Kernel Density Smoothing Research Articles

Conditional Cancer-Specific Survival for Inflammatory Breast Cancer: Analysis of SEER, 2010 to 2016

BackgroundConditional survival takes into account the time that has elapsed since diagnosis and may have additional informative value. Compared with the static traditional survival evaluation method, conditional survival predictions can be adapted to incorporate the dynamic changes during the disease and provide a more suitable way of identifying time-evolved prognoses. MethodsOf 3333 patients diagnosed with inflammatory breast cancer between 2010 and 2016 were extracted from the Surveillance, Epidemiology, and End Results database. The trend of the hazard rate over time was represented by the kernel density smoothing curve. The traditional cancer-specific survival (CSS) rate was estimated by the Kaplan-Meier method. Conditional CSS assessment was defined as the probability that a patient will survive y years given the x years who already survived after diagnosis, and the formula is as follows: CS(y)=CSS(x + y)/CSS(x). 3-year cancer-specific survival (CSS3) and 3-year conditional cancer-specific survival (CS3) were estimated. The Fine-Gray proportional subdistribution hazard model was constructed to screen for time-dependent risk factors associated with cancer-specific death. Subsequently, a nomogram was applied to predict a 5-year survival rate based on the number of years already survived. ResultsOf 3333 patients, the cancer-specific survival (CSS) rate decreased from 57% in the 4th year to 49% in the 6th year, while the comparable 3-year CS (CS3) rate improved from 65% in the first year to 76% in the third year. Overall, the CS3 rate was superior to actuarial cancer-specific survival, which was also found in subgroup analysis, especially in patients with high-risk characteristics. The Fine-Gray's model indicated that remote organ metastasis (M stage), lymph node metastasis (N stage), and surgery all significantly impacted the prognosis for cancer-specific survival. The Fine-Gray's model-based nomogram was constructed to predict 5-year cancer-specific survival immediately after diagnosis and given survival for 1, 2, 3, and 4 years after diagnosis. ConclusionHigh-risk patients had a significantly improved cancer-specific survival prognosis after surviving for 1 or more years after diagnosis with inflammatory breast cancer. The probability of reaching 5-year cancer-specific survival following diagnosis improves with each additional year survived. More effective follow-up is required for patients diagnosed at an advanced N stage, remote organ metastasis, or not received surgery. Additionally, a nomogram and web-based calculator may be helpful for patients with inflammatory breast cancer during follow-up counseling (https://ibccondsurv.shinyapps.io/dynnomapp/).

Pandemic and Gender Influences on Submissions to Epidemiology.

Pandemic and Gender Influences on Submissions to Epidemiology.

Kernel density smoothing of composite spatial data on administrative area level

Composite spatial data on administrative area level are often presented by maps. The aim is to detect regional differences in the concentration of subpopulations, like elderly persons, ethnic minorities, low-educated persons, voters of a political party or persons with a certain disease. Thematic collections of such maps are presented in different atlases. The standard presentation is by Choropleth maps where each administrative unit is represented by a single value. These maps can be criticized under three aspects: the implicit assumption of a uniform distribution within the area, the instability of the resulting map with respect to a change of the reference area and the discontinuities of the maps at the borderlines of the reference areas which inhibit the detection of regional clusters.In order to address these problems we use a density approach in the construction of maps. This approach does not enforce a local uniform distribution. It does not depend on a specific choice of area reference system and there are no discontinuities in the displayed maps. A standard estimation procedure of densities are Kernel density estimates. However, these estimates need the geo-coordinates of the single units which are not at disposal as we have only access to the aggregates of some area system. To overcome this hurdle, we use a statistical simulation concept. This can be interpreted as a Simulated Expectation Maximisation (SEM) algorithm of Celeux et al (1996). We simulate observations from the current density estimates which are consistent with the aggregation information (S-step). Then we apply the Kernel density estimator to the simulated sample which gives the next density estimate (E-Step).This concept has been first applied for grid data with rectangular areas, see Groß et al (2017), for the display of ethnic minorities. In a second application we demonstrated the use of this approach for the so-called “change of support” (Bradley et al 2016) problem. Here Groß et al (2020) used the SEM algorithm to recalculate case numbers between non-hierarchical administrative area systems. Recently Rendtel et al (2021) applied the SEM algorithm to display spatial-temporal clusters of Corona infections in Germany.Here we present three modifications of the basic SEM algorithm: 1) We introduce a boundary correction which removes the underestimation of kernel density estimates at the borders of the population area. 2) We recognize unsettled areas, like lakes, parks and industrial areas, in the computation of the kernel density. 3) We adapt the SEM algorithm for the computation of local percentages which are important especially in voting analysis.We evaluate our approach against several standard maps by means of the local voting register with known addresses. In the empirical part we apply our approach for the display of voting results for the 2016 election of the Berlin parliament. We contrast our results against Choropleth maps and show new possibilities for reporting spatial voting results.

Conditional Survival of female patients with operable invasive Breast Cancer in US: A population-based study.

Background: Conditional survival (CS) is used to describe the dynamic possibility of survival, considering the changes of death risk with time lapsing. This study aimed to estimate the conditional disease-specific survival (CDS) for the female with operable invasive breast cancer.Methods: The data was obtained from Surveillance, Epidemiology, and End Result Program of the National Cancer Institute. The hazard rate was calculated using kernel density smoothing method. The disease-specific survival (DSS) rates were estimated and compared using Kaplan-Meier method and log-rank test. The Cox regression model was used to adjust confounding factors. The CDS was calculated by CDS(y|x)=DSS(x + y)/DSS(x), where DSS(x) representatives the DSS at x year.Results: The 5-year, 10-year, and 15-year DSS was 88.7%, 82.0%, and 78.3%, respectively. The hazard rate after surgery increased initially and peaked at about 1.5 years, then decreased gradually. Meanwhile, the CDS decreased just after surgery then increased continuously, which showed a contrary trend with hazard rate. Patients with high risk factors had greater survival gap between cumulative DSS and CDS. The changing trend of CDS in patients with high risk factors was more significant, and the CDS gap between low-risk patients and high-risk patients gradually decreased over time.Conclusion: CS could provide a more precise long-term prognostic evaluation compared to traditional cumulative survival, especially for long-time survivors with high risk.

Updated radio Σ - D relation for galactic supernova remnants - II

In this paper we present the updated empirical radio surface- brightness-to-diameter (?-D) relation for Galactic supernova remnants (SNRs) calibrated using 110 SNRs with reliable distances. We apply orthogonal fitting procedure and kernel density smoothing in the ? ? D plane and compare the results with the latest theoretical ? - D relations derived from simulations of radio evolution of SNRs. We argue that the best agreement between the empirical and simulated ? ? D relations is achieved if the mixed-morphology SNRs and SNRs of both, low brightness and small diameter, are filtered out from the calibration sample. The distances to 5 newly discovered remnants and 27 new candidates for shell SNRs are estimated from our full and filtered calibration samples.

A Maximum-Entropy Method to Estimate Discrete Distributions from Samples Ensuring Nonzero Probabilities.

When constructing discrete (binned) distributions from samples of a data set, applications exist where it is desirable to assure that all bins of the sample distribution have nonzero probability. For example, if the sample distribution is part of a predictive model for which we require returning a response for the entire codomain, or if we use Kullback–Leibler divergence to measure the (dis-)agreement of the sample distribution and the original distribution of the variable, which, in the described case, is inconveniently infinite. Several sample-based distribution estimators exist which assure nonzero bin probability, such as adding one counter to each zero-probability bin of the sample histogram, adding a small probability to the sample pdf, smoothing methods such as Kernel-density smoothing, or Bayesian approaches based on the Dirichlet and Multinomial distribution. Here, we suggest and test an approach based on the Clopper–Pearson method, which makes use of the binominal distribution. Based on the sample distribution, confidence intervals for bin-occupation probability are calculated. The mean of each confidence interval is a strictly positive estimator of the true bin-occupation probability and is convergent with increasing sample size. For small samples, it converges towards a uniform distribution, i.e., the method effectively applies a maximum entropy approach. We apply this nonzero method and four alternative sample-based distribution estimators to a range of typical distributions (uniform, Dirac, normal, multimodal, and irregular) and measure the effect with Kullback–Leibler divergence. While the performance of each method strongly depends on the distribution type it is applied to, on average, and especially for small sample sizes, the nonzero, the simple “add one counter”, and the Bayesian Dirichlet-multinomial model show very similar behavior and perform best. We conclude that, when estimating distributions without an a priori idea of their shape, applying one of these methods is favorable.

RISK FACTORS FOR AND SPATIAL DISTRIBUTION OF LYMPHOPROLIFERATIVE DISEASE VIRUS (LPDV) IN WILD TURKEYS (MELEAGRIS GALLOPAVO) IN NEW YORK STATE, USA.

Lymphoproliferative disease virus (LPDV) is an oncogenic avian retrovirus that was previously thought to exclusively infect domestic turkeys but was recently shown to be widespread in Wild Turkeys ( Meleagris gallopavo ) throughout most of the eastern US. In commercial flocks, the virus spreads between birds housed in close quarters, but there is little information about potential risk factors for infection in wild birds. Initial studies focused on distribution of LPDV nationally, but investigation of state-level data is necessary to assess potential predictors of infection and detect patterns in disease prevalence and distribution. We tested wild turkey bone marrow samples (n=2,538) obtained from hunter-harvested birds in New York State from 2012 to 2014 for LPDV infection. Statewide prevalence for those 3 yr was 55% with a 95% confidence interval (CI) of 53-57%. We evaluated a suite of demographic, anthropogenic, and land cover characteristics with logistic regression to identify potential predictors for infection based on odds ratio (OR). Age (OR=0.16, 95% CI=0.13-0.19) and sex (OR=1.3, 95% CI=1.03-1.24) were strong predictors of LPDV infection, with juveniles less likely to test positive than adults, and females more likely to test positive than males. The number of birds released during the state's 40-yr translocation program (OR=0.993, 95% CI=0.990-0.997) and the ratio of agriculture to forest cover (OR=1.13, 95% CI=1.03-1.19) were also predictive of LPDV infection. Prevalence distribution was analyzed using dual kernel density smoothing to produce a risk surface map, combined with Kulldorff's spatial scan statistic and the Anselin Local Moran's I to identify statistically significant geographic clusters of high or low prevalence. These methods revealed the prevalence of LPDV was high (>50%) throughout New York State, with regions of variation and several significant clusters. We revealed new information about the risk factors and distribution of LPDV in New York State, which may be beneficial to game bird managers and producers of organic or pasture-raised poultry.

Characterizing and Predicting Traffic Accidents in Extreme Weather Environments

Motorists are vulnerable to extreme weather events, which are likely to be exacerbated by climate change throughout the world. Traffic accidents are conceptualized in this article as the result of a systemic failure that includes human, vehicular, and environmental factors. The snowstorm and concurrent accidents that occurred in the Northeastern United States on 26 January 2011 are used as a case study. Traffic accident data for Fairfax County, Virginia, are supplemented with Doppler radar and additional weather data to characterize the spatiotemporal patterns of the accidents resulting from this major snowstorm event. A kernel density smoothing method is implemented to identify and predict patterns of accident locations within this urban area over time. The predictive capability of this model increases over time with increasing accidents. Models such as these can be used by emergency responders to identify, plan for, and mitigate areas that are more susceptible to increased risk resulting from extreme weather events.

The independent effect of living in malaria hotspots on future malaria infection: an observational study from Misungwi, Tanzania.

BackgroundAs malaria transmission declines, continued improvements of prevention and control interventions will increasingly rely on accurate knowledge of risk factors and an ability to define high-risk areas and populations at risk for focal targeting of interventions. This paper explores the independent association between living in a hotspot and prospective risk of malaria infection.MethodsMalaria infection status defined by nPCR and AMA-1 status in year 1 were used to define geographic hotspots using two geospatial statistical methods (SaTScan and Kernel density smoothing). Other malaria risk factors for malaria infection were explored by fitting a multivariable model.ResultsThis study demonstrated that residing in infection hotspot of malaria transmission is an independent predictor of malaria infection in the future.ConclusionIt is likely that targeting such hotspots with better coverage and improved malaria control strategies will result in more cost-efficient uses of resources to move towards malaria elimination.

Early Warning System for Temporary Crime Hot Spots

We investigate the potential for preventing crimes at temporary hot spots in addition to chronic hot spots. Using data on serious violent crimes from Pittsburgh, Pennsylvania, we investigate an early warning system (EWS) for starting/stopping police deployments at temporary hot spots in coordination with constant prevention work at chronic hot spots. We estimate chronic hot spots using kernel density smoothing. We use simple rules for detecting flare-ups of temporary hot spots, predicting their persistence, deploying police, and stopping deployments. We also consider a combination program including the hottest chronic hot spots, with EWS applied to remaining areas. Using 2000–2010 data, we run computational experiments varying the size of chronic hot spots and varying rule thresholds to tune the EWS. Tradeoff curves with percentage of crimes exposed to prevention versus percentage area of the city with crime prevention workload provide tools for coordinating chronic and temporary hot spot programs. The combination program is the most efficient, equitable, and responsive program. After first allocating police prevention resources to the hottest chronic hot spots, the marginal benefits of adding more chronic hot spot area is not as high as adding temporary hot spots. Chronic hot spots are limited to large commercial and adjoining residential areas. Temporary hot spots are widely scattered throughout Pittsburgh. Temporary hot spots exist outside of chronic hot spots and are targets for prevention as supplements to chronic hot spots. A combination program targeting both chronic and temporary hot spots is recommended.

Regional Patterns of Major Nonnative Invasive Plants and Associated Factors in Upper Midwest Forests

Nonnative invasive plants (IPs) are rapidly spreading into natural ecosystems (e.g., forests and grasslands). Potential threats of IP invasion into natural ecosystems include biodiversity loss, structural and environmental change, habitat degradation, and economic losses. The Upper Midwest of the United States encompasses the states of Illinois, Indiana, Iowa, Michigan, Minnesota, Missouri, and Wisconsin, a region populated with 46 million people. Concerns of IP threats to the productive timberlands in the region have emerged with rapid expansion of urban areas and associated land cover changes caused by increasing human disturbances. Using the strategic inventory data from the 2005-2006 US Department of Agriculture Forest Service Forest Inventory and Analysis program and other data such as forestland cover and transportation coverage/layers, we modeled the regional patterns of IPs by using a combination of nonparametric techniques, including classification and regression tree analysis, kernel density smoothing, and bootstrapping. For the Midwest region, a probability map and historical records of human-related introduction of IPs of interest suggests that invasive shrubs, herbs, and grasses were initially introduced into the central (sparsely forested) areas and then spread north and south (densely forested areas), whereas invasive vines spread primarily from the south into other parts of the region. The probability of IPs in densely forested areas (0.1) was one-fifth of that in sparsely forested areas. Shrubs are the predominant IP threat and are distributed across the vast region with the exception of the northern part. Invasive grasses and herbs are most abundant in the central part of the region, and invasive vines are most common in the southern part. Percent forest cover and road proximity (distance to roads) as indicators of anthropogenic disturbances, were the most significant drivers of IP occurrence/abundance. Site factors, including forest productivity and stand biodiversity, were significantly correlated with the occurrence of vines.

On robust estimation via pseudo-additive information

We consider a robust parameter estimator minimizing an empirical approximation to the q-entropy and show its relationship to minimization of power divergences through a simple parameter transformation. The estimator balances robustness and efficiency through a tuning constant q and avoids kernel density smoothing. We derive an upper bound to the estimator mean squared error under a contaminated reference model and use it as a min-max criterion for selecting q.

A study of community design, greenness, and physical activity in children using satellite, GPS and accelerometer data

This study examined relationships between greenness exposure and free-living physical activity behavior of children in smart growth and conventionally designed communities. Normalized Difference Vegetation Index (NDVI) was used to quantify children's (n=208) greenness exposure at 30-s epoch accelerometer and GPS data points. A generalized linear mixed model with a kernel density smoothing term for addressing spatial autocorrelation was fit to analyze residential neighborhood activity data. Excluding activity at home and during school-hours, an epoch-level analysis found momentary greenness exposure was positively associated with the likelihood of contemporaneous moderate-to-vigorous physical activity (MVPA). This association was stronger for smart growth residents who experienced a 39% increase in odds of MVPA for a 10th to 90th percentile increase in exposure to greenness (OR=1.39, 95% CI 1.36–1.44). An individual-level analysis found children who experienced >20min of daily exposure to greener spaces (>90th percentile) engaged in nearly 5 times the daily rate of MVPA of children with nearly zero daily exposure to greener spaces (95% CI 3.09–7.20).

A structured approach to the measurement of uncertainty in 3D geological models

Abstract The use of 3D models to view complex and diverse geoscience datasets is now common practice for conceptual model evolution, communication to stakeholders, or for testing hypotheses. When applying these models it is important to recognize that their ability to replicate the true situation is controlled by the data used to generate the model and the model algorithms. For the models to be applied correctly the model uncertainty needs to be identified and, where possible, quantified. A method to quantify the uncertainty associated with geological surfaces in a 3D model is presented and tested. Kernel density smoothing and resampling of borehole locations along with expert–user interaction are utilized to provide an estimate of the uncertainty in a geological surface based on data quality, data density and geological complexity. The method is applied to a 3D geological model of shallow superficial deposits, where a sequence of river terrace gravels and alluvial deposits overlie mudstone bedrock. Outcomes indicate that the uncertainty model predictions match well with expert judgement.

On The Application of Fuzzy Clustering for Crime Hot Spot Detection

One of the fundamental challenges in crime mapping and analysis is pattern recognition. Efforts and methods to detect crime hot-spots, or geographic areas of elevated criminal activity, are wide ranging. For aggregate data, such as total crime events in a census tract(s), measures of spatial autocorrelation have proven useful. For disaggregate data (i.e. individual crime events), kernel density smoothing and non-hierarchical cluster analysis (e.g. k-means), are widely used. Non-hierarchical techniques are particularly effective in delineating geographic space into areas of higher or lower crime concentrations, because each observation is assigned to one and only one cluster. The resulting set of partitions provides clear-cut spatial boundaries that can be used for hot-spot evaluation and interpretation. However, the strength of non-hierarchical methods can also be viewed as a weakness. Although the hard-clustering of observations into a set of discrete clusters is helpful, there are many cases where ambiguity exists in the data. In such cases, a more generalized approach for hot-spot detection would be helpful. The purpose of this paper is to explore the use of a generalized partitioning method known as fuzzy clustering for hot-spot detection. Functional and visual comparisons of fuzzy clustering and two hard-clustering approaches (medoid and k-means), across a range of cluster values are analyzed. The empirical results suggest that a fuzzy clustering approach is better equipped to handle intermediate cases and spatial outliers.

Geographic Prediction of Human Onset of West Nile Virus Using Dead Crow Clusters: An Evaluation of Year 2002 Data in New York State

The risk of becoming a West Nile virus case in New York State, excluding New York City, was evaluated for persons whose town of residence was proximal to spatial clusters of dead American crows (Corvus brachyrhynchos). Weekly clusters were delineated for June-October 2002 by using both the binomial spatial scan statistic and kernel density smoothing. The relative risk of a human case was estimated for different spatial-temporal exposure definitions after adjusting for population density and age distribution using Poisson regression, adjusting for week and geographic region, and conducting Cox proportional hazards modeling, where the week that a human case was identified was treated as the failure time and baseline hazard was stratified by region. The risk of becoming a West Nile virus case was positively associated with living in towns proximal to dead crow clusters. The highest risk was consistently for towns associated with a cluster in the current or prior 1-2 weeks. Weaker, but positive associations were found for towns associated with a cluster in just the 1-2 prior weeks, indicating an ability to predict onset in a timely fashion.

Performance assessment of kernel density clustering for gene expression profile data

Kernel density smoothing techniques have been used in classification or supervised learning of gene expression profile (GEP) data, but their applications to clustering or unsupervised learning of those data have not been explored and assessed. Here we report a kernel density clustering method for analysing GEP data and compare its performance with the three most widely-used clustering methods: hierarchical clustering, K-means clustering, and multivariate mixture model-based clustering. Using several methods to measure agreement, between-cluster isolation, and withincluster coherence, such as the Adjusted Rand Index, the Pseudo F test, the r2 test, and the profile plot, we have assessed the effectiveness of kernel density clustering for recovering clusters, and its robustness against noise on clustering both simulated and real GEP data. Our results show that the kernel density clustering method has excellent performance in recovering clusters from simulated data and in grouping large real expression profile data sets into compact and well-isolated clusters, and that it is the most robust clustering method for analysing noisy expression profile data compared to the other three methods assessed.

A split-beam echo counting model: development of statistical procedures

Mulligan and Kieser (1996) (ICES ICES Journal of Marine Science, 53: 403-406) proposed a split-beam echo counting model that addressed the problem of non-uniform detection probability combined with non-uniform fish density over the beam cross- section. To apply the model to real data, statistical procedures to estimate three-dimensional density functions, to estimate kernel density smoothing parameters from the data, and to estimate a data-based smoothing parameter for kernel regression have been developed. In addition, a method to select echoes from individual fish that have been accurately tracked by the automatic tracking algorithm is described. The performance of the model was tested using data from a simulation program and from an experiment that compared acoustic estimates with visual counts of migrating salmon.