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      A Distribution-Based Multiple Imputation Method for Handling Bivariate Pesticide Data with Values below the Limit of Detection

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          Abstract

          Background

          Environmental and biomedical researchers frequently encounter laboratory data constrained by a lower limit of detection (LOD). Commonly used methods to address these left-censored data, such as simple substitution of a constant for all values < LOD, may bias parameter estimation. In contrast, multiple imputation (MI) methods yield valid and robust parameter estimates and explicit imputed values for variables that can be analyzed as outcomes or predictors.

          Objective

          In this article we expand distribution-based MI methods for left-censored data to a bivariate setting, specifically, a longitudinal study with biological measures at two points in time.

          Methods

          We have presented the likelihood function for a bivariate normal distribution taking into account values < LOD as well as missing data assumed missing at random, and we use the estimated distributional parameters to impute values < LOD and to generate multiple plausible data sets for analysis by standard statistical methods. We conducted a simulation study to evaluate the sampling properties of the estimators, and we illustrate a practical application using data from the Community Participatory Approach to Measuring Farmworker Pesticide Exposure (PACE3) study to estimate associations between urinary acephate (APE) concentrations (indicating pesticide exposure) at two points in time and self-reported symptoms.

          Results

          Simulation study results demonstrated that imputed and observed values together were consistent with the assumed and estimated underlying distribution. Our analysis of PACE3 data using MI to impute APE values < LOD showed that urinary APE concentration was significantly associated with potential pesticide poisoning symptoms. Results based on simple substitution methods were substantially different from those based on the MI method.

          Conclusions

          The distribution-based MI method is a valid and feasible approach to analyze bivariate data with values < LOD, especially when explicit values for the nondetections are needed. We recommend the use of this approach in environmental and biomedical research.

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          Most cited references32

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          Epidemiologic Evaluation of Measurement Data in the Presence of Detection Limits

          Quantitative measurements of environmental factors greatly improve the quality of epidemiologic studies but can pose challenges because of the presence of upper or lower detection limits or interfering compounds, which do not allow for precise measured values. We consider the regression of an environmental measurement (dependent variable) on several covariates (independent variables). Various strategies are commonly employed to impute values for interval-measured data, including assignment of one-half the detection limit to nondetected values or of “fill-in” values randomly selected from an appropriate distribution. On the basis of a limited simulation study, we found that the former approach can be biased unless the percentage of measurements below detection limits is small (5–10%). The fill-in approach generally produces unbiased parameter estimates but may produce biased variance estimates and thereby distort inference when 30% or more of the data are below detection limits. Truncated data methods (e.g., Tobit regression) and multiple imputation offer two unbiased approaches for analyzing measurement data with detection limits. If interest resides solely on regression parameters, then Tobit regression can be used. If individualized values for measurements below detection limits are needed for additional analysis, such as relative risk regression or graphical display, then multiple imputation produces unbiased estimates and nominal confidence intervals unless the proportion of missing data is extreme. We illustrate various approaches using measurements of pesticide residues in carpet dust in control subjects from a case–control study of non-Hodgkin lymphoma.
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            Organophosphate Pesticide Exposure and Neurodevelopment in Young Mexican-American Children

            Background Organophosphate (OP) pesticides are widely used in agriculture and homes. Animal studies suggest that even moderate doses are neurodevelopmental toxicants, but there are few studies in humans. Objectives We investigated the relationship of prenatal and child OP urinary metabolite levels with children’s neurodevelopment. Methods Participating children were from a longitudinal birth cohort of primarily Latino farm-worker families in California. We measured six nonspecific dialkylphosphate (DAP) metabolites in maternal and child urine as well as metabolites specific to malathion (MDA) and chlorpyrifos (TCPy) in maternal urine. We examined their association with children’s performance at 6 (n = 396), 12 (n = 395), and 24 (n = 372) months of age on the Bayley Scales of Infant Development [Mental Development (MDI) and Psychomotor Development (PDI) Indices] and mother’s report on the Child Behavior Checklist (CBCL) (n = 356). Results Generally, pregnancy DAP levels were negatively associated with MDI, but child measures were positively associated. At 24 months of age, these associations reached statistical significance [per 10-fold increase in prenatal DAPs: β = −3.5 points; 95% confidence interval (CI), −6.6 to −0.5; child DAPs: β = 2.4 points; 95% CI, 0.5 to 4.2]. Neither prenatal nor child DAPs were associated with PDI or CBCL attention problems, but both prenatal and postnatal DAPs were associated with risk of pervasive developmental disorder [per 10-fold increase in prenatal DAPs: odds ratio (OR) = 2.3, p = 0.05; child DAPs OR = 1.7, p = 0.04]. MDA and TCPy were not associated with any outcome. Conclusions We report adverse associations of prenatal DAPs with mental development and pervasive developmental problems at 24 months of age. Results should be interpreted with caution given the observed positive relationship with postnatal DAPs.
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              The limitations due to exposure detection limits for regression models.

              Biomarker use in exposure assessment is increasingly common, and consideration of related issues is of growing importance. Exposure quantification may be compromised when measurement is subject to a lower threshold. Statistical modeling of such data requires a decision regarding the handling of such readings. Various authors have considered this problem. In the context of linear regression analysis, Richardson and Ciampi (Am J Epidemiol 2003;157:355-63) proposed replacement of data below a threshold by a constant equal to the expectation for such data to yield unbiased estimates. Use of such an imputation has some limitations; distributional assumptions are required, and bias reduction in estimation of regression parameters is asymptotic, thereby presenting concerns about small studies. In this paper, the authors propose distribution-free methods for managing values below detection limits and evaluate the biases that may result when exposure measurement is constrained by a lower threshold. The authors utilize an analytical approach and a simulation study to assess the effects of the proposed replacement method on estimates. These results may inform decisions regarding analytical plans for future studies and provide a possible explanation for some amount of the discordance seen in extant literature.
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                Author and article information

                Journal
                Environ Health Perspect
                Environmental Health Perspectives
                National Institute of Environmental Health Sciences
                0091-6765
                1552-9924
                March 2011
                19 November 2010
                : 119
                : 3
                : 351-356
                Affiliations
                [1 ] Department of Biostatistical Sciences and
                [2 ] Department of Epidemiology and Prevention, Division of Public Health Sciences and
                [3 ] Department of Family and Community Medicine, Wake Forest University School of Medicine, Winston-Salem, North Carolina, USA
                Author notes
                Address correspondence to H. Chen, Department of Biostatistical Sciences, Division of Public Health Sciences, Wake Forest University School of Medicine, Medical Center Blvd., Winston-Salem, NC 27157 USA. Telephone: (336) 716-4431. Fax: (336) 716-6427. E-mail: hchen@ 123456wfubmc.edu

                The authors declare they have no actual or potential competing financial interests.

                Article
                ehp-119-351
                10.1289/ehp.1002124
                3059998
                21097385
                f95a769b-758b-461a-b8fd-e69651350cda
                This is an Open Access article: verbatim copying and redistribution of this article are permitted in all media for any purpose, provided this notice is preserved along with the article's original DOI.
                History
                : 4 March 2010
                : 19 November 2010
                Categories
                Research

                Public health
                left-censoring,limit of detection,maximum likelihood,repeated measures,longitudinal study,multiple imputation,nondetect

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