title: Statistical methods to study timing of vulnerability with sparsely sampled data on environmental toxicants.
abstract: BACKGROUND
  Identifying windows of vulnerability to environmental toxicants is an important area in children's health research.
  
  
  OBJECTIVE
  We compared and contrasted statistical approaches that may help identify windows of vulnerability by formally testing differences in exposure effects across time of exposure, incorporating continuous time metrics for timing of exposure, and efficiently incorporating incomplete cases.
  
  
  METHODS
  We considered four methods: 1) window-specific and simultaneously adjusted regression; 2) multiple informant models; 3) using features of individual exposure patterns to predict outcomes; and 4) models of population exposure patterns depending on the outcome. We illustrate them using a study of prenatal vulnerability to lead in relation to Bayley's Mental Development Index at 24 months of age (MDI24).
  
  
  RESULTS
  The estimated change in MDI24 score with a 1-loge-unit increase in blood lead during the first trimester was -2.74 [95% confidence interval (CI), -5.78 to 0.29] based on a window-specific regression. The corresponding change in MDI24 was -4.13 (95% CI, -7.54 to -0.72) based on a multiple informant model; estimated effects were similar across trimesters (p = 0.23). Results from method 3 suggested that blood lead levels in early pregnancy were significantly associated with reduced MDI24, but decreasing blood leads over the course of pregnancy were not. Method 4 results indicated that blood lead levels before 17 weeks of gestation were lower among children with MDI24 scores in the 90th versus the 10th percentile (p = 0.08).
  
  
  CONCLUSIONS
  Method 2 is preferred over method 1 because it enables formal testing of differences in effects across a priori-defined windows (e.g., trimesters of pregnancy). Methods 3 and 4 are preferred over method 2 when there is large variability in the timing of exposure assessments among participants. Methods 3 and 4 yielded smaller p-values for tests of the hypothesis that not only level but also timing of lead exposure are relevant predictors of MDI24; systematic power comparisons are warranted.
authors.affiliation: Department of Biostatistics, University of Michigan School of Public Health, Ann Arbor, 48109, USA. brisa@umich.edu
authors.forename: Brisa Ney
authors.initials: BN
authors.lastname: Sánchez
authors.forename: Howard
authors.initials: H
authors.lastname: Hu
authors.forename: Heather J
authors.initials: HJ
authors.lastname: Litman
authors.forename: Martha Maria
authors.initials: MM
authors.lastname: Téllez-Rojo
mesh_terms: D000328:Adult; D002657:Child Development / Q000187:drug effects; D002675:Child, Preschool; D004785:Environmental Pollutants / Q000097:blood*; D004787:Environmental Pollution / Q000706:statistics & numerical data*; D005260:Female; D006801:Humans; D007854:Lead / Q000097:blood*; D008297:Male; D018811:Maternal Exposure / Q000706:statistics & numerical data*; D011247:Pregnancy; D011297:Prenatal Exposure Delayed Effects / Q000453:epidemiology; D055815:Young Adult
chemical_list: D004785:Environmental Pollutants; D007854:Lead