Analyzing left-truncated right-censored data with uncertain onset time with parametric models

Prevalent sampling is an efficient and focused approach to the study of the natural history of disease. Right-censored time-to-event data observed from prospective prevalent cohort studies are often subject to left-truncated sampling. Left-truncated samples are not randomly selected from the population of interest and have a selection bias. Extensive studies have focused on estimating the unbiased distribution given left-truncated samples. However, in many applications, the exact date of disease onset was not observed. For example, in an HIV infection study, the exact HIV infection time is not observable. However, it is known that the HIV infection date occurred between two observable dates. Meeting these challenges motivated our study. We propose parametric models to estimate the unbiased distribution of left-truncated, right-censored time-to-event data with uncertain onset times. We first consider data from a length-biased sampling, a specific case in left-truncated samplings. Then we extend the proposed method to general left-truncated sampling. With a parametric model, we construct the full likelihood, given a biased sample with unobservable onset of disease. The parameters are estimated through the maximization of the constructed likelihood by adjusting the selection bias and unobservable exact onset. Simulations are conducted to evaluate the finite sample performance of the proposed methods. We apply the proposed method to an HIV infection study, estimating the unbiased survival function and covariance coefficients. ^

Mean dynamic topography and oceanographic parameters estimated from an inverse model and satellite geodesy, with link to model result in one single NetCDF file (392 MB), including the inverse data error covariance

Geostrophic surface velocities can be derived from the gradients of the mean dynamic topography-the difference between the mean sea surface and the geoid. Therefore, independently observed mean dynamic topography data are valuable input parameters and constraints for ocean circulation models. For a successful fit to observational dynamic topography data, not only the mean dynamic topography on the particular ocean model grid is required, but also information about its inverse covariance matrix. The calculation of the mean dynamic topography from satellite-based gravity field models and altimetric sea surface height measurements, however, is not straightforward. For this purpose, we previously developed an integrated approach to combining these two different observation groups in a consistent way without using the common filter approaches (Becker et al. in J Geodyn 59(60):99-110, 2012, doi:10.1016/j.jog.2011.07.0069; Becker in Konsistente Kombination von Schwerefeld, Altimetrie und hydrographischen Daten zur Modellierung der dynamischen Ozeantopographie, 2012, http://nbn-resolving.de/nbn:de:hbz:5n-29199). Within this combination method, the full spectral range of the observations is considered. Further, it allows the direct determination of the normal equations (i.e., the inverse of the error covariance matrix) of the mean dynamic topography on arbitrary grids, which is one of the requirements for ocean data assimilation. In this paper, we report progress through selection and improved processing of altimetric data sets. We focus on the preprocessing steps of along-track altimetry data from Jason-1 and Envisat to obtain a mean sea surface profile. During this procedure, a rigorous variance propagation is accomplished, so that, for the first time, the full covariance matrix of the mean sea surface is available. The combination of the mean profile and a combined GRACE/GOCE gravity field model yields a mean dynamic topography model for the North Atlantic Ocean that is characterized by a defined set of assumptions. We show that including the geodetically derived mean dynamic topography with the full error structure in a 3D stationary inverse ocean model improves modeled oceanographic features over previous estimates.

Isotopic composition of water in fog, rain, throughfall and stemflow in the Monte Verde, Costa Rica

Fog deposition, precipitation, throughfall and stemflow were measured in a windward tropical montane cloud forest near Monteverde, Costa Rica, for a 65-day period during the dry season of 2003. Net fog deposition was measured directly using the eddy covariance (EC) method and it amounted to 1.2 ± 0.1 mm/day (mean ± standard error). Fog water deposition was 5-9% of incident rainfall for the entire period, which is at the low end of previously reported values. Stable isotope concentrations (d18O and d2H) were determined in a large number of samples of each water component. Mass balance-based estimates of fog deposition were 1.0 ± 0.3 and 5.0 ± 2.7 mm/day (mean ± SE) when d18O and d2H were used as tracer, respectively. Comparisons between direct fog deposition measurements and the results of the mass balance model using d18O as a tracer indicated that the latter might be a good tool to estimate fog deposition in the absence of direct measurement under many (but not all) conditions. At 506 mm, measured water inputs over the 65 days (fog plus rain) fell short by 46 mm compared to the canopy output of 552 mm (throughfall, stemflow and interception evaporation). This discrepancy is attributed to the underestimation of rainfall during conditions of high wind.

Annual layer thicknesses and age-depth (oldest estimate) of Derwael Ice Rise (IC12), Dronning Maud Land, East Antarctica

A 120 m-long ice core was drilled in 2012 on the Derwael Ice Rise, coastal Dronning Maud Land, East Antarctica. Water stable isotopes (d18O and dD) stratigraphy is supplemented by discontinuous major ion profiles and continuous electrical conductivity measurements. The base of the ice core is dated to AD 1759 ± 16, providing a climate proxy for the past ~250 years. This data set presents the core's annual layer thickness history in meters water equivalent for the oldest age-depth estimate before correction for the influence of ice deformation.

North Atlantic late Miocene stable-isotope stratigraphy, biostratigraphy, and magnetostratigraphy

Upper Miocene foraminiferal nannofossil ooze and chalk from DSDP Hole 552A in the northeast Atlantic Ocean have been closely sampled for biostratigraphic, paleomagnetic, and stable-isotopic studies. Sampling at 10-cm intervals resulted in an uppermost Miocene isotope stratigraphy with a 1000- to 3000-yr. resolution. Covariance in benthic (Planulina wuellerstorfi) and planktonic (Globigerina bulloides) foraminiferal d18O records is taken as evidence for variability in continental ice volume. Our best estimate is that glacial maxima occurred at -5.0 and ~ 5.5 Ma and lasted no more than 20,000 yrs. These events probably lowered sea level by 60 m below the latest Miocene average. There is little oxygen-isotope evidence, however, for a prolonged glaciation during the last 2 m.y. of the late Miocene. High- and low-frequency variability in the d13C record of foraminifers is useful for correlation among North Atlantic DSDP Sites 408, 410, 522, 610, and 611, and for correlation with sites in other oceans. Similar d13C changes are seen in P. wuellerstorfi and G. bulloides, but the amplitude of the signal is always greater in G. bulloides. Variability in d13C common to both species probably reflects variability in the d13C of total CO2 in seawater. Major long-term features in the d13C record include a latest Miocene maximum (P. wuellerstorfi = 1.5 per mil ) in paleomagnetic Chron 7, an abrupt decrease in d13C at -6.2 Ma, and a slight increase at -5.5 Ma. The decrease in d13C at -6.2 Ma, which has been paleomagnetically dated only twice before, occurs in the upper reversed part of Chronozone 6 at Holes 552A and 611C, in excellent agreement with earlier studies. Cycles in d13C with a period of ~ 10 4 yrs. are interpreted as changes in seawater chemistry, which may have resulted from orbitally induced variability in continental biomass. Samples of P. wuellerstorfi younger than 6 Ma from throughout the North Atlantic have d13C near lo, on average ~ l per mil greater than samples of the same age in the Pacific Ocean. Thus, there is no evidence for cessation of North Atlantic Deep Water production resulting from the Messinian "salinity crisis." Biostratigraphic results indicate continuous sedimentation during the late Miocene after about -6.5 Ma at Hole 552A. Nannofossil biostratigraphy is complicated by the scarcity of low-latitude marker species, but middle and late Miocene Zones NN7 through NN11 are recognized. A hiatus is present at -6.5 Ma, on the basis of simultaneous first occurrences of Amaurolithusprimus, Amaurolithus delicatus, Amaurolithus amplificus, and Scyphosphaera globulata. The frequency and duration of older hiatuses increase downsection in Hole 552A, as suggested by calcareous nannofossil biostratigraphy and magnetostratigraphy. Paleomagnetic results at Hole 552A indicate a systematic pattern of inclination changes. Chronozone 6 was readily identified because of its characteristic nannoflora (sequential occurrences of species assigned to the genus Amaurolithus) and the d13C decrease in foraminifers, but its lower reversed interval is condensed. Only the lower normal interval of Chronozone 5 was recognized at Hole 552A; the upper normal interval and the lowest Gilbert sediment are not recognized, owing to low intensity of magnetization and to coring disturbance. Interpreting magnetic reversals below Chronozone 6 was difficult because of hiatuses, but a lower normally magnetized interval is probably Chronozone 7. Correlation between DSDP Hole 552A and other North Atlantic sites is demonstrated using coiling direction changes in the planktonic foraminifer Neogloboquadrina. At most sites this genus changed its coiling preference from dominantly right to dominantly left during the late Miocene. At Hole 552A this event probably occurred about 7 m.y. ago. At the same time, P. wuellerstorfi had maximum d13C values. A similar d13C maximum and coiling change occurred together in Chron 7 at Hole 611C, and at Hole 610E. In sediment younger than -5.5 Ma, the coiling of small Neogloboquadrina species is random, but the larger species N. atlantica retains preferential left coiling.