Environmental Health Criteria 214

HUMAN EXPOSURE ASSESSMENT
PM 2.5 concentration (Y) was regressed against outdoor air
concentrations ( X 1 ), smoking rates ( X 2 ), cooking durations
( X 3 ), air exchange rates ( X 4 ) and house volumes ( X 5 ) to
determine the major factors affecting indoor PM 2.5 concentrations
(Ozkaynak et al., 1996).
Further information on ANOVA and linear regression may be found
in Ott (1995), Kleinbaum et al. (1988) and most introductory
statistics textbooks.
4.4.4.2 Logistic regression
An approach which is different from the linear or additive
relationship described above is to consider a categorical outcome for
exposures, e.g., exposure measurements grouped into ordinal levels
such as low, medium and high. When the response is binary, that is, if
an exposure is either present or absent (i.e., a threshold effect),
then a linear relationship is not appropriate. In this case, we must
use an alternative model, for example:
logit P(Y = 1) = alpha + ß 1 X 1 + ß 2 X 2 + ... + ß k X k
where the logit function is logit (x) = ln ( x/(1- x)), the
function P(Y = 1) denotes the probability that the response variable
Y will take on the value 1 (denoting "success"), and the role of
epsilon from the previous model is taken by modelling the parameter
representing the probability that Y = 1, as opposed to Y itself.
This model is known as logistic regression. In this model, alpha
denotes the baseline odds for exposure given that the associated
factors, X ..., X k , are zero, and ß i denotes the change in the
log-odds that the response is Y = 1 given a 1-unit increase in
X i . This approach can be adjusted to allow for the analysis of
other types of categorical outcomes (McCullagh & Nelder, 1990). One
common parameter which describes logistic regression results is the
odds ratio. For a particular set of covariates, X i, the odds of
the event occurring ( Y = 1), is exp(ß X i) . To compare the odds
ratio for two situations, compute the first set of odds and take its
ratio over the second odds. Usually, the situations will be identical,
except that the covariate of interest will be zero for one of the
sets. For example, if the model for the linear combination of
covariates is 1.3 +2.5 X, then the odds ratio for Y = 1, comparing
X = 1 versus X = 0, is e (1.3+2.5) /e 1.3 . A similar computation can be
done when X is a continuous random variable, for two different
values of X. In exposure assessment, a logistic regression model
could be used to evaluate the importance of demographic or temporal
factors on the likelihood that an individual will engage in an
activity such as applying pesticides.
4.4.5 Sample size determination
Hypothesis testing attempts to determine if the data reject or
fail to reject a particular (null) hypothesis. The test is based upon
statistical considerations, and hence just reports how likely or
unlikely the null hypothesis is. If there is minimal information, it
will be difficult to statistically reject the null hypothesis; hence,
sample size calculations are done in order to ensure that there is
sufficient information from which to make a decision. The decision is
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