The number and timing of time -dependent covariate measurements for the Cox regression model

The problem of analyzing data with updated measurements in the time-dependent proportional hazards model arises frequently in practice. One available option is to reduce the number of intervals (or updated measurements) to be included in the Cox regression model. We empirically investigated the bias of the estimator of the time-dependent covariate while varying the effect of failure rate, sample size, true values of the parameters and the number of intervals. We also evaluated how often a time-dependent covariate needs to be collected and assessed the effect of sample size and failure rate on the power of testing a time-dependent effect.^ A time-dependent proportional hazards model with two binary covariates was considered. The time axis was partitioned into k intervals. The baseline hazard was assumed to be 1 so that the failure times were exponentially distributed in the ith interval. A type II censoring model was adopted to characterize the failure rate. The factors of interest were sample size (500, 1000), type II censoring with failure rates of 0.05, 0.10, and 0.20, and three values for each of the non-time-dependent and time-dependent covariates (1/4,1/2,3/4).^ The mean of the bias of the estimator of the coefficient of the time-dependent covariate decreased as sample size and number of intervals increased whereas the mean of the bias increased as failure rate and true values of the covariates increased. The mean of the bias of the estimator of the coefficient was smallest when all of the updated measurements were used in the model compared with two models that used selected measurements of the time-dependent covariate. For the model that included all the measurements, the coverage rates of the estimator of the coefficient of the time-dependent covariate was in most cases 90% or more except when the failure rate was high (0.20). The power associated with testing a time-dependent effect was highest when all of the measurements of the time-dependent covariate were used. An example from the Systolic Hypertension in the Elderly Program Cooperative Research Group is presented. ^

Seasonally resolved chemical records of six ice cores from the Dronning Maud Land, Antarctica

The ammonium, calcium, and sodium concentrations from three intermediate depth ice cores drilled in the area of Dronning Maud Land, East Antarctica, have been investigated. Since all measurements were performed by a high-resolution Continuous Flow Analysis system, for the first time seasonal signals of chemical trace species could be obtained from the interior of central Antarctica over a period of approximately 2 millennia. Although the elevation as well as the accumulation rate differ between the drilling sites, similar values were obtained by comparing mean concentrations spanning the last 900 years. However, a distinct lack of intersite correlation was found on decadal timescales. Despite a noticeable accumulation change, apparent in one core, no significant concentration change of all three species has occurred. All the measured ions show clear seasonal signals over the whole records. While the sea-salt-related component sodium peaks simultaneously with calcium, the maximum ammonium concentration occurs in the snow with a time lag of 2 months after the sea-salt peak. More than 60% of the calcium concentration can be attributed to an ocean source. Elevated sodium concentrations were found within this millennium compared to mean values of the whole records, but the spatially varying shape of the increase suggests that a possible climatic signal is biased by local deposition effects.

Time series of black carbon aerosol measurements from Neumayer Station, 1999-2011

Continuous black carbon (BC) observations were conducted from 1999 through 2009 by an Aethalometer (AE10) and from 2006 through 2011 by a Multi-Angle Absorption Photometer (MAAP) at Neumayer Station (NM) under stringent contamination control. Considering the respective observation period, BC concentrations measured by the MAAP were somewhat higher (median ± standard deviation: 2.1 ± 2.0 ng/m**3) compared to the AE10 results (1.6 ± 2.1 ng/m**3). Neither for the AE10 nor for the MAAP data set a significant long-term trend could be detected. Consistently a pronounced seasonality was observed with both instruments showing a primary annual maximum between October and November and a minimum in April with a maximum/minimum ratio of 4.5/1.6 = 3.8 and 2.7/0.64 = 4.2 for the MAAP and AE10 data, respectively. Occasionally a secondary summer maximum in January/February was visible. With the aim to assess the impact of BC on optical properties of the aerosol at NM, we evaluated the BC data along with particle scattering coefficients measured by an integrating nephelometer. We found the mean single scattering albedo of w550 = 0.992 ± 0.0090 (median: 0.994) at a wavelength of 550 nm with a range of values from 0.95 to 1.0.

First results from stable-istope measurements on ice cores from Dronning Maud Land

The European Project for Ice Coring in Antarctica (EPICA) focuses on the drilling of two deep ice cores, the first at Dome C and the second at Kohnen station (75°00' S, 0°04' E) in Dronning Maud Land (DML). This paper deals with stable-isotope records from ice cores drilled in DML. In the first season, the deep EPICA DML core reached a depth of 450 m, recovering ice approximately 7000 years old. Generally, the d18O record indicates a stable Holocene climate and shows low variability. However, during the last 4000 years (based on a preliminary time-scale) the d18O values decrease continuously by about 0.6%, and the deuterium excess values increase by about 0.5%. The correlation between d18O and the deuterium excess d is investigated for a 50m long core section and the near-surface snow. High-pass filtered profiles are positively correlated, whereas the correlation between low-pass filtered profiles is negative. A post-depositional effect due to diffusion processes can be seen in a sub-annually resolved profile from snow-pit samples. Changes in the seasonality of the evolution of the snow cover and the consequences for stable-isotope content are demonstrated with data from ice core B31.

Annual average Sr/Ca measurements from Porites lutea coral at Ha'afera Island, Tonga

In the South Pacific Convergence Zone (SPCZ), the variability in a sub-seasonally resolved microatoll Porites colony Sr/Ca record from Tonga and a previously published high-resolution record from Fiji are strongly influenced by sea surface temperature (SST) over the calibration period from 1981 to 2004 (R^2 = 0.67 - 0.68). However, the Sr/Ca-derived SST correlation to instrumental SST decreases back in time. The lower frequency secular trend (~1°C) and decadal-scale (~2 - 3°C) modes in Sr/Ca-derived SST are almost two times larger than that observed in instrumental SST. The coral Sr/Ca records suggest that local effects on SST generate larger amplitude variability than gridded SST products indicate. Reconstructed d18O of seawater (d18Osw) at these sites correlate with instrumental sea surface salinity (SSS; r = 0.64 - 0.67) but not local precipitation (r = -0.10 to - 0.22) demonstrating that the advection and mixing of different salinity water masses may be the predominant control on d18Osw in this region. The Sr/Ca records indicate SST warming over the last 100 years and appears to be related to the expansion of the western Pacific warm pool (WPWP) including an increasing rate of expansion in the last ~20 years. The reconstructed d18Osw over the last 100 years also shows surface water freshening across the SPCZ. The warming and freshening of the surface ocean in our study area suggests that the SPCZ has been shifting (expanding) southeast, possibly related to the southward shift and intensification of the South Pacific gyre over the last 50 years in response to strengthened westerly winds.

Pollen analysis, particle size analysis, end-member modelling and x-ray fluorescence measurements from sediment cores off Cape Ghir, Morocco

Understanding past human-climate-environment interactions is essential for assessing the vulnerability of landscapes and ecosystems to future climate change. This is particularly important in southern Morocco where the current vegetation is impacted by pastoralism, and the region is highly sensitive to climate variability. Here, we present a 2000-year record of vegetation, sedimentation rate, XRF chemical element intensities, and particle size from two decadal-resolved, marine sediment cores, raised from offshore Cape Ghir, southern Morocco. The results show that between 650 and 850 AD the sedimentation rate increased dramatically from 100 cm/1000 years to 300 cm/1000 years, and the Fe/Ca and pollen flux doubled, together indicating higher inputs of terrestrial sediment. Particle size measurements and end-member modelling suggest increased fluvial transport of the sediment. Beginning at 650 AD pollen levels from Cichorioideae species show a sharp rise from 10% to 20%. Pollen from Atemisia and Plantago, also increase from this time. Deciduous oak pollen percentages show a decline, whereas those of evergreen oak barely change. The abrupt increase in terrestrial/fluvial input from 650 to 850 AD occurs, within the age uncertainty, of the arrival of Islam (Islamisation) in Morocco at around 700 AD. Historical evidence suggests Islamisation led to population increase and development of southern Morocco, including expanded pastoralism, deforestation and agriculture. Livestock pressure may have changed the vegetation structure, accounting for the increase in pollen from Cichorioideae, Plantago, and Artemisia, which include many weedy species. Goats in particular may have played a dominant role as agents of erosion, and intense browsing may have led to the decline in deciduous oak; evergreen oak is more likely to survive as it re-sprouts more vigorously after browsing. From 850 AD to present sedimentation rates, Fe/Ca ratios and fluvial discharge remain stable, whereas pollen results suggest continued degradation. Pollen results from the past 150 years suggest expanded cultivation of olives and the native argan tree, and the introduction of Australian eucalyptus trees. The rapidly increasing population in southern Morocco is causing continued pressure to expand pastoralism and agriculture. The history of land degradation presented here suggests that the vegetation in southern Morocco may have been degraded for a longer period than previously thought and may be particularly sensitive to further land use changes. These results should be included in land management strategies for southern Morocco.