Evidence syntheses are often updated as new trials become available. A cumulative meta-analysis repeats a meta-analysis in chronological order, and trial sequential analysis applies group-sequential principles to cumulative meta-analysis to control the risk of spurious findings due to repeated testing. Despite the growing popularity of trial sequential analysis, existing methods rely heavily on normal approximations derived from interim analyses of randomized controlled trials, where participants are typically more homogeneous than in meta-analyses. In random-effects meta-analyses, the conventional assumption that the synthesized effect estimate follows a normal distribution can perform poorly when the number of studies is small. In such settings, the Hartung-Knapp-Sidik-Jonkman method, which is based on a t distribution, has been recommended for more reliable inference. This article introduces refined trial sequential procedures based on cumulative meta-analytic t statistics. The proposed methods are designed to reduce the risk of premature or spurious conclusions in updating evidence syntheses, particularly when between-study heterogeneity is present. Numerical studies demonstrate that the proposed methods provide improved control of type I error compared with existing methods, although the degree of improvement depends on the magnitude of heterogeneity and the true effect size.
We are grateful to the discussants for their generous and wide-ranging contributions. We structure this rejoinder around four themes: robustness and the trade-off between balance and randomness; inference and theoretical properties; the choice of selection criterion in the FSM; and the practical scope of the FSM. We conclude by collecting these and related points under a short agenda for future research. This rejoinder is written in the memory of our co-author and mentor Carl N. Morris.
Cancer remains the second most prevalent cause of death in the United States, claiming 605,213 lives in 2021, surpassing COVID-19 deaths. The cancer mortality rate continued to decline between 2019 and 2020, dropping by 1.5%, marking a significant 33% decrease since 1991. This ongoing improvement primarily mirrors advances in treatment, allowing patients to achieve clinical remission and recovery. Now, a cancer patient is simultaneously exposed to the risk of primary cancer as well as other risks, such as other cancer(s) or other diseases, leading to a competing risks scenario. Analysis of survival data under competing risks and the presence of cured patients have been extensively studied individually, but there is limited work in the current literature that models the possibility of cure from one risk in the presence of competing risks. Moreover, such a model should allow for the possibility of cure from the cause-specific risk of the primary cancer; however, the overall survival probability should eventually approach zero, thereby incorporating the prevalent belief of eventual failure with certainty. We propose a novel unified competing risks cure model, based on the cause-specific hazard approach, that satisfies the aforementioned desired properties. The conditions required to establish model identifiability are studied in detail. To find the maximum likelihood estimates of the model parameters, a computationally efficient expectation maximization algorithm is developed. An extensive simulation study is carried out to demonstrate the performance of the proposed model and estimation method under different parameter settings and in the presence of multiple competing risks. Finally, an application is illustrated using breast cancer data from the SEER cancer database.
Previous cross-sectional research has found correlation in the health outcomes of coresident adults. However, the study of household effects in longitudinal data is challenging due to the complex association structure arising from changes in household membership over time. We propose a 'grouped' multilevel model where the groups (called 'superhouseholds') are specified to capture changes in household structure. Correlated household random effects are used to capture correlations between households sharing an individual(s), and correlations between household pairs can depend on covariates that describe their relationship. We develop a constrained Markov chain Monte Carlo procedure for model estimation that ensures the group-specific correlation matrices (where dimensions can vary across groups) are positive definite, and implement it as an R package. The performance and robustness of our models are evaluated in a simulation study and then applied in analyses of household and area effects on self-rated physical and mental health in the UK using data from a national household panel survey.
Abstract We analyse 36 months of weekly US prescription claims spanning the COVID-19 pandemic to investigate overconsumption of the antiparasitic drug Ivermectin (IVM). To quantify the IVM overconsumption following the heightened public attention as a COVID-19 treatment, we adopt a causal framework, comparing IVM prescription trends to those of a large set of control medications. We employ a regularized synthetic control method using continuous spike-and-slab shrinkage priors to estimate state-level deviations in IVM consumption. This approach offers decision-theoretic guarantees on predictive risk, for downstream policy analysis at multiple-time points after the intervention. Its empirical robustness is demonstrated through extensive validation checks. We find a modest increase in IVM prescriptions following early reports of its potential therapeutic use, with no significant surge over the subsequent 8 months, followed by a pronounced increase coinciding with the peak in COVID-19 cases. Strikingly, elevated IVM use persisted even after COVID-19 vaccines became widely available and federal countermeasures were implemented. Our estimation captures the heterogeneity in long-term effectiveness of these countermeasures across states. We find that state-level political affiliation significantly explains variation in overconsumption, even after accounting for COVID-19 incidence, highlighting regional disparities and the need for more targeted and trusted public health messaging.
