Revival: Biological Effects of Low Level Exposures to Chemical and Radiation (1992)

BIOSTATISTICAL APPROACHES TO ASSESSMENT 131

The upper normal limit is obtained similarly from Table 7.5B:

upper normal limit = (10 x row number) + (column number)

For example, if the expected number of cases is 15.21, then the observed
number of cases should be between 8 and 23, inclusive, at least 95% of the
time. Observed values below 8 or above 23 constitute significant L or H
results, respectively.
To find 95% confidence limits for the true expected number as a function
of the observed number, convert the observed number to a row and column

via the formula

(observed number) = (10 x row number) + (column number)

Then the confidence limits for the true expected number are

lower limit = Table 7.5B entry for (observed number - 1)

upper limit = Table 7.5A entry for (observed number)

If (observed number) of cases is 30, then (observed number—1) is 29, so
that

lower limit = Table 7.5B entry for (29) = 20.24

upper limit = Table 7.5A entry for (30) = 42.83

To get a confidence interval for an SR, suppose the observed number of
cases is 30 and the expected number is 15.21. Then the SR is observed/
expected = 30/15.21, nearly double, and the confidence interval (Cl) for
the SR is

95% Cl for SR = (95% Cl for true expected)/(expected)

= (20.24,42.83)/15.21

= (1.33,2.82)

Since the lower limit of the Cl is greater than one, the result is H. Alterna­
tively, the observed 30 cases exceeds the upper normal limit of 23, so the
result is H. As a third approach, the hypothesized expected number of 15.21
is lower than the lower confidence limit of 20.24, so again the result is H.
These three methods give the same result, but emphasize different aspects.

Probabilities of Study Outcomes

Beaumont and Breslow discuss power calculations in occupational set­

tings when the Poisson distribution is involved.10 As a general rule, the

larger the expected number, the greater the power to detect H or L effects.

When the expected number is less than 3.69, then even an observed value of