Pesticides

If the goal is to evaluate pesticide use and analyte levels in carpet dust, represented by the β parameters, then the Tobit regression of Equation 1 is sufficient and no imputation is required. For further analysis or for graphical display, it is useful to generate values for measurements below DLs. We consider several different approaches, including inserting DL/2, inserting E[Z|Z < DL], or using a single or multiple imputation (Little and Rubin 1987 ).
A multiple imputation procedure is carried out as follows. Using all data (measured concentrations, missing data types I–III, and covariates), we create the log-likelihood function 1, solve for the MLEs of β and σ² (denoted β̂ and ς̂²), and impute a value by randomly sampling from a log-normal distribution with the estimated parameters. However, in selecting fill-in values we cannot ignore that β̂ and ς̂² are themselves estimates with uncertainties. We therefore do not use β̂ and ς̂² for the imputation, but rather β̃ and σ̃², which are estimated from a bootstrap sample of the data (Efron 1979 ). Bootstrap data are generated as described below by sampling with replacement, and represent a sample from the same universe as the original data. We repeat the process to create multiple data sets, which are then independently analyzed and combined in a way that accounts for the imputation. Differences in regression results in the multiple data sets reflect variability due to the imputation process.
This procedure, however, omits a source of variability. We have tacitly assumed that the LB and UB are fixed and known in advance. When there are no interfering compounds (missing type I), the assumption is justified because the DL is determined before the GC/MS dust analysis. When there are interfering compounds (missing types II and III), the assumption cannot be fully justified because the bounds depend on the amount of interference and therefore are random. In the NHL data, we assume this uncertainty is small relative to other uncertainties. The imputation proceeds as follows:
Step 1: Create a bootstrap sample and obtain estimates β̃ and σ̃² based on Equation 2. Bootstrap data are generated by sampling with replacement n times from the n subjects. Sampling “with replacement” selects one record at random and then “puts it back” and selects a second record. After n repetitions, some subjects are selected multiple times, whereas other subjects are not selected at all. If w_i is the number of times the ith subject is sampled, then the log-likelihood function for the bootstrap data is
Step 2: Impute analyte values based on sampling from LN (β̃^tX, σ̃²). For the ith subject, assign the value
This quantity consists of various elements. F(LB_i; β̃^tX, σ̃²) and F(UB_i; β̃^tX, σ̃²) are the cumulative probabilities at UL_i and UB_i, respectively, based on parameters β̃, σ̃². Both values lie between zero and one. Select randomly from a uniform distribution on the interval [a, b], denoted Unif[a, b], in particular the interval [F(LB_i; β̃^tX_i, σ̃²), F(UB_i; β̃^tX_i, σ̃²)]. The inverse cumulative distribution function, F⁻¹(•), is the required imputed value in original units between LB_i and UB_i. Repeat using the same β̃, σ̃² for each missing value. Detected values are not altered.
Step 3: Repeat steps 1 and 2 to create M plausible (or “fill-in”) data sets. Remarkably, M need not be large, and a recommended value is between 3 and 5, with larger values if greater proportions of data are missing (Little and Rubin 1987 ; Rubin 1987 ). We select M = 10 to fully account for the variance from the imputation.
Step 4: Fit a regression model to each of the M data sets and obtain M sets of parameter estimates and covariance matrices. Combine the M sets of estimates to account for the imputation (Little and Rubin 1987 ; Schafer 1997 ). The imputation procedure results in confidence intervals (CIs) that are wider than the single-imputation, fill-in approach.

We evaluate the association between analyte concentration and pesticide use by fitting a linear regression model of the logarithm of the analyte level on subject characteristics. Regression (independent) covariates include indicator variables for season of sample collection, presence of oriental rugs, study center, sex, age (< 45, 45–64, ≥ 65 years), race (African American, Caucasian, other), type of home (single family, townhouse/duplex/apartment, other), year of home construction (< 1940< 1940–1959–1960–1979, ≥ 1980), and educational level (< 12, 12–15, ≥ 16 years). As in Colt et al. (2004) (link), covariates vary slightly with analyte. Models also include five variables describing the use of insect treatment products: ever/never used products to treat for crawling insects, flying insects, fleas/ticks, termites, and lawn/garden insects. We use data from current homes only.
Regression analysis is hampered by the presence of measurements known only within bounds. We assume that the probability distributions of measurements below the DL (more precisely, within the LB and UB interval) depend only on observed data; that is, the interval-measured concentrations arise from the same distributions that generate the measured values. Let F(•) be the cumulative distribution function and f(•) the probability density function for a log-normal random variable. Suppose X_i = (X_i0, … ,X_iK)^t is the covariate vector for the ith of i = 1, … , n subjects. LB_i and UB_i are recorded for i = 1, … , n₀ individuals, whereas a specific Z_i measurement is recorded for i = n₀ + 1, … , n₀ + n₁ individuals. LB and UB are subscripted to allow different DLs. Using a Tobit regression approach (Gilbert 1987 ; Persson and Rootzen 1977 ; Tobin 1958 ), the log-likelihood function has the form
The first summand derives from the n₀ interval measured values and involves the difference of the cumulative distribution function F evaluated at UB and at LB; that is, the probability the measurement lies between the LB and UB. The second summand derives from the n₁ detected values. Maximum likelihood estimates (MLEs) for β and their covariance matrix are obtained by maximizing Equation 1 and computing the inverse information matrix using standard methods.

The need for organized in vivo toxicity data to evaluate alternative in vitro and in silico approaches led to the development of the ToxRefDB database to house a detailed collection of animal toxicity study data, primarily extracted from EPA pesticide registration documents [59 ]. The database is highly-structured, consisting of data extracted from thousands of studies on over 1000 chemicals, thus comprising one of the largest in vivo toxicity databases available to the public. The restrictions on transparency, study rigor, and required detail in ToxRefDB maintain a very clean and valuable database, but prevent the integration of less detailed data from many other sources. ToxValDB is a database designed to store a wider range of public toxicity information in a less restricted, more summarized form than ToxRef, while maintaining the linkages to original source information so that users can access available details.
In particular, ToxValDB collates publicly available toxicity dose–effect related summary values typically used in risk assessments. These include Point of Departure (POD) data collected from data sources within ACToR and ToxRefDB, and no-observed and lowest-observed (adverse) effect levels (NOEL, NOAEL, LOEL, LOAEL) data extracted from repeated dose toxicity studies submitted under REACH. Also included are reference dose and concentration values (RfDs and RfCs) from EPA’s Integrated Risk Information System (IRIS) [60 ] and dose descriptors from EPA’s Provisional Peer-Reviewed Toxicity Values (PPRTV) documents [61 ]. Acute toxicity information was extracted from a number of different sources, including: OECD eChemPortal, ECHA (European Chemicals Agency), NLM (National Library of Medicine) HSDB (Hazardous Substances Data Bank), ChemIDplus via EPA TEST (Toxicity Estimation Software Tool), and the EU JRC (Joint Research Centre) AcutoxBase [62 ]. Finally, data from the eChemPortal and the EU COSMOS project have also been included in ToxValDB.

Deer were assigned to groups using a random sequence generator, and groups were differentiated based on: (i) test group identity (treatment group [T], control [C]); and (ii) the length of the exposure (48 h [T48], 120 h [T120]) (Additional file 1: Table S1). While explicit guidelines for white-tailed deer are not available, federal guidelines recommend a sample size of 6–10 subjects per test group when evaluating pesticides against pests of humans and pets, such as fleas and ticks [39 ]. The size of the captive herd and the number of deer that its managers could afford to donate to this project limited the sample size that we were able to utilize, and we were unable to have an equal number of males (n = 15) and females (n = 9). It was determined that each test group could comprise eight animals (n = 24). A total of 16 deer were offered FDF, with eight deer being exposed to FDF for 48 h and eight deer being exposed to FDF for 120 h. An additional eight deer served as an untreated control group, with 50% of animals exposed to placebo for 48 h and 50% exposed to placebo for 120 h. Deer continued to be housed in the individual pens during the exposure period. Prior to tick attachment, deer within each test group were additionally assigned to subgroups, with 50% of deer to be parasitized with ticks at day 7 post-exposure to FDF, and 50% to be parasitized at day 21 post-exposure to FDF (4 animals/subgroup).

Plant seed materials used in this study were obtained from the following commercial and government sources: Brassicajuncea (Brown Mustard-Pacific Gold) and Sinapisalba (White Mustard—Ida Gold) from Pacific Northwest Farmers Cooperative, Spokane WA, USA; Lepidiumsativum (Garden Cress) from Kelly Seed and Hardware Co., Peoria, IL, USA; and Thlaspiarvense (Field Pennycress—Elisabeth) from USDA-ARS, Peoria, IL, USA. All seeds used in the study were not treated with pesticides for seed treatment. Processing and utilization of all seed materials in this study followed the local and national regulations in accordance with all relevant local State and national guidelines. There were no genetically modified plant cultivars examined in this study.