Estimating correlation with multiply censored data arising from the adjustment of singly censored data

Environmental data frequently are left censored due to detection limits of laboratory assay procedures. Left censored means that some of the observations are known only to fall below a censoring point (detection limit). This presents difficulties in statistical analysis of the data. In this paper, we examine methods for estimating the correlation between variables each of which is censored at multiple points. Multiple censoring frequently arises due to adjustment of singly censored laboratory results for physical sample size. We discuss maximum likelihood (ML) estimation of the correlation and introduce a new method (cp.mle2) that, instead of using the multiply censored data directly, relies on ML estimates of the covariance of the singly censored laboratory data. We compare the ML methods with Kendall's tau-b (ck.taub) which is a modification Kendall's tau adjusted for ties, and several commonly used simple substitution methods: correlations estimated with nondetects set to the detection limit divided by 2 and correlations based on detects only (cs.det) with nondetects setto missing. The methods are compared based on simulations and real data. In the simulations, censoring levels are varied from 0 to 90%, p from -0.8 to 0.8, and v (variance of physical sample size) is set to 0 and 0.5, for a total of 550 parameter combinations with 1000 replications at each combination. We find that with increasing levels of censoring most of the correlation methods are highly biased. The simple substitution methods in general tend toward zero if singly censored and one if multiply censored. ck.taub tends toward zero. Least biased is cp.mle2, however, it has higher variance than some of the other estimators. Overall, cs.det performs the worst and cp.mle2 the best.     

Compilation and application of Japanese inventories for energy consumption and air pollutant emissions using input-output tables

Preparing emission inventories is essential to the assessment and management of our environment. In this study, Japanese air pollutant emissions, energy consumption, and CO2 emissions categorized by approximately 400 sectors (as classified by Japanese input-output tables in 1995) were estimated, and the contributions of each sector to the total amounts were analyzed. The air pollutants examined were nitrogen oxides (NOx), sulfur oxides (SOx), and suspended particulate matter (SPM). Consumptions of about 20 fossil fuels and five other fuels were estimated according to sector. Air pollutant emission factors for stationary sources were calculated from the results of a survey on air pollution prevention in Japan. Pollutant emissions from mobile sources were estimated taking into consideration vehicle types, traveling speeds, and distances. This work also counted energy supply and emissions from seven nonfossil fuel sources, including nonthermal electric power, and CO2 emissions from limestone (for example, during cement production). The total energy consumption in 1995 was concluded to be 18.3 EJ, and the annual total emissions of CO2, NOx, SOx, and SPM were, respectively, 343 Mt-C, 3.51 Mt, 1.87 Mt, and 0.32 Mt. An input-output analysis of the emission inventories was used to calculate the amounts of energy consumption and emissions induced in each sector by the economic final demand.     

Development of parametric material, energy, and emission inventories for wafer fabrication in the semiconductor industry

Currently available data suggest that most of the energy and material consumption related to the production of an integrated circuit is due to the wafer fabrication process. The complexity of wafer manufacturing, requiring hundreds of steps that vary from product to product and from facility to facility and which change every few years, has discouraged the development of material, energy, and emission inventory modules for the purpose of insertion into life cycle assessments. To address this difficulty, a flexible, process-based system for estimating material requirements, energy requirements, and emissions in wafer fabrication has been developed. The method accounts for mass and energy use atthe unit operation level. Parametric unit operation modules have been developed that can be used to predict changes in inventory as the result of changes in product design, equipment selection, or process flow. A case study of the application of the modules is given for energy consumption, but a similar methodology can be used for materials, individually or aggregated.     

Second-order modeling of variability and uncertainty in microbial hazard characterization

This study describes an analytical framework that permits quantitative consideration of variability and uncertainty in microbial hazard characterization. Second-order modeling that used two-dimensional Monte Carlo simulation and stratification into homogeneous population subgroups was applied to integrate uncertainty and variability. Specifically, the bootstrap method was used to simulate sampling error due to the limited sample size in microbial dose-response modeling. A data set from human feeding trials with Campylobacter jejuni was fitted to the log-logistic dose-response model, and results from the analysis of FoodNet surveillance data provided further information on variability and uncertainty in Campylobacter susceptibility due to the effect of age. Results of our analyses indicate that uncertainty associated with dose-response modeling has a dominating influence on the analytical outcome. In contrast, inclusion of the age factor has a limited impact. While the advocacy of more closely modeling variability in hazard characterization is warranted, the characterization of key sources of uncertainties and their consistent propagation throughout a microbial risk assessment actually appear of greater importance.     

Analysis of censored data for such as colostral immunoglobulin transfer in calves.

Passive immunity in the neonatal calf is dependent upon colostral immunoglobulin transfer into the systemic circulation. Critical in this transfer is the period of absorption, which is dependent upon age of initial feeding of the calf and amount fed. For some calves known only was that absorption extended beyond duration of the experiment, causing the data to be censored. Analysis of the length of absorption showed a two-phase regression model when censored data were used with uncensored data. Incorrect inferences may be drawn if censored data are not incorporated into the analysis.     

Quantification of particle number emission factors for motor vehicles from on-road measurements

The database on particle number emission factors has been very limited to date despite the increasing interest in the effects of human exposure to particles in the submicrometer range. There are also major questions on the comparability of emission factors derived through dynamometer versus on-road studies. Thus, the aims of this study were (1) to quantify vehicle number emission factors in the submicrometer (and also supermicrometer) range for stop-start and free-flowing traffic at about 100 km h(-1) driving conditions through extensive road measurements and (2) to compare the emission factors from the road measurements with those obtained previously from dynamometer studies conducted in Brisbane. For submicrometer particles the average emission factors for Tora Street were estimated at (1.89 +/- 3.40) x 10(13) particles km(-1) (mean +/- standard error; n = 386) for petrol and (7.17 +/- 2.80) x 10(14) particles km(-1) (diesel; n = 196) and for supermicrometer particles at 2.59 x 10(9) particles km(-1) and 1.53 x 10(12) particles km(-1), respectively. The average number emission factors for submicrometer particles estimated for Ipswich Road (stop-start traffic mode) were (2.18 +/- 0.57) x 10(13) particles km(-1) (petrol) and (2.04 +/- 0.24) x 10(14) particles km(-1) (diesel). One implication of the conclusion that emission factors of heavy duty diesel vehicles are over 1 order of magnitude higher than emission factors of petrol-fueled passenger cars is that future control and management strategies should in particular target heavy duty vehicles, as even a moderate decrease in emissions of these vehicles would have a significant impact on lowering atmospheric concentrations of particles. The finding that particle number emissions per vehicle-km are significantly larger for higher speed vehicle operation has an important implication on urban traffic planning and optimization of vehicle speed to lower their impact on airborne pollution. Additionally, statistical analysis showed that neither the measuring method (dynamometer or on-road), nor data origin (Brisbane or elsewhere in the world), is associated with a statistically significant difference between the average values of emission factors for diesel, petrol, and vehicle fleet mix. However, statistical analyses of the effect of fuel showed that the mean values of emission factors for petrol and diesel are different at a 5% significance level.     

Hierarchical Bayesian analysis of censored microbiological contamination data for use in risk assessment and mitigation

Microbiological contamination data often is censored because of the presence of non-detects or because measurement outcomes are known only to be smaller than, greater than, or between certain boundary values imposed by the laboratory procedures. Therefore, it is not straightforward to fit distributions that summarize contamination data for use in quantitative microbiological risk assessment, especially when variability and uncertainty are to be characterized separately. In this paper, distributions are fit using Bayesian analysis, and results are compared to results obtained with a methodology based on maximum likelihood estimation and the non-parametric bootstrap method. The Bayesian model is also extended hierarchically to estimate the effects of the individual elements of a covariate such as, for example, on a national level, the food processing company where the analyzed food samples were processed, or, on an international level, the geographical origin of contamination data. Including this extra information allows a risk assessor to differentiate between several scenario’s and increase the specificity of the estimate of risk of illness, or compare different scenario’s to each other. Furthermore, inference is made on the predictive importance of several different covariates while taking into account uncertainty, allowing to indicate which covariates are influential factors determining contamination.     

Quantification of time trends in vintage scores and their variability for major wine regions of Australia

This paper quantifies time‐trends of vintage scores and their variability in 24 wine regions of Australia. Our working hypotheses are that, owing to improved crop husbandry and winemaking techniques, (1) vintage scores had increased with time, and (2) variability in vintage scores had decreased with time, whereas (3) interactions between improved technologies and climate should be reflected in temperature‐related time trends of vintage score and its variability. Published data were used to calculate rates of change in vintage score and its variability for the period 1980–2005. Rates were calculated as the slopes of regressions between two dependent variables, i.e. 3‐year running average of vintage score (10‐point scale) and 3‐year running coefficient of variation of vintage score (%), and year of vintage as independent variable. The statistical agreement (r= 0.86, P < 0.05) between rates of change in vintage score derived from two independent sources indicated the vintage scores used in this analysis were fairly robust. Our analysis supported the hypotheses of improvement in vintage score and reduction in variability. More importantly, we provide a quantitative assessment of these trends: the rate of change in vintage scores averaged 0.09 per year, ranged from –0.07 to 0.20 per year, was dominantly positive (35 out of 48 cases), and significant (P < 0.05) in 29 cases, whereas the rate of change in variability of vintage scores averaged –0.52%/year, ranged from –2.1 to 0.8%/year, was dominantly negative (37 out of 48 cases), and significant (P < 0.05) in 19 cases. Consistent with hypothesis 3, the rate of change in vintage score for red wine and the rate of change in variability of vintage score for white wine, were inversely related to temperature (long‐term daily mean during the month prior to harvest in each of the regions). By contrast, the rate of change in vintage score for white wine and the rate of change in variability of vintage score for red wine were unrelated to daily mean regional temperature. Owing to the intricate correlations between climate variables, however, the associations between change in vintage scores and temperature cannot be interpreted in terms of cause and effect.     

Optimization under variability and uncertainty: a case study for NOx emissions control for a gasification system

Methods for optimization of process technologies considering the distinction between variability and uncertainty are developed and applied to case studies of NOx control for Integrated Gasification Combined Cycle systems. Existing methods of stochastic optimization (SO) and stochastic programming (SP) are demonstrated. A comparison of SO and SP results provides the value of collecting additional information to reduce uncertainty. For example, an expected annual benefit of 240,000 dollars is estimated if uncertainty can be reduced before a final design is chosen. SO and SP are typically applied to uncertainty. However, when applied to variability, the benefit of dynamic process control is obtained. For example, an annual savings of 1 million dollars could be achieved if the system is adjusted to changes in process conditions. When variability and uncertainty are treated distinctively, a coupled stochastic optimization and programming method and a two-dimensional stochastic programming method are demonstrated via a case study. For the case study, the mean annual benefit of dynamic process control is estimated to be 700,000 dollars, with a 95% confidence range of 500,000 dollars to 940,000 dollars. These methods are expected to be of greatest utility for problems involving a large commitment of resources, for which small differences in designs can produce large cost savings.     

Quantification of cadmium and lead in offal by SF-ICP-MS: Method development and uncertainty estimate

Offal of bovine, ovine and porcine are able to accumulate potentially toxic heavy metals, such as Cd and Pb, posing a risk for human health. For this reason, the Commission Regulation no. 466/2001 provided the maximum admitted levels for these metals in this kind of matrix (Cd, 500 ng g⁻¹ in all kinds of offal; Pb, 500 ng g⁻¹ in liver and 1000 ng g⁻¹ in kidney). A method based on sector field inductively coupled plasma mass spectrometry for Cd and Pb quantification in calf liver was developed and further applied to offal of different animals. The uncertainty of measurements was calculated according to the Eurachem/Citac Guide. The method LoDs and LoQs were 3.5 and 11 ng g⁻¹ for Cd, and 2.0 and 6.0 ng g⁻¹ for Pb. The repeatability and the intra-laboratory reproducibility showed relative standard deviations equal to 2.25% and 1.99% for Cd and 1.49% and 6.55% for Pb. Relative expanded uncertainties at the mean value in calf liver were 4.74% for Cd and 13.8% for Pb. In Italian offal the following concentration intervals were found (in ng g⁻¹): (i) Cd: calf, from <3.5 in spleen and lung to 96.4 in kidney; lamb, <3.5 in all offal; pig, 114 in liver and (ii) Pb: calf, from 4.03 in lung to 31.8 in liver; lamb, from 4.71 in heart to 279 in liver; pig, 9.19 in liver.     

Evaluation of passive samplers for assessment of community exposure to toxic air contaminants and related pollutants

The precision, accuracy, and sampling rates of Radiello and Ogawa passive samplers were evaluated in the laboratory using a flow-through chamber and under field conditions prior to their use in the 2007 Harbor Community Monitoring Study (HCMS), a saturation monitoring campaign in the communities adjacent to the Ports of Los Angeles and Long Beach. Passive methods included Radiello samplers for volatile organic compounds (benzene, toluene, ethylbenzene, xylenes, 1,3-butadiene), aldehydes (formaldehyde, acetaldehyde, acrolein) and hydrogen sulfide, and Ogawa samplers for nitrogen oxides and sulfur dioxide. Additional experiments were conducted to study the robustness of the passive sampling methods under variable ambient wind speed, sampling duration, and storage time before analysis. Our experimentally determined sampling rates were in agreement with the rates published by Radiello and Ogawa with the following exceptions: we observed a diffusion rate of 22.4 ± 0.1 mL/min for benzene and 37.4 ± 1.5 mL/min for ethylbenzene compared to the Radiello published values of 27.8 and 25.7 mL/min, respectively. With few exceptions, the passive monitoring methods measured one-week average ambient concentrations of selected pollutants with sensitivity and precision comparable to conventional monitoring methods averaged over the same period. Radiello Carbograph 4 VOC sampler is not suitable for the collection of 1,3-butadiene due to backdiffusion. Results for the Radiello aldehyde sampler were inconclusive due to lack of reliable reference methods for all carbonyl compounds of interest.     

Quantification and variability analysis of bacterial cross-contamination rates in common food service tasks

This study investigated bacterial transfer rates between hands and other common surfaces involved in food preparation in the kitchen. Nalidixic acid-resistant Enterobacter aerogenes B199A was used as a surrogate microorganism to follow the cross-contamination events. Samples from at least 30 different participants were collected to determine the statistical distribution of each cross-contamination rate and to quantify the natural variability associated with that rate. The transfer rates among hands, foods, and kitchen surfaces were highly variable, being as low as 0.0005% and as high as 100%. A normal distribution was used to describe the variability in the logarithm of the transfer rates. The mean +/- SD of the normal distributions were, in log percent transfer rate, chicken to hand (0.94 +/- 0.68), cutting board to lettuce (0.90 +/- 0.59), spigot to hand (0.36 +/- 0.90), hand to lettuce (-0.12 +/- 1.07), prewashed hand to postwashed hand (i.e., hand washing efficiency) (-0.20 +/- 1.42), and hand to spigot (-0.80 +/- 1.09). Quantifying the cross-contamination risk associated with various steps in the food preparation process can provide a scientific basis for risk management efforts in both home and food service kitchens.     

Quantification of particle number and mass emission factors from combustion of Queensland trees

The quantification of particle emission factors under controlled laboratory conditions for burning of the following five common tree species found in South East Queensland forests has been studied: Spotted Gum (Corymbia citriodora), Blue Gum (Eucalyptus tereticornis), Bloodwood (Eucalyptus intermedia), Iron Bark (Eucalyptus crebra), and Stringybark (Eucalyptus umbra). The results of the study show that the particle number emission factors and PM2.5 mass emission factors depend on the type of tree and the burning rate. For fast burning conditions, the average particle number emission factors are in the range of 3.3-5.7 x 10(15) particles/kg for woods and 0.5-6.9 x 10(15) particles/kg for leaves and branches, and the PM2.5 emission factors are in the range of 140-210 mg/kg for woods and 450-4700 mg/kg for leaves and branches. For slow burning conditions, the average particle number emission factors are in the range of 2.8-44.8 x 10(13) particles/kg for woods and 0.5-9.3 x 10(13) particles/kg for leaves and branches, and the PM2.5 emissions factors are in the range of 120-480 mg/kg for woods and 3300-4900 mg/kg for leaves and branches.     

Genetic evaluation for length of productive life with censored records.

This study was conducted to investigate the impact of censoring on the accuracy of sire evaluation for the length of productive life estimated by means of survival analysis using simulated and real dairy cattle data from the Swiss Braunvieh population. Data were simulated under a Weibull model with two fixed effects and a random sire effect with a sire variance of 0.04. Two different family structures investigated were 1000 sires with 10 daughters each and 200 sires with 50 daughters each. Sires were assumed to be related through their sires. The reference data were generated assuming no censoring. Sire effects were estimated from the reference data with and without considering the relationships among sires and referred to as the estimated transmitting abilities (ETA) of sires. The impact of censoring on accuracy of ETA and ranking of sires was investigated by computing rank correlations among true and estimated sire effects and among estimated sire effects from the reference data and from several different data files with increased proportion of censored records. Estimated transmitting abilities were generally more accurate with a large number of daughters. The rank correlations among the ETA of sires from the data with censored records and the ETA from the reference data decreased with an increased proportion of censored records. Considering relationships among sires resulted in higher rank correlations when the proportion of censored records was large. With 50 daughters per sire, accuracy of 70% can be achieved approximately 2 yr after first calving of the daughters with about 50% censored records. With the real data, a rank correlation with the ETA of sires from the reference data of 0.70 to 0.80 can be achieved with about 65% of records censored and about 2.5 yr after the first calving of the youngest daughters of the sires.     

Quantification of local and global benefits from air pollution control in Mexico City

Complex sociopolitical, economic, and geographical realities cause the 20 million residents of Mexico City to suffer from some of the worst air pollution conditions in the world. Greenhouse gas emissions from the city are also substantial, and opportunities for joint local-global air pollution control are being sought. Although a plethora of measures to improve local air quality and reduce greenhouse gas emissions have been proposed for Mexico City, resources are not available for implementation of all proposed controls and thus prioritization must occur. Yet policy makers often do not conduct comprehensive quantitative analyses to inform these decisions. We reanalyze a subset of currently proposed control measures, and derive cost and health benefit estimates that are directly comparable. This study illustrates that improved quantitative analysis can change implementation prioritization for air pollution and greenhouse gas control measures in Mexico City.     

Analysis of fertility and dystocia in Holsteins using recursive models to handle censored and categorical data

A method based on the analysis of recursive multiple-trait models was used to 1) estimate genetic and phenotypic relationships of calving ease (CE) with fertility traits and 2) analyze whether dystocia negatively affects reproductive performance in the next reproductive cycle. Data were collected from 1995 through 2002, and contained 33,532 records of CE and reproductive data of 17,558 Holstein cows distributed across 560 herds in official milk recording from the Basque Country Autonomous Community (Spain). The following fertility traits were considered: days open (DO), days to first service, number of services per pregnancy (NINS), and outcome of first insemination (OFI). Four bivariate sire and sire-maternal grandsire models were used for the analyses. Censoring existed in DO (26.49% of the data) and NINS (12.22% of the data) because of cows having been sold or culled before reaching the next parturition. To avoid bias, a data augmentation technique was applied to censored data. Threshold models were used for CE and OFI. To consider that CE affects fertility and the genetic determination of CE and fertility traits, recursive models were applied, which simultaneously considered CE as a fixed effect on fertility performance and the existence of a genetic correlation between CE and fertility traits. The effects of CE score 3 (difficult birth) with respect to score 1 (no problem) for days to first service, DO, NINS, and OFI were 8 d, 31 d, 0.5 services, and - 12% success at first insemination, respectively. These results showed poorer fertility after dystocia. Genetic correlations between genetic effects of fertility traits and CE were close to zero, except for the genetic correlations between direct effects of DO and CE, which were positive, moderate, and statistically different from 0 (0.47 ± 0.24), showing that genes associated with difficult births also reduce reproductive success.     

The origin and significance of short-term variability of semivolatile contaminants in air

Persistent semivolatile contaminants such as polychlorinated biphenyls (PCBs) cycle between air and surface media in the environment. At different locations and times, PCB concentrations in air over a diel (24-hour) period have been observed to have maxima either during the day or at night. These observations have been interpreted as evidence of temperature-mediated air-surface exchange and of degrading reactions with hydroxyl radicals in the atmosphere. However, a general explanation of the processes responsible for the observed diel variability in concentrations has not been provided. Here, we interpret diel monitoring data using a multimedia mass balance model parametrized with local data on temperature, wind speed, atmospheric mixing height, and hydroxyl radical concentrations. We demonstrate that four factors are sufficient to account for the variability of PCB concentrations in air over a diel period; temperature, local atmospheric stability, hydroxyl radical concentration, and source type. We apply the model to re-interpret past diel monitoring studies and find that the observed patterns of concentrations can be rationalized by consideration of these factors. Using insights from this study, future diel monitoring campaigns can be targeted to observe the influence of specific fate and transport processes. Such studies will contribute to more accurate understanding of the processes controlling the short-term local, and long-term global fate of persistent semivolatile contaminants.