Environmental Health Criteria 214

HUMAN EXPOSURE ASSESSMENT
house dust or in water could be important factors, whereas gender and
age might have an indirect effect on exposure by influencing the
location and patterns of play. However, both types of data will be
important in determining response, even though one is only an indirect
cause. The average outcome described above could be the annual average
exposure to lead or perhaps the maximum daily exposure, depending upon
whether a cumulative or a threshold effect is the focus.
As noted in Chapter 3, by considering the statistical model
before finalizing the study design one can help ensure that most
influential factors would be accounted for, and more importantly, that
the true effects of factors can be estimated from the study data. It
is possible to design a study where some influential factors were not
accounted for. Suppose there is interest in the effects of location
and time of day on outdoor ultraviolet radiation exposures. If
measures are only taken at one site at one time of day, and then at
another site at a different time of day, then the effects of location
and time of day are not distinguishable from the collected data.
The mean, or average, outcome is the most common summary used for
modelling and testing of situations of different conditions, but other
parameters, such as the variance, the percentiles or the median, can
be used for estimation and testing. Common models and statistical
analyses, such as the multiple linear regression model, the t-test
and analysis of variance (ANOVA) use the mean for modelling and
testing. The models can be as simple as taking the sample, dividing it
into groups and comparing the means in the different groups. The
models can also be as complex as trying to construct a physical model
for the means with the addition of terms which incorporate randomness
due to unmeasured factors or other sources of variation.
4.4.4.1 Analysis of variance and linear regression
ANOVA is a technique for assessing how several nominal
independent variables affect a continuous dependent variable, and is
usually concerned with comparisons involving several group means.
Regression and ANOVA models are closely related and can be analysed
within the same framework. The major difference is that for ANOVA, all
the independent variables are treated as being nominal; whereas for
regression analysis, any mixture of measurement scales (nominal,
ordinal, or interval) is allowable for the independent variables.
Examples of ANOVA used in exposure assessment can be found in Liu et
al. (1994a), who used ANOVA models to examine the effects of wind
speed, ozone concentrations, human subject and interaction between
wind speed and concentration on the performance of an ozone passive
personal sampler.
Estimation for both ANOVA and linear regression models consists
of obtaining point estimates for the parameters that describe the mean
exposure under a certain set of conditions. Part of the estimation
procedure is to determine how well the model fits. The first
diagnostic is to examine the residual error (residual). A residual is
simply the difference between the exposure estimated by the model and
the actual exposure. By examining the residuals, one can determine for
what ranges of actual exposures or conditions the model does not fit
well, and use this to decide how to adjust the model.
The simplest design (and corresponding model) occurs when
measurements are taken while varying only one possible factor over a
finite, k, number of levels. Consider PM 2.5 exposure; let the factor
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