Foreword

Causal inference is a central pillar of many scientific queries where statistics plays a critical role in data-driven causal inference. Despite its wide applications and outstanding practical performance, there are growing inquiries and demands for more tutorials and discussions, especially from human health research studies. We are happy to present this special issue of Biostatistics and Epidemiology, which aims at gathering recent advances in theory and application in causal inference from various perspectives. Nowadays researchers on causal inference are generating new models and methods to deal with more and more sophisticated problems in medical and economic studies. Facing such a broad range of possibilities, we have chosen to publish the following eight manuscripts in this issue.

Dr. Zhang studied the analysis-based method for causal parameter estimation without the need to derive a numerical balance for covariate sampling distribution. Response surface was learned using a tree partitioning algorithm. Her approach was demonstrated with a series of Monte Carlo studies and was a new tool to compute the average treatment effect for clinical researchers.

Dr. Liu considered the bootstrap inference for the same causal parameter as Dr. Zhang when high-dimensional covariates are present. Using the resampling estimator, the author investigated its asymptotic properties under the Neyman–Rubin causal model and showed the validity of this approach. These theoretical issues are not trivial and also not uncommon in genetic applications. An interesting counter-example was provided in this paper when the bootstrap might fail, offering some insights and guidelines.

Dr. Cuerden and co-authors proposed doubly weighted estimating equations and weighted multiple imputations for marginal causal effect with incomplete subgroup information. When justifying the proposed estimators, Cuerden et al. (2023) used Rubin's formula to directly compute the asymptotic covariance. This novel method was implemented for a biologic therapy trial conducted at the Toronto Western Hospital where missingness for key marker information was simulated to provide some illustration and comparison.

Dr. Avagyan and Dr. Vansteelandt contributed a technical discussion on high-dimensional inference for the average treatment effect under the mis-specified model. A new penalized estimation framework was introduced in their paper to facilitate the inference of the conditional mean parameter. Clearly, this rigorous work is a further extension of double robust procedures available in the literature. Avagyan and Vansteelandt (2023) can now deal with a difficult situation with relatively weaker conditions.

Dr. Mao considered the compiler quantile treatment effect (cQTE) as a useful causal estimand and constructed a nonparametric estimation and inference methodology. A sensitivity bound for the cQTE was obtained when the instrument variable does not meet the monotone condition. The simulation comparison showed a favorable performance of this new approach. A health insurance program in India was analyzed in this paper and the estimated treatment effects may “tell important stories” about the insurance policy impact on the households.

Dr. Poorolajal recommends a new observational study design to address the rare exposure problem. Not many papers were published on the design aspects of causal inference and we believe this work is a nice encouragement for more researchers to pay attention to this direction.

Drs Yuan, Yin, and Tan wrote a paper on flexible and robust subgroup analysis. Their semiparametric modeling approach can accurately identify the subgroups with high probability, as shown in their numerical works. Drug trial data was analyzed and the estimated treatment effects are rather distinguishable between the groups. Their findings are quite relevant to precision medicine.

Drs Rahman and Mushfiquee reviewed the covariate-adjusted ROC analysis and proposed a propensity score adjustment for multivariate confounders. This work is meaningful to both causal inference and diagnostic medicine.

We congratulate all the authors! These papers solved hard questions in causal inference and also motivated new developments. We hope their works could attract more research efforts to push this field forward.