Chemistry Reference
In-Depth Information
5 DATA ANALYSIS
incidence data based on a total population are avail-
able, the life-table method (see Section 1) can be used
to estimate incidence rate ratios between the exposed
group and the total population. The rate ratios for
groups with different dose levels are compared with
the average dose in the groups to yield a dose-response
relationship.
If the data show an apparent increase in the response
with increasing dose, a statistical test is used to deter-
mine whether it is likely that the data have emerged this
way just by chance. A confi dence interval for the dose-
response relationship can also be calculated. These cal-
culations are simplifi ed if any of the three mathematical
transformations mentioned in the following are used.
The shape of the dose-response curve is often sigmoidal
as a cumulative normal distribution. Such a curve can be
transformed to a straight line by probit transformation.
Another method of mathematical transformation that
produces a sigmoidal dose-response curve for binary
data is the logit transformation (Ashton, 1972; Cox, 1970).
This has been used to assess the prevalence of prenatally
induced CNS effects of methylmercury (Figure 4). It can
be adjusted for a background prevalence. However, the
dose range may represent only part of this curve, which
would then be either concave or convex. For some out-
come variables, there may be a “ceiling,” so that a result
cannot exceed a certain level. Vice versa, other outcomes
may exhibit a “fl oor” effect, where the result cannot be
recorded below a certain level. These properties may
affect the shape of the dose-effect curve. The assump-
tion of a“fl oor” and a straight line dose-response is the
basis for the “hockey stick” method (Figure 4).
Data analysis is the stage in an epidemiological study
where the data are arranged and calculations made so
that conclusions can be drawn. In descriptive studies,
the conclusion would be in the form of a description
of the occurrence of a variable in the population group
studied. In an analytical or intervention study it would
be in the form of rejecting or accepting a hypothesis
about an association between an exposure and an effect.
If the study was designed for ascertaining a dose-effect
or dose-response relationship, the conclusion may be
that this has or has not been found, and the result is
often expressed as a mathematical relationship with
confi dence intervals. In drawing these conclusions, a
number of statistical techniques are used, which will
not be discussed in detail here. The reader is referred
to more detailed texts, such as Jewell (2004).
We can express the dose as population dose, which
is the sum of all individual doses in a population. This
is the approach often used in radiation protection,
and basically it assumes a linear dose-response rela-
tionship down to very low doses. A certain popula-
tion dose is assumed to be associated with a certain
number of affected cases. If the dose data are in the
form of environmental measurements of emissions, it
may also be relevant to estimate the dose commitment.
This is the estimated total future population dose that
will arise from the emissions. Quantitative effect data
can also be expressed as distributions.
When the effects are measured as the number of cases
of a particular disease (e.g., primary liver cancer) and
Abnormal
2
1.0
0.8
0.6
0.4
0.2
0.0
Normal
17
6
4
2 2
2
2
1
5
10
20
50
150
400
1100
Maternal hair conc. (Hg, ppm)
FIGURE 4
The frequency of retarded walking in prenatally exposed children versus the estimated maxi-
mum body burden in the mother during pregnancy, as expressed in terms of the hair-mercury concentration:
(Straight line) “Hockey stick” method. (Curve) Logit analysis. The data are taken from Marsh
et al.
(1979) and
clarkson
et al.
(1981). +, Motor retardation is defi ned as failure to walk by the age of 18 months.
