DRUG TOXICITY
The use of plasma drug concentrations in the
clinical assessment of the risk of drug toxicity has
been discussed in a number of places in the preced-
ing sections. Plasma drug concentrations can also
provide useful information in the diagnostic evalua-
tion of drug toxicity.
Drug toxicity must be considered whenever a
patient manifests symptoms or signs that could be
attributable to a drug that the patient is taking. The
question to be resolved is whether the clinical
findings are due to the drug or from some other
cause. As with other diagnostic queries, this
question is answered in terms of probabilities. To
calculate the probability of drug toxicity being the
cause of the clinical findings, the following form of
Bayes’ formula is used,
P
[
drug toxicity
] =
P
[
sick
/
drug
]
P
[
sick
/
drug
] +
P
[
sick
/
other
]
where
P[sick/drug]
is the probability of developing
the findings while receiving drug therapy (i.e., the
risk of drug toxicity) and
P[sick/other]
is the
probability of developing the findings for some other
reason.
Referring to the frequency plot for toxic effect
risk versus plasma drug concentration shown in
Figure 12.10, for a measured drug concentration of
100 µg/ml, the probability of developing mild
nausea due to drug therapy is 0.66. For the sake of
this example, the estimated probability of developing
mild nausea as a result of the illness under
treatment, as a result of intercurrent illness, or in
response to a dietary indiscretion is 0.10. There-
fore, the probability that drug toxicity explains the of
clinical finding of mild nausea is,
P
[
drug toxicity
] =
0.66
0.66
+
0.10
=
0.87
What if the clinical finding is a new arrhythmia? If
the probability of the patient developing the arrhyth-
mia for reasons other than drug toxicity is estimated
to be low, say 0.02, then
P
[
drug toxicity
] =
0.10
0.10
+
0.02
=
0.83
where 0.10 is the probability of developing an
arrhythmia given a plasma drug concentration of 100
µg/ml. For both these cases, precision in the
characterization of the condition being evaluated is
essential. For example, if the new arrhythmia were
of a different type, one less often associated with
drug use (say, a probability of 0.02) and more often
evolving from the arrhythmia under treatment (say, a
probability of 0.20) then,
P
[
drug toxicity
] =
0.02
0.02
+
0.20
=
0.09
making drug toxicity a much less likely cause of the
finding.
These probabilities can also be generated using
the posterior probability approach discussed in
Chapter 3. For that purpose the prior probability
must be calculated. This is done using the preceding
form of Bayes’ formula but here the probability of
developing the clinical findings while receiving drug
therapy is the probability as found in all patients
receiving the drug at the dose given the patient; i.e.,
without reference to the plasma drug concentration.
Say that probability is 0.025 in the case of a new
arrhythmia. Then,
P
[
pre
] =
0.025
0.025
+
0.02
=
0.56
Recall that the likelihood ratio from of Bayes’
formula is,
P
[
post
] =
P
[
pre
]
likelihood ratio
P
[
pre
]
likelihood ratio
+ (
1
−
P
[
pre
])
In this formula, the value of the likelihood ratio is
equal to the ratio of the drug toxicity risk estimates.
The risk estimate for a patient with a plasma drug
concentration of 100 µg/ml is 0.10 and the risk esti-
mate without reference to the plasma drug concen-
tration is 0.025, so the likelihood ratio is 4. Thus,
P
[
post
] =
0.56
%
4
0.56
%
4
+
0.44
=
0.83
which is equal to the value calculated previously. In
fact, the probability estimates will always be equal
because the calculations are algebraically equivalent
so it does not matter which approach is used.
REFERENCES
Some of the text in this chapter has been excerpted from
Noe DA. 1994.
A Short Course in Clinical Pharmacoki-
netics.
Williams & Wilkins, Baltimore.
Brown GR, Miyata M, and McCormack JP. 1993. Drug
concentration monitoring. An approach to rational
use. Clin Pharmacokinet 24:187.
Bruguerolle B. 1998. Chronopharmacokinetics. Current
status. Clin Pharmacokinet 35:83.
Cockcroft DW and Gault MM. 1976. Prediction of creati-
nine clearance from serum creatinine. Nephron 16:31.
Drug Therapy
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