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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. 

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. 

Abstract The prevailing hypothesis to explain pCO₂rise at the last glacial termination calls upon enhanced ventilation of excess respired carbon that accumulated in the deep sea during the glacial. Recent studies argue lower [O₂] in the glacial ocean is indicative of increased carbon respiration. The magnitude of [O₂] depletion was 100–140 µ mol/kg at the glacial maximum. Because respiration is coupled toδ¹³C of dissolved inorganic carbon (DIC), [O₂] depletion of 100–140 µ mol/kg from carbon respiration would lower deep waterδ¹³C_DICby ∼1‰ relative to surface water. Prolonged sequestration of respired carbon would also lower the amount of¹⁴C in the deep sea. We show that Pacific Deep Waterδ¹³C_DICdid not decrease relative to the surface ocean and Δ¹⁴C was only ∼50‰ lower during the late glacial. Model simulations of the hypothesized ventilation change during deglaciation lead to large increases inδ¹³C_DIC, Δ¹⁴C, andε¹⁴C that are not recorded in observations.