## Abstract

Context. Recent publications have graphically demonstrated a curvilinear relationship between measures of intelligence and blood lead levels at low concentrations (< 10 mcg/dl). This led to speculation that a greater biologic effect occurs at lower concentrations. Critics of this conclusion hypothesized that this graphical relationship may be a function of the underlying distributions of these variables. Objective. To study the impact of the distribution of data on the shape of apparent dose-response curves. Methods. Random data based on varied distributions were constructed to simulate a previous study using a single, randomly generated covariate income (Inc) to demonstrate the impact of normally versus exponentially distributed data on the shape of the graph of intelligence quotient (IQ) versus blood lead. We also used an existing database of US blood lead levels and constructed a similar model of income and IQ using both assumptions of distribution for the intermediate variable income. Results. When both lead and income are exponentially distributed, the graph of lead and IQ will be a curve. Conclusion. The apparent shape of a dose-response relationship from simulated epidemiological data is nonlinear when one variable and a covariate are exponentially distributed. A non-linear biological relationship should not be assumed and in fact may be the least likely explanation. The use of observational epidemiological data to discern a dose-response relationship between two variables may be misleading.

Original language | English (US) |
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Pages (from-to) | 113-117 |

Number of pages | 5 |

Journal | Clinical Toxicology |

Volume | 52 |

Issue number | 2 |

DOIs | |

State | Published - Feb 2014 |

## Keywords

- Covariate
- Distribution
- Income
- Modeling
- Regression

## ASJC Scopus subject areas

- Toxicology