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Summary Cross‐validation (CV) is one of the most widely used techniques in statistical learning for estimating the test error of a model, but its behavior is not yet fully understood. It has been shown that standard confidence intervals for test error using estimates from CV may have coverage below nominal levels. This phenomenon occurs because each sample is used in both the training and testing procedures during CV and as a result, the CV estimates of the errors become correlated. Without accounting for this correlation, the estimate of the variance is smaller than it should be. One way to mitigate this issue is by estimating the mean squared error of the prediction error instead using nested CV. This approach has been shown to achieve superior coverage compared to intervals derived from standard CV. In this work, we generalize the nested CV idea to the Cox proportional hazards model and explore various choices of test error for this setting. 

Abstract The COVID-19 pandemic has taken a devastating toll around the world. Since January 2020, the World Health Organization estimates 14.9 million excess deaths have occurred globally. Despite this grim number quantifying the deadly impact, the underlying factors contributing to COVID-19 deaths at the population level remain unclear. Prior studies indicate that demographic factors like proportion of population older than 65 and population health explain the cross-country difference in COVID-19 deaths. However, there has not been a comprehensive analysis including variables describing government policies and COVID-19 vaccination rate. Furthermore, prior studies focus on COVID-19 death rather than excess death to assess the impact of the pandemic. Through a robust statistical modeling framework, we analyze 80 countries and show that actionable public health efforts beyond just the factors intrinsic to each country are important for explaining the cross-country heterogeneity in excess death. 

Knowing how policy-induced salary schedule changes affect teacher recruitment and retention will significantly advance our understanding of how resources matter for K–12 student learning. This study sheds light on this issue by estimating how legislative funding changes in Washington state in 2018–2019—induced by the McCleary court-ordered reform—affected teacher salaries and labor market outcomes. By embedding a simulated instrumental variables approach in a mixed-methods design, we observed that local collective bargaining negotiations directed new state funding allocations to substantially increase certificated base salaries, particularly for senior teachers with 16 years or more of teaching experience. Variability in political power, priorities, and interests of both districts and unions led to greater heterogeneity in teacher salary schedules. Suggestive evidence shows that state average teacher turnover rate was significantly reduced in the first year of reform. The McCleary-induced salary increase particularly reduces mid-career teachers’ (8–15 years of teaching experience) mobility rate and late-career teachers’ (23+ years of teaching experience) leaving rate. The McCleary-induced base salary increase has mostly null effects on teacher hiring in the first 2 years of implementation.