ERF of TCDD

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Study-specific E-R functions | Species-specific E-R functions | E-R function for children

Scope

Exposure-response functions for tooth defects caused by TCDD (study-specific) describes study-specific exposure-response functions for either enamel defects in molars or missing or smaller molars.

Definition

Causality

List of parents:

Exposure: TCDD concentration in body fat at the age of 0-14 days (in rats) or 0-5 years (children)
Response: Probability of a missing third molar in rats, or an enamel lesion in children (studied in adulthood)

Data

Miettinen et al. rat study

Alaluusua et al. 2004 Seveso children study

Unit

(ng/kg in fat)^-1

Formula

We are trying to make a logistic regression on a binary outcome ("response") with one independent variable ("exposure"). There are 75 individual observations. However, they are uncertain and they are described as distributions with 1000 samples. Each variable is stored in a text file.

Data format for TXT files

Row	Observation #	Var_id	Observation	Sample #
1	1	8	72.18119502378521	1
2	2	8	144.7285650341189	1
3	3	8	18.93289686579553	1
...
75	75	8	19.26856210444296	1
76	1	8	43.44587536201471	2
77	2	8	41.70910709409909	2
...
75000	75	8	70.81169222799284	1000

R Code for the logistic regression


+ Show code- Hide code
 #Code for rat data
 expdata = read.table("N:/YTOS/Projects/INTARESE/WP1_3/Combine_epi_tox/Model/Expr.txt", header = TRUE)
 respdata = read.table("N:/YTOS/Projects/INTARESE/WP1_3/Combine_epi_tox/Model/Respr.TXT", header = TRUE)
 #Alustetaan muuttuja, johon parametrit talletetaan
 fm <- NULL
 #Alla olevan silmukan jälkeen jokaisen iteraation parametrit ovat muuttujassa
 #fm iteraatiokierrosta vastaavalla rivillä.
 for (z in 1:1000) {
   y <- (z-1)*140+1
   b <- glm(respdata[(y:(y+140)),4] ~ expdata[(y:(y+140)),4], family = binomial)
  fm <- rbind(fm,b$coefficients)
 }
 fm
 
 #Code for human data
 expdata = read.table("N:/YTOS/Projects/INTARESE/WP1_3/Combine_epi_tox/Model/Exph.txt", header = TRUE)
 respdata = read.table("N:/YTOS/Projects/INTARESE/WP1_3/Combine_epi_tox/Model/Resph.TXT", header = TRUE)
 #Alustetaan muuttuja, johon parametrit talletetaan
 fm <- NULL
 #Alla olevan silmukan jälkeen jokaisen iteraation parametrit ovat muuttujassa
 #fm iteraatiokierrosta vastaavalla rivillä.
 for (z in 1:1000) {
   y <- (z-1)*75+1
   b <- glm(respdata[(y:(y+75)),4] ~ expdata[(y:(y+75)),4], family = binomial)
  fm <- rbind(fm,b$coefficients)
 }
 fm

Narrative description

Measurement error models (MEM) and analogy extrapolation models (AEM) are used to derive estimates from the data. Measurement error models are used in situations where the actual item of interest is observed, but the measurement is imperfect. Analogy extrapolation models are used where the actual item of interest is not observed, but instead something similar to the item is used to make inferences about the item.

Exposure MEM: The exposure in the study is not known perfectly. Instead, we use measurements together with information about the error in the measurements to estimate the true exposure.
Response MEM: The response in the study is not known perfectly. Instead, we use measurements together with information about the error in the measurements to estimate the true response.
Selection MEM: The study is supposed to represent a base population, from which the studied individuals are a representative sample. However, there may be non-random selection of study individuals. This may cause bias. Therefore, information about selection bias is used to correct the E-R function.
Confounder MEM: The individuals are exposed to a large number of factors. There may be a systematic difference in other exposures in the exposed and non-exposed individuals. In epidemiology, these are called confounders. This MEM corrects the E-R function for the impacts of confounders.
Shape of curve near data: In each E-R study, some assumption was made about the shape of the E-R function. The same assumption is usually used to derive the result distribution for the E-R function. If the original exposure and response data is available, it is also possible to use another function.

Result