John Crowley

A topic that has received attention in both the statistical and medical literature is the estimation of the probability of failure for endpoints that are subject to competing risks. Despite this, it is not uncommon to see the complement of the Kaplan-Meier estimate used in this setting and interpreted as the probability of failure. If one desires an estimate that can be interpreted in this way, however, the cumulative incidence estimate is the appropriate tool to use in such situations. We believe the more commonly seen representations of the Kaplan-Meier estimate and the cumulative incidence estimate do not lend themselves to easy explanation and understanding of this interpretation. We present, therefore, a representation of each estimate in a manner not ordinarily seen, each representation utilizing the concept of censored observations being 'redistributed to the right.' We feel these allow a more intuitive understanding of each estimate and therefore an appreciation of why the Kaplan-Meier method is inappropriate for estimation purposes in the presence of competing risks, while the cumulative incidence estimate is appropriate.

A nonparametric asymptotic confidence interval for the median survival time is developed for the case where data are subject to arbitrary right censoring. This is accomplished by inverting a generalization of the sign test for censored data. A simulation study shows that this nonparametric confidence interval performs well for a variety of underlying survival functions. The procedure is applied to data from a clinical trial that compared f'our dosage regimens of 5-uorouracil.

A method is developed for obtaining tree-structured relative risk estimates for censored survival data. The first step of a full likelihood estimation procedure is used in a recursive partitioning algorithm that adopts most aspects of the widely used Classification and Regression Tree (CART) algorithm of Breiman et al. (1984, Classification and Regression Trees, Belmont, California: Wadsworth). The performance of the technique is investigated through stimulation and compared to the tree-structured survival methods proposed by Davis and Anderson (1989, Statistics in Medicine 8, 947-961) and Therneau, Grambsch, and Fleming (1990, Biometrika 77, 147-160).

GRACE satellite gravity data is used to estimate terrestrial (surface plus ground) water storage within the Congo Basin in Africa for the period of April, 2002–May, 2006. These estimates exhibit significant seasonal (30 ± 6 mm of equivalent water thickness) and long‐term trends, the latter yielding a total loss of ∼280 km 3 of water over the 50‐month span of data. We also combine GRACE and precipitation data sets (CMAP, TRMM) to explore the relative contributions of the source term to the seasonal hydrological balance within the Congo Basin. We find that the seasonal water storage tends to saturate for anomalies greater than 30–40 mm of equivalent water thickness. Furthermore, precipitation contributed roughly three times the peak water storage after anomalously rainy seasons, in early 2003 and 2005, implying a ∼60–70% loss from runoff and evapotranspiration. Finally, a comparison of residual land water storage (monthly estimates minus best‐fitting trends) in the Congo and Amazon Basins shows an anti‐correlation, in agreement with the “see‐saw” variability inferred by others from runoff data.