In the causal analysis of observational data, the positivity assumption requires that all treatments of interest be observed in every patient subgroup. Violations of this assumption are indicated by nonoverlap in the data in the sense that patients with certain covariate combinations are not observed to receive a treatment of interest, which may arise from contraindications to treatment or small sample size. In this paper, we emphasize the importance and implications of this often-overlooked assumption. Further, we elaborate on the challenges nonoverlap poses to estimation and inference and discuss previously proposed methods. We distinguish between structural and practical violations and provide insight into which methods are appropriate for each. To demonstrate alternative approaches and relevant considerations (including how overlap is defined and the target population to which results may be generalized) when addressing positivity violations, we employ an electronic health record-derived data set to assess the effects of metformin on colon cancer recurrence among diabetic patients.
Numerous designs have been proposed for phase I clinical trials. Although studies have compared their performances, few have considered the effects of changing design parameters. In this article, we review a few popular designs, including the 3 + 3, continuous reassessment method (CRM), Bayesian optimal interval (BOIN) design, and Keyboard design, and evaluate how varying design parameters (such as number of dose levels, target toxicity rate, maximum sample size, and cohort size) could impact the performances of each design through simulations. Excluded from our analysis is the mTPI-2 design, which operates in the same way as the Keyboard. Our results suggest that regardless of the choices of design parameters, the 3 + 3 design performs worse than the other ones, and BOIN and Keyboard have comparable performance to CRM. For any design, the performance varies with the choice of parameters. In particular, it improves as sample sizes increase, but the magnitude of benefit from increasing sample sizes varies substantially across scenarios. The impact of cohort size on design performances seems to have no clear direction. Therefore, BOIN and Keyboard designs are generally recommended due to their simplicity and good performance. With regard to choices of sample size and cohort size in designing a trial, it is recommend that simulations be performed for the particular clinical settings to aid decision making.
This study investigated the geographic variation and the clustering of lung cancer incidence rates in Philadelphia and the surrounding areas using addresses at the time of diagnosis. Using 60,844 cases from Pennsylvania Cancer Registry, we calculated and mapped the age-adjusted incidence rates for five Pennsylvania (PA) counties near Philadelphia between 1998–2007 and 2008–2017. We identified ZIP codes with significantly higher incidence rates than the state rates and examined their demographic and exposure characteristics. Further, we tested for spatial autocorrelation and identified spatial clusters using Moran’s I statistic. Our results showed that approximately one in four ZIP codes had an incidence rate that was significantly higher than the PA state rate in each period studied. Clusters of higher incidences were detected in the southeastern part of PA bordering New Jersey. These areas tended to be more populated, of lower socioeconomic status, and closer to manufacturing facilities and major highways. Possibly driven by the community and environmental factors, the observed differences in disease incidence suggest the importance of including residential location in risk assessment tools for lung cancer.
In observational studies, causal inference relies on several key identifying assumptions. One identifiability condition is the positivity assumption, which requires the probability of treatment be bounded away from 0 and 1. That is, for every covariate combination, it should be possible to observe both treated and control subjects the covariate distributions should overlap between treatment arms. If the positivity assumption is violated, population‐level causal inference necessarily involves some extrapolation. Ideally, a greater amount of uncertainty about the causal effect estimate should be reflected in such situations. With that goal in mind, we construct a Gaussian process model for estimating treatment effects in the presence of practical violations of positivity. Advantages of our method include minimal distributional assumptions, a cohesive model for estimating treatment effects, and more uncertainty associated with areas in the covariate space where there is less overlap. We assess the performance of our approach with respect to bias and efficiency using simulation studies. The method is then applied to a study of critically ill female patients to examine the effect of undergoing right heart catheterization.
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