title: Fitting distributions to microbial contamination data collected with an unequal probability sampling design.
abstract: OBJECTIVE
  The fitting of statistical distributions to microbial sampling data is a common application in quantitative microbiology and risk assessment applications. An underlying assumption of most fitting techniques is that data are collected with simple random sampling, which is often times not the case. This study develops a weighted maximum likelihood estimation framework that is appropriate for microbiological samples that are collected with unequal probabilities of selection.
  
  
  RESULTS
  A weighted maximum likelihood estimation framework is proposed for microbiological samples that are collected with unequal probabilities of selection. Two examples, based on the collection of food samples during processing, are provided to demonstrate the method and highlight the magnitude of biases in the maximum likelihood estimator when data are inappropriately treated as a simple random sample.
  
  
  CONCLUSIONS
  Failure to properly weight samples to account for how data are collected can introduce substantial biases into inferences drawn from the data.
  
  
  CONCLUSIONS
  The proposed methodology will reduce or eliminate an important source of bias in inferences drawn from the analysis of microbial data. This will also make comparisons between studies and the combination of results from different studies more reliable, which is important for risk assessment applications.
authors.affiliation: Risk Assessment Division, Office of Public Health Science, Food Safety Inspection Service, USDA, Fort Collins, CO 80526, USA. mike.williams@fsis.usda.gov
authors.forename: M S
authors.initials: MS
authors.lastname: Williams
authors.forename: E D
authors.initials: ED
authors.lastname: Ebel
authors.forename: Y
authors.initials: Y
authors.lastname: Cao
mesh_terms: D000818:Animals; D015982:Bias; D002167:Campylobacter / Q000302:isolation & purification; D002417:Cattle; D002645:Chickens; D003198:Computer Simulation; D005506:Food Contamination / Q000032:analysis*; D005516:Food Microbiology; D016013:Likelihood Functions; D008460:Meat / Q000382:microbiology; D011336:Probability; D012107:Research Design; D018570:Risk Assessment / Q000379:methods; D012475:Salmonella / Q000302:isolation & purification