Environmental Health Criteria 214

HUMAN EXPOSURE ASSESSMENT
be the time of day when the levels are measured. For simplicity,
divide time into three categories -- morning, afternoon, or evening --
so k = 3. If there is no known or hypothesized functional form for
the relationship, the resulting abstract model for exposure, Y,
during a particular time period, i, should be the sum of the mean
(average) during the time period i, denoted by gamma i, and an
error, epsilon, which will represent the natural variation of the
measurement. It is common to assume that the variation of the outcome
is the same among all levels of the factor; this assumption is known
as homoscedasticity.
This model is referred to as the one-way ANOVA. The resulting
model for the observed data, with Y ij denoting the jth PM 2.5
measurement collected during the ith time period with i ranging
from 1 to 3, is Y ij = gamma i + epsilon ij where gamma i represents
the average outcome due to the ith factor level (in this example
i ranges from 1 to 3), and epsilon ij (the error term) represents
independent random variation. One common assumption is that the error
terms follow a normal distribution with variance rho 2 . The parameters
which need to be estimated in this model from the data are the means
of the subsamples, gamma i , and the variance of the outcome, rho 2 .
This type of model, which compares the means of distinct groups, is
the basis for ANOVA.
Increasing the level of complexity leads to multiway or
multifactor ANOVA as well as the multiple linear regression model,
which is a more specific model for the effects of independent
variables on the dependent variable. Let Y denote the exposure level
for a particular person or location; this is the dependent variable.
Let X, ..., X n denote n independent variables (known as
covariates) which potentially influence the exposure level Y. If the
assumption of the existence of a linear relationship between the
independent and dependent variables is reasonable, then a model for
the outcome, Y, based on the covariates X i , can be written as
where the information not conveyed by the covariates results in the
error (epsilon), which is assumed to be normally distributed. theta 0
denotes the average exposure when all the X values are zero, and
theta i denotes the change in exposure for a unit change in the ith
variable. An example would be 24-h personal exposures to nitrogen
dioxide. In this case, the factors may be distinct times and locations
(or microenvironments) where nitrogen dioxide exposure may occur; for
example, outdoors, indoors while home cooking on a gas range, and in
an automobile.
A regression model is used to evaluate the relationship of one or
more independent variables X 1 , X 2 , ..., X k to a single,
continuous dependent variable Y. It is often used in exposure
assessment to characterize the relationship between the dependent and
independent variables (continuous and discrete) by determining the
extent, direction and strength of the association. For example, in the
particle total exposure assessment methodology (PTEAM) study, indoor
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