How to analyze data when there is violation of the positivity assumption? Several possible solutions exist in the literature. In this paper, we consider propensity score (PS) methods that are commonly used in observational studies to assess causal treatment effects in the context where the positivity assumption is violated. We focus on and examine four specific alternative solutions to the inverse probability weighting (IPW) trimming and truncation: matching weight (MW), Shannon\'s entropy weight (EW), overlap weight (OW), and beta weight (BW) estimators. We first specify their target population, the population of patients for whom clinical equipoise, that is, where we have sufficient PS overlap. Then, we establish the nexus among the different corresponding weights (and estimators); this allows us to highlight the shared properties and theoretical implications of these estimators. Finally, we introduce their augmented estimators that take advantage of estimating both the propensity score and outcome regression models to enhance the treatment effect estimators in terms of bias and efficiency. We also elucidate the role of the OW estimator as the flagship of all these methods that target the overlap population. Our analytic results demonstrate that OW, MW, and EW are preferable to IPW and some cases of BW when there is a moderate or extreme (stochastic or structural) violation of the positivity assumption. We then evaluate, compare, and confirm the finite-sample performance of the aforementioned estimators via Monte Carlo simulations. Finally, we illustrate these methods using two real-world data examples marked by violations of the positivity assumption.

In a clustered observational study, a treatment is assigned to groups and all units within the group are exposed to the treatment. We develop a new method for statistical adjustment in clustered observational studies using approximate balancing weights, a generalization of inverse propensity score weights that solve a convex optimization problem to find a set of weights that directly minimize a measure of covariate imbalance, subject to an additional penalty on the variance of the weights. We tailor the approximate balancing weights optimization problem to the clustered observational study setting by deriving an upper bound on the mean square error and finding weights that minimize this upper bound, linking the level of covariate balance to a bound on the bias. We implement the procedure by specializing the bound to a random cluster-level effects model, leading to a variance penalty that incorporates the signal-to-noise ratio and penalizes the weight on individuals and the total weight on groups differently according to the the intra-class correlation.

Randomized controlled trials are the gold standard for measuring causal effects. However, they are often not always feasible, and causal treatment effects must be estimated from observational data. Observational studies do not allow robust conclusions about causal relationships unless statistical techniques account for the imbalance of pretreatment confounders across groups and key assumptions hold. Propensity score and balance weighting (PSBW) are useful techniques that aim to reduce the observed imbalances between treatment groups by weighting the groups to look alike on the observed confounders. Notably, there are many methods available to estimate PSBW. However, it is unclear a priori which will achieve the best trade-off between covariate balance and effective sample size for a given application. Moreover, it is critical to assess the validity of key assumptions required for robust estimation of the needed treatment effects, including the overlap and no unmeasured confounding assumptions. We present a step-by-step guide to the use of PSBW for estimation of causal treatment effects that includes steps on how to evaluate overlap before the analysis, obtain estimates of PSBW using multiple methods and select the optimal one, check for covariate balance on multiple metrics, and assess sensitivity of findings (both the estimated treatment effect and statistical significance) to unobserved confounding. We illustrate the key steps using a case study examining the relative effectiveness of substance use treatment programs and provide a user-friendly Shiny application that can implement the proposed steps for any application with binary treatments.

BACKGROUND: The outbreak of the COVID-19 pandemic had a major effect on the consumption of health care services. Changes in the use of routine diagnostic exams, increased incidences of postacute COVID-19 syndrome (PCS), and other pandemic-related factors may have influenced detected clinical conditions.
OBJECTIVE: This study aimed to analyze the impact of COVID-19 on the use of outpatient medical imaging services and clinical findings therein, specifically focusing on the time period after the launch of the Israeli COVID-19 vaccination campaign. In addition, the study tested whether the observed gains in abnormal findings may be linked to PCS or COVID-19 vaccination.
METHODS: Our data set included 572,480 ambulatory medical imaging patients in a national health organization from January 1, 2019, to August 31, 2021. We compared different measures of medical imaging utilization and clinical findings therein before and after the surge of the pandemic to identify significant changes. We also inspected the changes in the rate of abnormal findings during the pandemic after adjusting for changes in medical imaging utilization. Finally, for imaging classes that showed increased rates of abnormal findings, we measured the causal associations between SARS-CoV-2 infection, COVID-19-related hospitalization (indicative of COVID-19 complications), and COVID-19 vaccination and future risk for abnormal findings. To adjust for a multitude of confounding factors, we used causal inference methodologies.
RESULTS: After the initial drop in the utilization of routine medical imaging due to the first COVID-19 wave, the number of these exams has increased but with lower proportions of older patients, patients with comorbidities, women, and vaccine-hesitant patients. Furthermore, we observed significant gains in the rate of abnormal findings, specifically in musculoskeletal magnetic resonance (MR-MSK) and brain computed tomography (CT-brain) exams. These results also persisted after adjusting for the changes in medical imaging utilization. Demonstrated causal associations included the following: SARS-CoV-2 infection increasing the risk for an abnormal finding in a CT-brain exam (odds ratio [OR] 1.4, 95% CI 1.1-1.7) and COVID-19-related hospitalization increasing the risk for abnormal findings in an MR-MSK exam (OR 3.1, 95% CI 1.9-5.3).
CONCLUSIONS: COVID-19 impacted the use of ambulatory imaging exams, with greater avoidance among patients at higher risk for COVID-19 complications: older patients, patients with comorbidities, and nonvaccinated patients. Causal analysis results imply that PCS may have contributed to the observed gains in abnormal findings in MR-MSK and CT-brain exams.

A common goal in comparative effectiveness research is to estimate treatment effects on prespecified subpopulations of patients. Though widely used in medical research, causal inference methods for such subgroup analysis (SGA) remain underdeveloped, particularly in observational studies. In this article, we develop a suite of analytical methods and visualization tools for causal SGA. First, we introduce the estimand of subgroup weighted average treatment effect and provide the corresponding propensity score weighting estimator. We show that balancing covariates within a subgroup bounds the bias of the estimator of subgroup causal effects. Second, we propose to use the overlap weighting (OW) method to achieve exact balance within subgroups. We further propose a method that combines OW and LASSO, to balance the bias-variance tradeoff in SGA. Finally, we design a new diagnostic graph-the Connect-S plot-for visualizing the subgroup covariate balance. Extensive simulation studies are presented to compare the proposed method with several existing methods. We apply the proposed methods to the patient-centered results for uterine fibroids (COMPARE-UF) registry data to evaluate alternative management options for uterine fibroids for relief of symptoms and quality of life.

Sequences of treatments that adapt to a patient\'s changing condition over time are often needed for the management of chronic diseases. An adaptive treatment strategy (ATS) consists of personalized treatment rules to be applied through the course of a disease that input the patient\'s characteristics at the time of decision-making and output a recommended treatment. An optimal ATS is the sequence of tailored treatments that yields the best clinical outcome for patients sharing similar characteristics. Methods for estimating optimal adaptive treatment strategies, which must disentangle short- and long-term treatment effects, can be theoretically involved and hard to explain to clinicians, especially when the outcome to be optimized is a survival time subject to right-censoring. In this paper, we describe dynamic weighted survival modeling, a method for estimating an optimal ATS with survival outcomes. Using data from the Clinical Practice Research Datalink, a large primary-care database, we illustrate how it can answer an important clinical question about the treatment of type 2 diabetes. We identify an ATS pertaining to which drug add-ons to recommend when metformin in monotherapy does not achieve the therapeutic goals.