for PSA concentration as a function of prostate size
as modeled by Oesterling
et al.
(1993). The lines in
the figure can be used like linear discriminant
functions for screening classification. For instance,
to achieve a screening specificity of 0.90, PSA
concentration and prostatic volume measurement
pairs above the “90 percentile” line would be
considered screen-positive and those below would be
considered screen-negative. Alternatively, the PSA
concentration and prostatic volume measurements
can be used to derive a discriminant score that is
used to classify result pairs. The most appropriate
algebraic form for the discriminant score is a linear
equation. The algebraic form that is actually used
clinically, however, is the ratio of PSA concentra-
tion to prostate volume, referred to as the PSA
density. Evaluation of this ratio in a modest number
of men indicates that a ratio of 0.05 has a sensitivity
of 0.95 for cancer confined to the prostate and a
specificity of 0.70; a ratio of 0.10 has a sensitivity
of 0.80 and a specificity of 0.95 (Benson
et al.
1992). This is far better screening performance than
that achieved by the PSA concentration. The speci-
ficity estimates are consistent with the data reported
by Oesterling
et al.
(1993) in their large study of
PSA concentration and prostate volume (Figure
11.7; the 75th percentile line approximates a PSA
density of 0.06 and the 95th percentile line approxi-
mates a PSA density of 0.11). The sensitivity esti-
mates are similar to those found for PSA density in a
large study reported by Catalona
et al.
(1994a): 0.71
and 0.90 for PSA densities of 0.05 and 0.10,
respectively. The specificity estimates reported by
Catalona
et al.
(1994a) are lower than those reported
by Benson
et al.
(1992). However, the study by
Catalona
et al.
(1994a) was confined to men with
PSA concentrations above 4.0 µg/L or with abnor-
mal digital rectal examinations, resulting in a strong
bias toward higher values of PSA density among
men with BPH, and thereby leading to significant
underestimation of the specificity. (Unfortunately,
this design limitation is not widely appreciated and
the low specificity estimates found in the study are
cited as evidence that the PSA density is not a better
screening study than PSA concentration).
It is sometimes possible to increase the clinical
information provided by a laboratory measurement
by interpreting the result in the context of a physiol-
ogic model. An example of this would be the inter-
pretation of arterial blood gas measurements using a
quantitative model of acid-base metabolism. Model-
based interpretation can also be used to improve the
discriminatory power of a screening study. In
cancer screening, a model of tumor growth is a
logical choice. As a tumor grows, the amount of
marker substance released by it usually increases;
although this will not be so if the growth results
from, or is accompanied by, malignant evolution of
the cancer with reduction in the expression of the
marker. As the rate of entry of the marker into the
circulation increases, the plasma concentration of the
marker increases. If the marker is followed over
time, the steady increase in its concentration can be
demonstrated and the presence of the growing tumor
inferred. An advantage of this approach is that an
upward trend in marker concentration may be detect-
able at concentrations of the marker that are below
what would otherwise be the critical value for the
marker. Hence, a cancer can be detected when it is
smaller. A disadvantage of the approach is that an
individual must be tested a number of times over an
interval of time long enough to allow for a trend in
marker concentration to be detected.
In screening for prostate cancer, the trend in
PSA concentrations over time is called the PSA
velocity. It is usually evaluated as the average of two
consecutive measurements of the rate of change of
the PSA concentration. Studies of the variability of
PSA concentration in healthy men and in men with
BPH indicate that an interval of at least a year
between concentration determinations is desirable
when computing the rate of change in the concentra-
tion (Carter
et al.
1995, Kadmon
et al.
1996). That
Cancer
11-11
Figure 11.7
Plasma PSA concentration as a function of
prostate volume. The dots represent the observed data.
The lines are contours of the frequency distribution as
calculated based on a lognormal statistical model of PSA
values. Reprinted Oesterling JE, Jacobsen SJ, Chute CG,
Guess HA, Girman CJ, Panser LA, and Lieber MM. 1993.
Serum prostate-specific antigen in a community-based
population of healthy men. JAMA 270:860.
