Statistical Methods in Medical Research 4ed

labelled antigen so that the count is low. The dose±response curve is typically
sigmoid in shape, with an upper asymptote, D, to the mean response, at zero
dose, and a lower asymptote, C, at very high doses. If the mean bound count at
log dose x is U, the quantity
U C
Y ˆ ln …20:10†
D U
is analogous to the logit transformation for proportions (14.5) and it is often
(though not always) found that Y is approximately linearly related to x.
In an immunoradiometric assay (IRMA) the roles of antigen and antibody are
interchanged, but the principles are otherwise the same as for RIAs.
RIAs are used routinely in clinical chemistry, and specimens from many
different patients may be assayed against the same standard. The precision of
RIAs is relatively high, and it is common for responses to be made at a single
dose of each test preparation, for comparison with a standard curve determined
from readings at several doses. This design may achieve potency estimates of
adequate precision, but it permits no test of parallelism, and should only be used
if the assay validity has already been established by a larger design.
Although potencies are often estimated by eye, a formal approach, providing
estimates of error and validity tests, is preferable. Finney (1978) gives details of
such an approach, and the author also (Finney, 1979) describes the desiderata
for computer programs intended for the routine analysis of RIAs. See also
Govindarajulu (2000). The statistical methodology is a direct extension of that
described earlier in this section, with some additional features. In particular: (i) the
lower and upper asymptotes, C and D, need to be estimated from the data (counts
will usually have been observed at each of the extremes of dose level); and (ii) the
variance of the observed count u is likely to increase with the mean U. Ideally, u
might be expected to follow a Poisson distribution, but there is often some
additional source of variation, causing the variance to be greater than the mean.
A full analysis may assume a normal approximation, but the need to estimate the
asymptotes and to take account of the logit transformation (20.10) leads to an
iterative least squares or maximum likelihood solution, as in §12.4. The relationship
of var(u)toUmay be estimated as part of the solution, or it may be possible to
assume some functional relationship on the basis of past experience.
Combination of assays
20.2 Parallel-line assays 723
Assays to determine the relative potency of a particular (S, T) pair may
be replicated, as in other scientific experiments, to improve precision and
extend the validity of the results. More specifically, T may be intended as a
future standard preparation, and collaborative studies to compare T with the
previous standard S may involve many different laboratories.