title: A non-parametric framework for estimating threshold limit values.
abstract: BACKGROUND
  To estimate a threshold limit value for a compound known to have harmful health effects, an 'elbow' threshold model is usually applied. We are interested on non-parametric flexible alternatives.
  
  
  METHODS
  We describe how a step function model fitted by isotonic regression can be used to estimate threshold limit values. This method returns a set of candidate locations, and we discuss two algorithms to select the threshold among them: the reduced isotonic regression and an algorithm considering the closed family of hypotheses. We assess the performance of these two alternative approaches under different scenarios in a simulation study. We illustrate the framework by analysing the data from a study conducted by the German Research Foundation aiming to set a threshold limit value in the exposure to total dust at workplace, as a causal agent for developing chronic bronchitis.
  
  
  RESULTS
  In the paper we demonstrate the use and the properties of the proposed methodology along with the results from an application. The method appears to detect the threshold with satisfactory success. However, its performance can be compromised by the low power to reject the constant risk assumption when the true dose-response relationship is weak.
  
  
  CONCLUSIONS
  The estimation of thresholds based on isotonic framework is conceptually simple and sufficiently powerful. Given that in threshold value estimation context there is not a gold standard method, the proposed model provides a useful non-parametric alternative to the standard approaches and can corroborate or challenge their findings.
authors.affiliation: MRC Biostatistics Unit, Cambridge, UK. georgia.salanti@mrc-bsu.cam.ac.uk
authors.forename: Georgia
authors.initials: G
authors.lastname: Salanti
authors.forename: Kurt
authors.initials: K
authors.lastname: Ulm
mesh_terms: D000395:Air Pollutants, Occupational / Q000009:adverse effects / Q000032:analysis*; D000465:Algorithms; D029481:Bronchitis, Chronic / Q000209:etiology; D003625:Data Collection; D004391:Dust / Q000032:analysis; D006801:Humans; D016013:Likelihood Functions; D016015:Logistic Models; D015233:Models, Statistical; D012044:Regression Analysis; D018570:Risk Assessment; D018709:Statistics, Nonparametric; D020711:Threshold Limit Values
chemical_list: D000395:Air Pollutants, Occupational; D004391:Dust