title: A distribution-based multiple imputation method for handling bivariate pesticide data with values below the limit of detection.
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.
authors.affiliation: Department of Biostatistical Sciences, Division of Public Health Sciences, Wake Forest University School of Medicine, Winston-Salem, North Carolina 27157, USA. hchen@wfubmc.edu
authors.forename: Haiying
authors.initials: H
authors.lastname: Chen
authors.forename: Sara A
authors.initials: SA
authors.lastname: Quandt
authors.forename: Joseph G
authors.initials: JG
authors.lastname: Grzywacz
authors.forename: Thomas A
authors.initials: TA
authors.lastname: Arcury
mesh_terms: D000383:Agriculture; D000704:Analysis of Variance; D002623:Chemistry Techniques, Analytical / Q000379:methods*; D004785:Environmental Pollutants / Q000032:analysis* / Q000737:chemistry / Q000652:urine; D004787:Environmental Pollution / Q000706:statistics & numerical data; D006801:Humans; D057230:Limit of Detection; D008137:Longitudinal Studies; D016273:Occupational Exposure / Q000032:analysis / Q000706:statistics & numerical data; D010575:Pesticides / Q000032:analysis* / Q000737:chemistry / Q000652:urine
chemical_list: D004785:Environmental Pollutants; D010575:Pesticides