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  1. Summary

    Nonparametric covariate adjustment is considered for log-rank-type tests of the treatment effect with right-censored time-to-event data from clinical trials applying covariate-adaptive randomization. Our proposed covariate-adjusted log-rank test has a simple explicit formula and a guaranteed efficiency gain over the unadjusted test. We also show that our proposed test achieves universal applicability in the sense that the same formula of test can be universally applied to simple randomization and all commonly used covariate-adaptive randomization schemes such as the stratified permuted block and the Pocock–Simon minimization, which is not a property enjoyed by the unadjusted log-rank test. Our method is supported by novel asymptotic theory and empirical results for Type-I error and power of tests.

     
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  2. Summary

    Covariate-adaptive randomization is popular in clinical trials with sequentially arrived patients for balancing treatment assignments across prognostic factors that may have influence on the response. However, existing theory on tests for the treatment effect under covariate-adaptive randomization is limited to tests under linear or generalized linear models, although the covariate-adaptive randomization method has been used in survival analysis for a long time. Often, practitioners will simply adopt a conventional test to compare two treatments, which is controversial since tests derived under simple randomization may not be valid in terms of type I error under other randomization schemes. We derive the asymptotic distribution of the partial likelihood score function under covariate-adaptive randomization and a working model that is subject to possible model misspecification. Using this general result, we prove that the partial likelihood score test that is robust against model misspecification under simple randomization is no longer robust but conservative under covariate-adaptive randomization. We also show that the unstratified log-rank test is conservative and the stratified log-rank test remains valid under covariate-adaptive randomization. We propose a modification to variance estimation in the partial likelihood score test, which leads to a score test that is valid and robust against arbitrary model misspecification under a large family of covariate-adaptive randomization schemes including simple randomization. Furthermore, we show that the modified partial likelihood score test derived under a correctly specified model is more powerful than log-rank-type tests in terms of Pitman’s asymptotic relative efficiency. Simulation studies about the type I error and power of various tests are presented under several popular randomization schemes.

     
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  3. null (Ed.)
    Abstract. During the early part of the last glacial termination (17.2–15 ka) and coincident with a ∼35 ppm rise in atmospheric CO2, a sharp 0.3‰–0.4‰ decline in atmospheric δ13CO2 occurred, potentially constraining the key processes that account for the early deglacial CO2 rise. A comparable δ13C decline has also been documented in numerous marine proxy records from surface and thermocline-dwelling planktic foraminifera. The δ13C decline recorded in planktic foraminifera has previously been attributed to the release of respired carbon from the deep ocean that was subsequently transported within the upper ocean to sites where the signal was recorded (and then ultimately transferred to the atmosphere). Benthic δ13C records from the global upper ocean, including a new record presented here from the tropical Pacific, also document this distinct early deglacial δ13C decline. Here we present modeling evidence to show that rather than respired carbon from the deep ocean propagating directly to the upper ocean prior to reaching the atmosphere, the carbon would have first upwelled to the surface in the Southern Ocean where it would have entered the atmosphere. In this way the transmission of isotopically light carbon to the global upper ocean was analogous to the ongoing ocean invasion of fossil fuel CO2. The model results suggest that thermocline waters throughout the ocean and 500–2000 m water depths were affected by this atmospheric bridge during the early deglaciation. 
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