Bayesian and survival model for tumor relapse status and disease-specific survival, with applications to breast cancer

Breast cancer is the most common non-skin cancer and the second leading cause of cancer-related death in women in the United States. Studies on ipsilateral breast tumor relapse (IBTR) status and disease-specific survival will help guide clinic treatment and predict patient prognosis.^ After breast conservation therapy, patients with breast cancer may experience breast tumor relapse. This relapse is classified into two distinct types: true local recurrence (TR) and new ipsilateral primary tumor (NP). However, the methods used to classify the relapse types are imperfect and are prone to misclassification. In addition, some observed survival data (e.g., time to relapse and time from relapse to death)are strongly correlated with relapse types. The first part of this dissertation presents a Bayesian approach to (1) modeling the potentially misclassified relapse status and the correlated survival information, (2) estimating the sensitivity and specificity of the diagnostic methods, and (3) quantify the covariate effects on event probabilities. A shared frailty was used to account for the within-subject correlation between survival times. The inference was conducted using a Bayesian framework via Markov Chain Monte Carlo simulation implemented in softwareWinBUGS. Simulation was used to validate the Bayesian method and assess its frequentist properties. The new model has two important innovations: (1) it utilizes the additional survival times correlated with the relapse status to improve the parameter estimation, and (2) it provides tools to address the correlation between the two diagnostic methods conditional to the true relapse types.^ Prediction of patients at highest risk for IBTR after local excision of ductal carcinoma in situ (DCIS) remains a clinical concern. The goals of the second part of this dissertation were to evaluate a published nomogram from Memorial Sloan-Kettering Cancer Center, to determine the risk of IBTR in patients with DCIS treated with local excision, and to determine whether there is a subset of patients at low risk of IBTR. Patients who had undergone local excision from 1990 through 2007 at MD Anderson Cancer Center with a final diagnosis of DCIS (n=794) were included in this part. Clinicopathologic factors and the performance of the Memorial Sloan-Kettering Cancer Center nomogram for prediction of IBTR were assessed for 734 patients with complete data. Nomogram for prediction of 5- and 10-year IBTR probabilities were found to demonstrate imperfect calibration and discrimination, with an area under the receiver operating characteristic curve of .63 and a concordance index of .63. In conclusion, predictive models for IBTR in DCIS patients treated with local excision are imperfect. Our current ability to accurately predict recurrence based on clinical parameters is limited.^ The American Joint Committee on Cancer (AJCC) staging of breast cancer is widely used to determine prognosis, yet survival within each AJCC stage shows wide variation and remains unpredictable. For the third part of this dissertation, biologic markers were hypothesized to be responsible for some of this variation, and the addition of biologic markers to current AJCC staging were examined for possibly provide improved prognostication. The initial cohort included patients treated with surgery as first intervention at MDACC from 1997 to 2006. Cox proportional hazards models were used to create prognostic scoring systems. AJCC pathologic staging parameters and biologic tumor markers were investigated to devise the scoring systems. Surveillance Epidemiology and End Results (SEER) data was used as the external cohort to validate the scoring systems. Binary indicators for pathologic stage (PS), estrogen receptor status (E), and tumor grade (G) were summed to create PS+EG scoring systems devised to predict 5-year patient outcomes. These scoring systems facilitated separation of the study population into more refined subgroups than the current AJCC staging system. The ability of the PS+EG score to stratify outcomes was confirmed in both internal and external validation cohorts. The current study proposes and validates a new staging system by incorporating tumor grade and ER status into current AJCC staging. We recommend that biologic markers be incorporating into revised versions of the AJCC staging system for patients receiving surgery as the first intervention.^ Chapter 1 focuses on developing a Bayesian method to solve misclassified relapse status and application to breast cancer data. Chapter 2 focuses on evaluation of a breast cancer nomogram for predicting risk of IBTR in patients with DCIS after local excision gives the statement of the problem in the clinical research. Chapter 3 focuses on validation of a novel staging system for disease-specific survival in patients with breast cancer treated with surgery as the first intervention. ^

Spatial analysis of cardiovascular disease mortality and air pollution in Harris County, Texas

The association between fine particulate matter air pollution (PM2.5) and cardiovascular disease (CVD) mortality was spatially analyzed for Harris County, Texas, at the census tract level. The objective was to assess how increased PM2.5 exposure related to CVD mortality in this area while controlling for race, income, education, and age. An estimated exposure raster was created for Harris County using Kriging to estimate the PM2.5 exposure at the census tract level. The PM2.5 exposure and the CVD mortality rates were analyzed in an Ordinary Least Squares (OLS) regression model and the residuals were subsequently assessed for spatial autocorrelation. Race, median household income, and age were all found to be significant (p<0.05) predictors in the model. This study found that for every one μg/m3 increase in PM2.5 exposure, holding age and education variables constant, an increase of 16.57 CVD deaths per 100,000 would be predicted for increased minimum exposure values and an increase of 14.47 CVD deaths per 100,000 would be predicted for increased maximum exposure values. This finding supports previous studies associating PM2.5 exposure with CVD mortality. This study further identified the areas of greatest PM2.5 exposure in Harris County as being the geographical locations of populations with the highest risk of CVD (i.e., predominantly older, low-income populations with a predominance of African Americans). The magnitude of the effect of PM2.5 exposure on CVD mortality rates in the study region indicates a need for further community-level studies in Harris County, and suggests that reducing excess PM2.5 exposure would reduce CVD mortality.^

Slope estimation in a parametric measurement error model: A simulation study

In regression analysis, covariate measurement error occurs in many applications. The error-prone covariates are often referred to as latent variables. In this proposed study, we extended the study of Chan et al. (2008) on recovering latent slope in a simple regression model to that in a multiple regression model. We presented an approach that applied the Monte Carlo method in the Bayesian framework to the parametric regression model with the measurement error in an explanatory variable. The proposed estimator applied the conditional expectation of latent slope given the observed outcome and surrogate variables in the multiple regression models. A simulation study was presented showing that the method produces estimator that is efficient in the multiple regression model, especially when the measurement error variance of surrogate variable is large.^

Spatial distribution of orofacial cleft birth defects and uranium-radium concentrations in tap water in Atascosa, Bee, Brooks, Calhoun, Duval, Goliad, Hidalgo, Jim Hogg, Jim Wells, Karnes, Kleberg, Live Oak, McMullen, Nueces, San Patricio, Refugio, Starr, Victoria, Webb, and Zavala Counties, Texas

Background Past and recent evidence shows that radionuclides in drinking water may be a public health concern. Developmental thresholds for birth defects with respect to chronic low level domestic radiation exposures, such as through drinking water, have not been definitely recognized, and there is a strong need to address this deficiency in information. In this study we examined the geographic distribution of orofacial cleft birth defects in and around uranium mining district Counties in South Texas (Atascosa, Bee, Brooks, Calhoun, Duval, Goliad, Hidalgo, Jim Hogg, Jim Wells, Karnes, Kleberg, Live Oak, McMullen, Nueces, San Patricio, Refugio, Starr, Victoria, Webb, and Zavala), from 1999 to 2007. The probable association of cleft birth defect rates by ZIP codes classified according to uranium and radium concentrations in drinking water supplies was evaluated. Similar associations between orofacial cleft birth defects and radium/radon in drinking water were reported earlier by Cech and co-investigators in another of the Gulf Coast region (Harris County, Texas).50, 55 Since substantial uranium mining activity existed and still exists in South Texas, contamination of drinking water sources with radiation and its relation to birth defects is a ground for concern. ^ Methods Residential addresses of orofacial cleft birth defect cases, as well as live births within the twenty Counties during 1999-2007 were geocoded and mapped. Prevalence rates were calculated by ZIP codes and were mapped accordingly. Locations of drinking water supplies were also geocoded and mapped. ZIP codes were stratified as having high combined uranium (≥30μg/L) vs. low combined uranium (<30μg/L). Likewise, ZIP codes having the uranium isotope, Ra-226 in drinking water, were also stratified as having elevated radium (≥3 pCi/L) vs. low radium (<3 pCi/L). A linear regression was performed using STATA® generalized linear model (GLM) program to evaluate the probable association between cleft birth defect rates by ZIP codes and concentration of uranium and radium via domestic water supply. These rates were further adjusted for potentially confounding variables such as maternal age, education, occupation, and ethnicity. ^ Results This study showed higher rates of cleft births in ZIP codes classified as having high combined uranium versus ZIP codes having low combined uranium. The model was further improved by adding radium stratified as explained above. Adjustment for maternal age and ethnicity did not substantially affect the statistical significance of uranium or radium concentrations in household water supplies. ^ Conclusion Although this study lacks individual exposure levels, the findings suggest a significant association between elevated uranium and radium concentrations in tap water and high orofacial birth defect rates by ZIP codes. Future case-control studies that can measure individual exposure levels and adjust for contending risk factors could result in a better understanding of the exposure-disease association.^

Bcr: A conditional inhibitor of Bcr -Abl oncoprotein

Chronic myelogenous leukemia (CML) is characterized cytogenetically by the presence of the Philadelphia chromosome and clinically by the clonal expansion of the hematopoietic stem cells and the accumulation of large numbers of myeloid cells. Philadelphia chromosome results from the reciprocal translocation between chromosomes 9 and 22 [t(9;22)(324;q11)], which fuses parts of the ABL proto-oncogene to 5′ portions of the BCR gene. The product of the fused gene is Bcr-Abl oncoprotein. Bcr-Abl oncoprotein has elevated protein tyrosine kinase activity, and is the cause of Philadelphia chromosome associated leukemias. The Bcr sequence in the fusion protein is crucial for the activation of Abl kinase activity and transforming phenotype of Bcr-Abl oncoprotein. Although the Bcr-Abl oncoprotein has been studied extensively, its normal counterpart, the Bcr protein, has been less studied and its function is not well understood. At this point, Bcr is known to encode a novel serine/threonine protein kinase. In Bcr-Abl positive leukemia cells, we found that the serine kinase activity of Bcr is impaired by tyrosine phosphorylation. Both the Bcr protein sequences within Bcr-Abl and the normal cellular Bcr protein lack serine/threonine kinase activity when they become phosphorylated on tyrosine residues by Bcr-Abl. Therefore, the goal of this study was to investigate the role of Bcr in Bcr-Abl positive leukemia cells. We found that overexpression of Bcr can inhibit Bcr-Abl tyrosine kinase activity, and the inhibition is dependent on its intact serine/threonine kinase function. Using the tet repressible promoter system, we demonstrated that Bcr when induced in Bcr-Abl positive leukemia cells inhibited the Bcr-Abl oncoprotein tyrosine kinase. Furthermore, induction of Bcr also increased the number of cells undergoing apoptosis and inhibited the transforming ability of Bcr-Abl. In contrast to the wild-type Bcr, the kinase-inactive mutant of Bcr (Y328F/Y360F) had no effects on Bcr-Abl tyrosine kinase in cells. Results from other experiments indicated that phosphoserine-containing Bcr sequences within the first exon, which are known to bind to the Abl SH2 domain, are responsible for observed inhibition of the Bcr-Abl tyrosine kinase. Several lines of evidence suggest that the phosphoserine form of Bcr, which binds to the Abl SH2 domain, strongly inhibits the Abl tyrosine kinase domain of Bcr-Abl Previously published findings from our laboratory have also shown that Bcr is phosphorylated on tyrosine residue 177 in Bcr-Abl positive cells and that this form of Bcr recruits the Grb2 adaptor protein, which is known to activate the Ras pathway. These findings implicate Bcr as an effector of Bcr-Abl's oncogenic activity. Therefore based on the findings presented above, we propose a model for dual Function of Bcr in Bcr-Abl positive leukemia cells. Bcr, when active as a serine/threonine kinase and thus autophosphorylating its own serine residues, inhibits Bcr-Abl's oncogenic functions. However, when Ber is tyrosine phosphorylated, its Bcr-Abl inhibitory function is neutralized thus allowing Bcr-Abl to exert its full oncogenic potential. Moreover, tyrosine phosphorylated Bcr would compliment Bcr-Abl's neoplastic effects by the activation of the Ras signaling pathway. ^

The Chilean wheat market and its price support mechanism : a spatial market integration analysis

This research investigates the spatial market integration of the Chilean wheat market in relation with its most representative international markets by using a vector error correction model (VECM) and how a price support policy, as a price band, affect it. The international market was characterized by two relevant wheat prices: PAN from Argentina and Hard Red Winter from the United States. The spatial market integration level, expressed in the error correction term (ECT), allowed concluding that there is a high integration degree among these markets with a variable influence of the price band mechanism mainly related with its estimation methodology. Moreover, this paper showed that Chile can be seen as price taker as long as the speed of its adjustment to international shocks, being these reactions faster than in the United States and Argentina. Finally, the results validated the "Law of the One Price", which assumes price equalization across all local markets in the long run.

Age model and color measurements of sediment cores from the eastern equatorial Pacific

High-resolution records of glacial-interglacial variations in biogenic carbonate, opal, and detritus (derived from non-destructive core log measurements of density, P-wave velocity and color; r >= 0.9) from 15 sediment sites in the eastern equatorial (sampling resolution is ~1 kyr) clear response to eccentricity and precession forcing. For the Peru Basin, we generate a high-resolution (21 kyr increment) orbitally-based chronology for the last 1.3 Ma. Spectral analysis indicates that the 100 kyr cycle became dominant at roughly 1.2 Ma, 200-300 kyr earlier than reported for other paleoclimatic records. The response to orbital forcing is weaker since the Mid-Brunhes Dissolution Event (at 400 ka). A west-east reconstruction of biogenic sedimentation in the Peru Basin (four cores; 91-85°W) distinguishes equatorial and coastal upwelling systems in the western and eastern sites, respectively. A north-south reconstruction perpendicular to the equatorial upwelling system (11 cores, 11°N-°3S) shows high carbonate contents (>= 50%) between 6°N and 4°S and highly variable opal contents between 2°N and 4°S. Carbonate cycles B-6, B-8, B-10, B-12, B-14, M-2, and M-6 are well developed with B-10 (430 ka) as the most prominent cycle. Carbonate highs during glacials and glacial-interglacial transitions extended up to 400 km north and south compared to interglacial or interglacial^glacial carbonate lows. Our reconstruction thus favors glacial-interglacial expansion and contraction of the equatorial upwelling system rather than shifting north or south. Elevated accumulation rates are documented near the equator from 6°N to 4°S and from 2°N to 4°S for carbonate and opal, respectively. Accumulation rates are higher during glacials and glacial-interglacial transitions in all cores, whereas increased dissolution is concentrated on Peru Basin sediments close to the carbonate compensation depth and occurred during interglacials or interglacial-glacial transitions.

Ocean temperature response to idealized Gleissberg and de Vries solar cycles in a comprehensive climate model

The ~90-year Gleissberg and ~200-year de Vries cycles have been identified as two distinctive quasi-periodic components of Holocene solar activity. Evidence exists for the impact of such multi-decadal to centennial-scale variability in total solar irradiance (TSI) on climate, but concerning the ocean, this evidence is mainly restricted to the surface response. Here we use a comprehensive global climate model to study the impact of idealized solar forcing, representing the Gleissberg and de Vries cycles, on global ocean potential temperature at different depth levels, after a recent proxy record indicates a signal of TSI anomalies in the northeastern Atlantic at mid-depth. Potential impacts of TSI anomalies on deeper oceanic levels are climatically relevant due to their possible effect on ocean circulation by altering water mass characteristics. Simulated solar anomalies are shown to penetrate the ocean down to at least deep-water levels. Despite the fact that the two forcing periods differ only by a factor of ~2, the spatial pattern of response is significantly distinctive between the experiments, suggesting different mechanisms for solar signal propagation. These are related to advection by North Atlantic Deep Water flow (200-year forcing), and barotropic adjustment in the South Atlantic in response to a latitudinal shift of the westerly wind belt (90-year forcing).

Modeling the sensitivity of precipitation oxygen isotopes to the Last Glacial Maximum boundary conditions: A study using Community Atmosphere Model (CAM3.0)

To understand the validity of d18O proxy records as indicators of past temperature change, a series of experiments was conducted using an atmospheric general circulation model fitted with water isotope tracers (Community Atmosphere Model version 3.0, IsoCAM). A pre-industrial simulation was performed as the control experiment, as well as a simulation with all the boundary conditions set to Last Glacial Maximum (LGM) values. Results from the pre-industrial and LGM simulations were compared to experiments in which the influence of individual boundary conditions (greenhouse gases, ice sheet albedo and topography, sea surface temperature (SST), and orbital parameters) were changed each at a time to assess their individual impact. The experiments were designed in order to analyze the spatial variations of the oxygen isotopic composition of precipitation (d18Oprecip) in response to individual climate factors. The change in topography (due to the change in land ice cover) played a significant role in reducing the surface temperature and d18Oprecip over North America. Exposed shelf areas and the ice sheet albedo reduced the Northern Hemisphere surface temperature and d18Oprecip further. A global mean cooling of 4.1 °C was simulated with combined LGM boundary conditions compared to the control simulation, which was in agreement with previous experiments using the fully coupled Community Climate System Model (CCSM3). Large reductions in d18Oprecip over the LGM ice sheets were strongly linked to the temperature decrease over them. The SST and ice sheet topography changes were responsible for most of the changes in the climate and hence the d18Oprecip distribution among the simulations.

Digital surface model, hillshade and Lambertian reflectance model of the rock glaciers Oelgrube and Aeusseres Hochebenkar (Oetztal Alps, Tyrol, Austria)

With full-waveform (FWF) lidar systems becoming increasingly available from different commercial manufacturers, the possibility for extracting physical parameters of the scanned surfaces in an area-wide sense, as addendum to their geometric representation, has risen as well. The mentioned FWF systems digitize the temporal profiles of the transmitted laser pulse and of its backscattered echoes, allowing for a reliable determination of the target distance to the instrument and of physical target quantities by means of radiometric calibration, one of such quantities being the diffuse Lambertian reflectance. The delineation of glaciers is a time-consuming task, commonly performed manually by experts and involving field trips as well as image interpretation of orthophotos, digital terrain models and shaded reliefs. In this study, the diffuse Lambertian reflectance was compared to the glacier outlines mapped by experts. We start the presentation with the workflow for analysis of FWF data, their direct georeferencing and the calculation of the diffuse Lambertian reflectance by radiometric calibration; this workflow is illustrated for a large FWF lidar campaign in the Ötztal Alps (Tyrol, Austria), operated with an Optech ALTM 3100 system. The geometric performance of the presented procedure was evaluated by means of a relative and an absolute accuracy assessment using strip differences and orthophotos, resp. The diffuse Lambertian reflectance was evaluated at two rock glaciers within the mentioned lidar campaign. This feature showed good performance for the delineation of the rock glacier boundaries, especially at their lower parts.

Digital elevation model (DEM) of the ice sheet in western Dronning Maud Land, Antarctica

In this paper, a new digital elevation model (DEM) is derived for the ice sheet in western Dronning Maud Land, Antarctica. It is based on differential interferometric synthetic aperture radar (SAR) from the European Remote Sensing 1/2 (ERS-1/2) satellites, in combination with ICESat's Geoscience Laser Altimeter System (GLAS). A DEM mosaic is compiled out of 116 scenes from the ERS-1 ice phase in 1994 and the ERS-1/2 tandem mission between 1996 and 1997 with the GLAS data acquired in 2003 that served as ground control. Using three different SAR processors, uncertainties in phase stability and baseline model, resulting in height errors of up to 20 m, are exemplified. Atmospheric influences at the same order of magnitude are demonstrated, and corresponding scenes are excluded. For validation of the DEM mosaic, covering an area of about 130,000 km**2 on a 50-m grid, independent ICESat heights (2004-2007), ground-based kinematic GPS (2005), and airborne laser scanner data (ALS, 2007) are used. Excluding small areas with low phase coherence, the DEM differs in mean and standard deviation by 0.5 +/- 10.1, 1.1 +/- 6.4, and 3.1 +/- 4.0 m from ICESat, GPS, and ALS, respectively. The excluded data points may deviate by more than 50 m. In order to suppress the spatially variable noise below a 5-m threshold, 18% of the DEM area is selectively averaged to a final product at varying horizontal spatial resolution. Apart from mountainous areas, the new DEM outperforms other currently available DEMs and may serve as a benchmark for future elevation models such as from the TanDEM-X mission to spatially monitor ice sheet elevation.

Lagrangian back-tracing results for Kohnen station; output of time dependent numerical experiment with a 3D nested Antarctic ice sheet model

A nested ice flow model was developed for eastern Dronning Maud Land to assist with the dating and interpretation of the EDML deep ice core. The model consists of a high-resolution higher-order ice dynamic flow model that was nested into a comprehensive 3-D thermomechanical model of the whole Antarctic ice sheet. As the drill site is on a flank position the calculations specifically take into account the effects of horizontal advection as deeper ice in the core originated from higher inland. First the regional velocity field and ice sheet geometry is obtained from a forward experiment over the last 8 glacial cycles. The result is subsequently employed in a Lagrangian backtracing algorithm to provide particle paths back to their time and place of deposition. The procedure directly yields the depth-age distribution, surface conditions at particle origin, and a suite of relevant parameters such as initial annual layer thickness. This paper discusses the method and the main results of the experiment, including the ice core chronology, the non-climatic corrections needed to extract the climatic part of the signal, and the thinning function. The focus is on the upper 89% of the ice core (appr. 170 kyears) as the dating below that is increasingly less robust owing to the unknown value of the geothermal heat flux. It is found that the temperature biases resulting from variations of surface elevation are up to half of the magnitude of the climatic changes themselves.

Planimetric ice-flow convergence and flow-orthonormal strain rate across the Antarctic Ice Sheet, with links to model result files

Fast-flowing ice streams discharge most of the ice from the interior of the Antarctic Ice Sheet coastward. Understanding how their tributary organisation is governed and evolves is essential for developing reliable models of the ice sheet's response to climate change. Despite much research on ice-stream mechanics, this problem is unsolved, because the complexity of flow within and across the tributary networks has hardly been interrogated. Here I present the first map of planimetric flow convergence across the ice sheet, calculated from satellite measurements of ice surface velocity, and use it to explore this complexity. The convergence map of Antarctica elucidates how ice-stream tributaries draw ice from the interior. It also reveals curvilinear zones of convergence along lateral shear margins of streaming, and abundant convergence ripples associated with nonlinear ice rheology and changes in bed topography and friction. Flow convergence on ice-stream tributaries and their feeding zones is markedly uneven, and interspersed with divergence at distances of the order of kilometres. For individual drainage basins as well as the ice sheet as a whole, the range of convergence and divergence decreases systematically with flow speed, implying that fast flow cannot converge or diverge as much as slow flow. I therefore deduce that flow in ice-stream networks is subject to mechanical regulation that limits flow-orthonormal strain rates. These properties and the gridded data of convergence and flow-orthonormal strain rate in this archive provide targets for ice- sheet simulations and motivate more research into the origin and dynamics of tributarization.

Global LAI uncertainty and relative uncertainty datasets derived from a Triple Collocation Error Model (TCEM)

Uncertainty information for global leaf area index (LAI) products is important for global modeling studies but usually difficult to systematically obtain at a global scale. Here, we present a new method that cross-validates existing global LAI products and produces consistent uncertainty information. The method is based on a triple collocation error model (TCEM) that assumes errors among LAI products are not correlated. Global monthly absolute and relative uncertainties, in 0.05° spatial resolutions, were generated for MODIS, CYCLOPES, and GLOBCARBON LAI products, with reasonable agreement in terms of spatial patterns and biome types. CYCLOPES shows the lowest absolute and relative uncertainties, followed by GLOBCARBON and MODIS. Grasses, crops, shrubs, and savannas usually have lower uncertainties than forests in association with the relatively larger forest LAI. With their densely vegetated canopies, tropical regions exhibit the highest absolute uncertainties but the lowest relative uncertainties, the latter of which tend to increase with higher latitudes. The estimated uncertainties of CYCLOPES generally meet the quality requirements (± 0.5) proposed by the Global Climate Observing System (GCOS), whereas for MODIS and GLOBCARBON only non-forest biome types have met the requirement. Nevertheless, none of the products seems to be within a relative uncertainty requirements of 20%. Further independent validation and comparative studies are expected to provide a fair assessment of uncertainties derived from TCEM. Overall, the proposed TCEM is straightforward and could be automated for the systematic processing of real time remote sensing observations to provide theoretical uncertainty information for a wider range of land products.

Model results of sensitivity experiments for marine nitrogen cycle in four NetCDF files

The marine nitrogen (N) inventory is thought to be stabilized by negative feedback mechanisms that reduce N inventory excursions relative to the more slowly overturning phosphorus inventory. Using a global biogeochemical ocean circulation model we show that negative feedbacks stabilizing the N inventory cannot persist if a close spatial association of N2 fixation and denitrification occurs. In our idealized model experiments, nitrogen deficient waters, generated by denitrification, stimulate local N2 fixation activity. But, because of stoichiometric constraints, the denitrification of newly fixed nitrogen leads to a net loss of N. This can enhance the N deficit, thereby triggering additional fixation in a vicious cycle, ultimately leading to a runaway N loss. To break this vicious cycle, and allow for stabilizing negative feedbacks to occur, inputs of new N need to be spatially decoupled from denitrification. Our idealized model experiments suggest that factors such as iron limitation or dissolved organic matter cycling can promote such decoupling and allow for negative feedbacks that stabilize the N inventory. Conversely, close spatial co-location of N2 fixation and denitrification could lead to net N loss.