacco-use states among youth and young adults. The model's capacity in identifying high-dimensional risk factors for underlying hidden variables substantiates its potential for enhancing public health research and informing interventions.