Cancer Deaths among Radiation Workers
911
We will assume that we can find an appropriate control population and that
it is identical {o the radiation work force execpt that it is not occupationally
exposed to radiation. In practice it will probably be necessary to draw the
control group from among those radiation workers with the lowest exposures.
In this way we can be sure that the control and the exposed populations have
been subjected to the same selection procedures.
We must considerthe confidence that we will be able to place on the rejection
of the null hypothesis (that there is no risk involved in exposure to radiation
and consequently that the mean numbers of cancer deaths will be equal in the
control and exposed groups). This is normally assessed as a significance level
«x, defined such that « is the probability that we will reject the null hypothesis
whenit is true. The corresponding confidence limit is expressed as a pereentage
and is (1a) x 100.
‘
We must also consider the powerof the test we apply to the acceptance or
rejection of the null hypothesis. The power (1 —f) ofa test is defined such that
8 is the probability that we will accept the null hypothesis whenit is false.
formulating the significance level and the powerof the test as in Armitage
(1971), we find that the observed mean numberof exccss cancer deaths (52%) is
significant at the PY level (P = 100e) if
88> U,,0 \(2/n)
(2)
where U,,, is the standardized normal deviate cxecededin the positive clirection
with probability «, o is the standard deviation of the population mean (taken
to be the same in exposed and control groups) and 7 is the numberof observations which, in our case, is the numberof years, since there is one ‘observation’
per year. A differcnee in the numberof cancer deaths between the two groups
will be detected with a probability 1—f if the truc mean difference (§;.) satisfies
Spe > (Oat Tyg) o (2/22).
(3)
Ifwe now put du =m, the truc number of radiation-induced cancers, and
rearrange eqn (3) we have an expression for the time required for a survey to
have probability | —8 of rejecting the null hypothesis at the a significance level:
1 > AO. + Tyg)? 0?/m?.
(4)
In these expressions o* (the variance) has been taken to be equal to the mean
number of non-raciation-induced cancer deaths; that is, we have assumed a
Poisson distribution.
Table & has been compiled to showvalues of x for « = 0-05 and 0-2, B = 0-5
and m as given in table 2, column If; that is, the times necessary to have a 50%
chance of showing a positive radiation risk at the 5% and 20% significance
levels. ‘The values in this table may be interpreted another way. Rearranging
eqn (2) with » on the left hand side, we sce that, if after » years the observed
mean execss cancer deaths ave as in table 2, column I*, the survey shows
positive radiation risk at the 5% (or 20%) level. ‘Chis is an appropriate interpretation once the survey is running since we will then have an observed mean
difference and will ask what is its significance.