Nonparametric inference of general while-alive estimands for recurrent events

Measuring the treatment effect on recurrent events like hospitalization in the presence of death has long challenged statisticians and clinicians alike. Traditional inference on the cumulative frequency unjustly penalizes survivorship as longer survivors also tend to experience more adverse events. Expanding a recently suggested idea of the "while-alive" event rate, we consider a general class of such estimands that adjust for the length of survival without losing causal interpretation. Given a user-specified loss function that allows for arbitrary weighting, we define as estimand the average loss experienced per unit time alive within a target period and use the ratio of this loss rate to measure the effect size. Scaling the loss rate by the width of the corresponding time window gives us an alternative, and sometimes more photogenic, way of showing the data. To make inferences, we construct a nonparametric estimator for the loss rate through the cumulative loss and the restricted mean survival time and derive its influence function in closed form for variance estimation and testing. As simulations and analysis of real data from a heart failure trial both show, the while-alive approach corrects for the false attenuation of treatment effect due to patients living longer under treatment, with increased statistical power as a result. The proposed methods are implemented in the R-package WA, which is publicly available from the Comprehensive R Archive Network (CRAN).

Risk Control Values and Remediation Goals for Benzo[a]pyrene in Contaminated Sites: Sectoral Characteristics, Temporal Trends, and Empirical Implications

Benzo[a]pyrene (BaP) is a highly carcinogenic pollutant of global concern. There is a need for a comprehensive assessment of regulation decisions for BaP-contaminated site management. Herein, we present a quantitative evaluation of remediation decisions from 206 contaminated sites throughout China between 2011 and 2021 using the cumulative distribution function (CDF) and related statistical methodologies. Generally, remediation decisions seek to establish remediation goals (RGs) based on the risk control values (RCVs). Cumulative frequency distributions, followed non-normal S-curve, emerged multiple nonrandom clusters. These clusters are consistent with regulatory guidance values (RGVs), of national and local soil levels in China. Additionally, priority interventions for contaminated sites were determined by prioritizing RCVs and identifying differences across industrial sectors. Notably, we found that RCVs and RGs became more relaxed over time, effectively reducing conservation and unsustainable social and economic impacts. The joint probability curve was applied to model decision values, which afforded a generic empirically important RG of 0.57 mg/kg. Overall, these findings will help decision-makers and governments develop appropriate remediation strategies for BaP as a ubiquitous priority pollutant.