Time-varying networks arise in a variety of ubiquitous applications, such as functional brain connectivity [Thompson et al., 2017, Zhang et al., 2020], gene and genomic regulatory processes [Zhang and Cao, 2017, Bartlett et al., 2021], and social or economic environments [Snijders et al., 2010, Kolar et al., 2010]. In these contexts, measurements collected at different time points record how observed connections fluctuate, forming a sequence of network snapshots that reflect the temporal evolution of the underlying system. For example, fMRI studies yield time-indexed measurements of activity across brain regions, from which researchers construct connectivity networks that change over the scanning period [Bassett et al., 2011, Rubinov and Sporns, 2010]. Similarly, in political systems such as the U.S. Senate, legislative cosponsorship records give rise to network snapshots that naturally vary across sessions [Fowler, 2006, Kirkland and Gross, 2014]. General reviews of time-varying network analysis, including methodological developments and representative applications, are provided in Holme and Saram aki [2012] and Kim et al. [2018].

Cross-region dynamic connectivity, which describes the spatio-temporal dependence of neural activity among multiple brain regions of interest (ROIs), can provide important information for understanding cognition. For estimating such connectivity, magnetoencephalography (MEG) and electroencephalography (EEG) are well-suited tools because of their millisecond temporal resolution. However, localizing source activity in the brain requires solving an under-determined linear problem. In typical two-step approaches, researchers first solve the linear problem with generic priors assuming independence across ROIs, and secondly quantify cross-region connectivity. In this work, we propose a one-step state-space model to improve estimation of dynamic connectivity. The model treats the mean activity in individual ROIs as the state variable and describes non-stationary dynamic dependence across ROIs using time-varying auto-regression. Compared with a two-step method, which first obtains the commonly used minimum-norm estimates of source activity, and then fits the auto-regressive model, our state-space model yielded smaller estimation errors on simulated data where the model assumptions held. When applied on empirical MEG data from one participant in a scene-processing experiment, our state-space model also demonstrated intriguing preliminary results, indicating leading and lagged linear dependence between the early visual cortex and a higher-level scene-sensitive region, which could reflect feedforward and feedback information flow within the visual cortex during scene processing.

Whether or not a country is at war, or experiencing escalating or deescalating levels of conflict, has massive ramifications on a country's national and foreign policy. Given a country's history of conflict, or lack thereof, future predictions about the war-status of a country are valuable information. In this paper, we present the use of conformal prediction on temporally-dependent data to obtain prediction sets of possible future conflict state-sequences. More specifically, we compare the results of conformal prediction to a likelihood-based prediction strategy when the data are assumed to come from a discrete-state Markov process. A point-prediction may not supply sufficient information because the penalty for a wrong prediction is extreme, and so we consider a machine learning alternative that gives valid uncertainty quantification and is robust to model misspecification. In the data analysis, we present real forecasts of conflict dynamics across multiple countries. Lastly, we comment on the possible limitations of existing approaches for applying conformal prediction to Markovian data, where the exchangeability assumption is violated.

The Hilbert-Schmidt Independence Criterion (HSIC) is a powerful kernel-based statistic for assessing the generalized dependence between two multivariate variables. However, independence testing based on the HSIC is not directly possible for cluster-correlated data. Such a correlation pattern among the observations arises in many practical situations, e.g., family-based and longitudinal data, and requires proper accommodation. Therefore, we propose a novel HSIC-based independence test to evaluate the dependence between two multivariate variables based on clustercorrelated data. Using the previously proposed empirical HSIC as our test statistic, we derive its asymptotic distribution under the null hypothesis of independence between the two variables but in the presence of sample correlation. Based on both simulation studies and real data analysis, we show that, with clustered data, our approach effectively controls type I error and has a higher statistical power than competing methods.

Estimating heterogeneous treatment effects in survival settings is complicated by right censoring as well as the time-varying nature of the estimand. While the conditional average treatment effect (CATE) provides a natural target, most existing approaches focus on a single prespecified time point and do not account for the temporal trajectory, leading to instability in estimation. We propose a deep survival learner (DSL) for estimating heterogeneous treatment effects with right-censored outcomes. The method is based on a doubly robust pseudo-outcome whose conditional expectation identifies time-specific CATEs under standard assumptions. This construction remains unbiased if either the outcome model or the treatment assignment model is correctly specified, when properly accounting for censoring. To estimate CATEs over a clinically relevant time spectrum, DSL employs a multi-output deep neural network with shared representations, enabling joint estimation of treatment effect trajectories. From a theoretical perspective, we derive error bounds for both pointwise and joint estimation over time. We show that joint estimation can leverage temporal structure to control estimation error without incurring much additional approximation cost under smoothness conditions, leading to improved stability relative to separate estimation. Cross-fitting is incorporated to reduce overfitting and mitigate bias arising from flexible nuisance estimation. Simulation studies demonstrate favorable finite-sample performance, particularly under nuisance model misspecification. Applied to the Boston Lung Cancer Study, DSL reveals heterogeneity in the effects of perioperative chemotherapy across patient characteristics and over time.

Quasi-experimental evaluations are central for generating real-world causal evidence and complementing insights from randomized trials. The regression discontinuity design (RDD) is a quasi-experimental design that can be used to estimate the causal effect of treatments that are assigned based on a running variable crossing a threshold. Such threshold-based rules are ubiquitous in healthcare, where predictive and prognostic biomarkers frequently guide treatment decisions. However, standard RD estimators rely on complete outcome data, an assumption often violated in time-to-event analyses where censoring arises from loss to follow-up. To address this issue, we propose a nonparametric approach that leverages doubly robust censoring corrections and can be paired with existing RD estimators. Our approach can handle multiple survival endpoints, long follow-up times, and covariate-dependent variation in survival and censoring. We discuss the relevance of our approach across multiple areas of applications and demonstrate its usefulness through simulations and the prostate component of the Prostate, Lung, Colorectal and Ovarian (PLCO) Cancer Screening Trial where our new approach offers several advantages, including higher efficiency and robustness to misspecification. We have also developed an open-source software package, $\texttt{rdsurvival}$, for the $\texttt{R}$ language.

In recent years, there has been growing interest in causal machine learning estimators for quantifying subject-specific effects of a binary treatment on time-to-event outcomes. Estimation approaches have been proposed which attenuate the inherent regularisation bias in machine learning predictions, with each of these estimators addressing measured confounding, right censoring, and in some cases, left truncation. However, the existing approaches are found to exhibit suboptimal finite-sample performance, with none of the existing estimators fully leveraging the temporal structure of the data, yielding non-smooth treatment effects over time. We address these limitations by introducing surv-iTMLE, a targeted learning procedure for estimating the difference in the conditional survival probabilities under two treatments. Unlike existing estimators, surv-iTMLE accommodates both left truncation and right censoring while enforcing smoothness and boundedness of the estimated treatment effect curve over time. Through extensive simulation studies under both right censoring and left truncation scenarios, we demonstrate that surv-iTMLE outperforms existing methods in terms of bias and smoothness of time-varying effect estimates in finite samples. We then illustrate surv-iTMLE's practical utility by exploring heterogeneity in the effects of immunotherapy on survival among non-small cell lung cancer (NSCLC) patients, revealing clinically meaningful temporal patterns that existing estimators may obscure.