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Antimicrobial Agents and Chemotherapy, May 2000, p. 1302-1308, Vol. 44, No. 5
0066-4804/00/$04.00+0
Copyright © 2000, American Society for Microbiology. All rights reserved.
Combinations of Artemisinin and Quinine for
Uncomplicated Falciparum Malaria: Efficacy and
Pharmacodynamics
Peter J.
de
Vries,1,*
Nguyen Ngoc
Bich,2
Huynh
Van
Thien,3
Le Ngoc
Hung,2
Trinh Kim
Anh,2
Piet A.
Kager,1 and
Siem H.
Heisterkamp4
Division of Infectious Diseases, Tropical
Medicine and AIDS1 and Department of
Clinical Epidemiology and Biostatistics,4
Academic Medical Center, Amsterdam, The Netherlands, and
Tropical Diseases Clinical Research Center, Cho Ray
Hospital, Ho Chi Minh City,2 and Lam
Dong Provincial Hospital II, Bao Loc, Lam Dong
Province,3 Vietnam
Received 17 June 1999/Returned for modification 31 October
1999/Accepted 9 February 2000
 |
ABSTRACT |
Combinations of artemisinin and quinine for uncomplicated
falciparum malaria were studied. A total of 268 patients were
randomized to 7 days of quinine at 10 mg/kg of body weight three times
a day (Q) or to artemisinin at 20 mg/kg of body weight followed by 3 (AQ3) or 5 (AQ5) days of quinine. Recrudescence rates were 16, 38, and
15% for the Q, AQ3, and AQ5 groups, respectively (P < 0.001). Recrudescence was associated with shorter parasite clearance time (PCT) and longer treatment after the blood smear had become negative (eradication time). However, classification of patients to
outcome
recrudescence or radical curewas correct in only 77% of
patients. The population kinetics of the parasitemia was estimated with
nonlinear mixed-effect models. Several models were tested, but the best
model was a monoexponential decline of the parasitemia in which the
mean parasite elimination half-life was shorter after artemisinin (5.1 h; 95% confidence interval [CI], 4.9 to 5.2 h) than after
quinine (8.0 h [95% CI, 7.5 to 8.3 h]). Attempts to simulate the
initial increase of the parasitemia did not result in better models
with a biologically plausible interpretation. Recrudescence was
associated with slower parasite clearance and a higher simulated
terminal parasitemia (Pterm). The
classification of patients to outcome groups based on
Pterm was correct in 78% of patients. The data
suggest that parasite strains with reduced sensitivity to quinine are
prevalent in Vietnam, with slower parasite clearance and consequent
recrudescence. A single dose of artemisinin induces rapid parasite
reduction and lowers the value of Pterm, but to
prevent recrudescence, this should be followed by quinine for at least
3 days after parasite clearance, or 5 days in total.
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INTRODUCTION |
Combination of drugs is an important
contribution to the rational design of anti-infective treatment
regimens. There are several reasons for this, among which are drug
resistance, pharmacological arguments, and arguments concerning the
therapeutic index. Combination of antimalarial drugs has been studied
and applied for more than 30 years. To date it has been felt that such
combinations should contain an artemisinin drug (16). The
theoretical risk of selection of resistant strains is probably less
when the biomass of parasites is eliminated early, and thus combination
with an artemisinin drug may retard the development of resistance
(15). However, there are other arguments in favor of
combination with artemisinin drugs. They induce rapid clinical recovery
and parasite clearance, and this feature might allow for shortening of
treatment courses of drugs with a moderately short half-life, such as
quinine and tetracyclines. This would enhance compliance with therapy,
and, in the case of quinine, lead to a shorter duration of symptoms of cinchonism.
There are also arguments for why artemisinin drugs should not be used
alone. Since the introduction of the artemisinin drugs, it is known
that recrudescence is frequent when monotherapy is applied
(5). Initially this was explained by the short residence time of artemisinin, but recently another argument was added. It was
shown that after repeated dosing, the concentrations of artemisinin in
plasma decline, which may limit the efficacy of monotherapy (2,
6).
Artemisinin and its derivatives are often used in combination with
mefloquine, especially in Thailand, where multidrug resistance has
become a problem (9, 10, 18). Due to its slow elimination, mefloquine can be administered as a single dose or a split dose. Nowadays in Vietnam, mefloquine is used as the first choice in combination with artemisinin or artesunate for treatment of confirmed falciparum malaria (8, 13). However, other regimens, some adequate and some inadequate, are also being applied (4).
Quinine is also used for the treatment of uncomplicated malaria
(1, 7). It is cheap, widely available, and generally
considered to be effective, but nowadays is less popular than the
artemisinin drugs. The combination of quinine and artemisinin has been
studied to a limited extent only, although it offers a relatively cheap and effective treatment. Quinine doesn't have as long a residence time
as mefloquine, and therefore repeated dosages are required. The
question is how many dosages are required, or, in other words, what is
the minimum duration of quinine therapy after a starting dose of artemisinin?
Previously we reported on the interim analysis of a study of treatment
regimens with a single dose of artemisinin combined with quinine or
doxycycline in comparison with quinine monotherapy (3).
Three days of doxycycline in combination with a single dose of
artemisinin appeared unsatisfactory. To investigate whether this could
be improved, doxycycline was replaced by quinine and treatment was
extended to 5 days after the initial dose of artemisinin. This
restructured the study into an open-label comparison of 7 days of
quinine monotherapy (Q) and a single dose of artemisinin followed by
either 3 (AQ3) or 5 days (AQ5) of quinine.
The reasons for comparing these three regimens were as follows. Quinine
monotherapy for 7 days was the standard recommended treatment in
Vietnam, and in many areas where malaria is endemic, it still is. As
mentioned above, quinine monotherapy has several drawbacks: drug
administration longer than 3 days suffers from poor compliance, because
cinchonism starts after a few days of treatment, when the patient is
already recovering, and because of declining efficacy of quinine in
Southeast Asia. It was hypothesized that a combination with artemisinin
would retain the benefits and overcome the drawbacks. Regimen AQ3 was
kept in the study because at the interim analysis, as reported
previously, this regimen was comparable to quinine monotherapy, and we
wanted to increase the sample size as originally planned
(3). AQ5 was added to the study to establish its clinical
efficacy, but also because in this way the three regimens were
principally different with respect to the kinetics of the parasite
clearance. Mathematical models that describe the parasitemia over time
are difficult to design (17), but some characteristics of
the parasitemia during treatment may have a clinical meaning and can be
used for prediction of recrudescence (15). These
characteristics include the initial parasitemia, the elimination rate
of parasites, and the duration of treatment. The three regimens in the
study differed from each other in two important aspects, namely, in
antiparasitic activityartemisinin versus quinineand in duration of
therapy; initial parasitemia was expected to vary equally in each
treatment group.
(Part of this information was presented at the 2nd European Congress on
Tropical Medicine, September 1998, Liverpool, United Kingdom.)
| |
MATERIALS AND METHODS |
All patients were admitted to the hospital and discharged only
after full clinical recovery, parasite clearance, and completion of
drug treatment. Intake of drugs was supervised. The methods of this
study have been described in detail elsewhere (3). Informed
consent was obtained from all patients who participated in the study
before randomization. The study protocol was approved by the medical
ethics committee of the Academic Medical Center Amsterdam and the
boards of Cho Ray Hospital, Ho Chi Minh City, and Bao Loc Provincial
Hospital. In aggregate, patients admitted to Lam Dong Provincial
Hospital II, Bao Loc, Vietnam, for uncomplicated falciparum malaria,
with a parasite density of between 1,000 and 100,000/µl, and between
8 and 65 years of age were included. Among others, exclusion criteria
included inability to take oral medication; allergy to one of the study
drugs; and verbal confirmation of the intake of quinine in the previous
12 h; artemisinin or derivatives in the previous 24 h; or
mefloquine, tetracycline, or doxycycline during the previous 7 days. As
reported previously, traces of quinine could be detected in many
patients in this area, but concentrations were low. In this study, we
did not assess prereferral use of effective antimalarial agents, but
this was probably not a significant bias, because antimalarials such as
artemisinin and mefloquine were not available outside the official
health sector. Examination of the original sample size of 360 patients,
aimed at detecting a difference in cure rate in three regimens with
statistical significance at 
= 0.05 and 
= 0.2 (power,
0.8), was completed, and after deduction of the artemisinin- and
doxycycline-treated patients, 268 patients were available for the
analysis presented here.
Treatment.
The patients were treated with one of the
following regimens: quinine at 10 mg/kg of body weight three times a
day (t.i.d.) orally (250-mg quinine sulfate tablets; Pharmaceutical
Factory no. 24, Hanoi, Vietnam) for 7 days (Q), or a single dose of
artemisinin at 20 mg/kg of body weight orally (250-mg capsules; ACE
Chemie, Maarssen, The Netherlands) followed after 6 h by quinine
at 10 mg/kg of body weight t.i.d. orally for either 3 (AQ3) or 5 (AQ5) days.
Closed envelopes, containing the computer-generated randomization
codes, were consecutively drawn after inclusion. A total of 120 randomized numbers were originally allocated to each of the three
treatment regimens. The numbers of the original artemisinin-doxycycline group were used for the AQ5 group. Toward the end of the study, the
regimens Q and AQ3 were discontinued, and the study continued with AQ5
as the only treatment regimen for the last 36 consecutive patients. In
this way, the three groups would be approximately the same size at the
end of the study.
The patients of groups Q and AQ3 who had been analyzed in the previous
report were included again in this analysis. The reasons
for this are
that the numbers of patients in these groups had
increased since then
and the interpretation of the kinetic data
of parasite clearance had
not been performed yet. Besides, the
change of treatment regimens was
regarded not to introduce bias
because the procedures for inclusion had
not been
changed.
Clinical assessments.
All patients were admitted to the
hospital. Vital signs were recorded every 8 h, and a complete
physical examination was performed every day. A full blood count and
liver tests were performed prior to patient inclusion and on the third
day thereafter. Giemsa-stained thick and thin blood smears were
obtained for identification and counting of asexual parasites by light
microscopy prior to patient inclusion. The parasitemia was then counted
every 8 h until three negative smears had been obtained.
Hereafter, blood smears were taken 7, 14, 21, and 28 days after the
start of treatment on an outpatient basis. The parasite density was
expressed as the number of parasites per microliter of blood,
calculated as the ratio with the leukocyte count in 100 microscopic oil
immersion fields in the thick smear or with the erythrocyte count in
the thin smear.
Fever clearance time and parasite clearance time (PCT) were defined as
the time from initiation of treatment to the first
of three consecutive
normal temperature readings (<37°C axillary)
or negative blood
smears, respectively. Clinical and parasitological
outcome were
assessed separately. Clinical failure was defined
as no improvement,
necessitating additional treatment within the
first 48 h of
treatment (early failure) or after 48 h of therapy
(late failure).
Additional therapy consisted of artesunate with
quinine or
mefloquine.
Parasitological response was defined, independently from clinical
outcome, as follows. Radical cure means parasite clearance
by day 7 without recrudescence up to day 28. R1 represents initial
disappearance
of parasites with recrudescence before day 14 (early
R1) or from day 14 to day 28 (late R1). This is a conventional
subdivision with the
notification that late recrudescence cannot
be discriminated from
reinfection in our situation. R2 represents
an initial decrease of
parasite count to <25% of the initial value,
followed by resurgence,
without clearance by day 7. R3 represents
no response or a small
decrease in parasitemia to not less than
25% of the initial value,
assessed at 48 h after initiation of
therapy.
Population kinetics of the parasitemia.
The population
kinetics of the time course of the parasitemia was estimated by using
several nonlinear mixed-effect models (see Appendix). These models
estimated the kinetic parameters of the time course of the parasite density.
The initial parasitemia [
P(0)], the duration of effective
drug treatment, and the elimination rate converge in a single value:
the parasitemia at the end of the treatment
(
Pterm). The end of
therapy was defined as the
time of the last dose of quinine plus
8 h, which represents the
duration of one dosing interval.
Pterm can be
derived from the kinetic models of the
parasitemia.
At the end of treatment, the replication of parasites leading to
recrudescence can be simulated as an exponential increase,
the
replication rate being the slope of the line connecting
Pterm and the parasite density of the
recrudescence on a semilogarithmic
plot. This value is a rather crude
estimate, connecting a simulated
value and a single data point.
However, it may serve as a reference
to other
literature.
Another parameter, the eradication time (ET), was defined as the
duration of treatment after parasite clearance. Thus, PCT
plus ET
equals the duration of effective therapy. ET was introduced
to evaluate
if this could be a better predictor for recrudescence
than PCT and if
this would be useful in individualizing the duration
of therapy in
future
studies.
Statistical analysis.
The individual data were analyzed with
the aid of the statistical package SPSS (version 8.0; SPSS Inc.,
Chicago, Ill.). All statistics concerning parasitemia were calculated
according to its log transformation. The clinical outcome was analyzed
with contingency tables and 
2 tests with continuity
correction for categorical parameters and with analysis of variance
(ANOVA) or nonparametric tests for numerical parameters. The effects of
treatment and kinetic parameters on the occurrence of parasite
clearance or recrudescence were analyzed by logistic regression and in
a Cox proportional hazard model. Statistical significance was accepted
at P < 0.05.
| |
RESULTS |
Clinical assessment.
Some baseline patient characteristics are
shown in Table 1. There were no
significant differences between the groups. Some patients with
hyperparasitemia had been introduced into the study. They were not
excluded from the analysis, because there were no complications of
malaria. The outcome is shown in Table 2.
In two patients, hemoglobinuria was observed after 24 h of
treatment. This was regarded as an adverse effect of quinine, and the
patients were withdrawn from the study and treated with artesunate.
These patients could not be evaluated for clinical and parasitological outcome. Other side effects were not considered to be a clinically significant problem in this study. Cinchonism and malaria-related complaints were reported in all three groups.
Four patients left the hospital before any endpoint was reached. There
was one early clinical failure, as well as one late
clinical failure
with a parasitological R3 response, both in regimen
Q. These two
patients needed additional intravenous
therapy.
The recrudescence (R1 response) rate in regimen AQ3 was significantly
higher than in the other two regimens. When the recrudescence
rate was
calculated in a best-case or worst-case scenario (i.e.,
all patients
who were lost to follow-up classified as radically
cured or as
recrudescent, respectively), the difference between
regimen AQ3 and the
other two regimens was still significant (
P = 0.007 and
P = <0.001, respectively). The median days of
diagnosing
recrudescence were day 21 (earliest, day 11; latest, day 28)
in
group Q7, day 18 (earliest, day 7; latest, day 27) in group AQ3,
and
day 23 (earliest, day 17; latest, day 28) in group AQ5. The
proportional cumulative recrudescence of patients, including those
who
were lost to follow-up between days 7 and 28, is shown in
Fig.
1. Recrudescence was less frequent in
groups Q and AQ5 than
in regimen AQ3 (relative risk for Q and AQ5
versus AQ3, 0.37;
95% CI, 0.19 to 0.72).
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FIG. 1.
Kaplan Meier curve of the cumulative recrudescence of
P. falciparum after treatment with quinine monotherapy for 7 days (Q [ ]) or a single dose of artemisinin followed by either 3 days of quinine (AQ3 [ ]) or 5 days of quinine (AQ5 [ ])
(P < 0.001; log-rank test).
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The mean fever clearance times were not different among the three
treatment groups: 47 h (95% CI, 41 to 53 h) in regimen Q,
41 h (95% CI, 37 to 46 h) in regimen AQ3, and 43 h
(95% CI, 38
to 47 h) in regimen AQ5. The mean observed PCTs were
62 h (95%
CI, 57 to 67 h), 41 h (95% CI, 38 to 44 h), and 42 h (95% CI,
39 to 46 h) for regimens Q, AQ3, and
AQ5, respectively. The observed
P(0), PCT, and ET for
treatment groups and outcome are shown in
Table
3.
Kinetic models.
Population kinetic models of the parasitemia
were fitted with the mixed nonlinear regression program of S-Plus
(version 4.5; Math Soft, Inc., Seattle, Wash.). The buildup of the
models is shown in the Appendix. In two patients of regimen Q with
radical cure, the time series was incomplete and could not be used for the kinetic analysis.
As shown in the
Appendix, model I with a monoexponential decline of the
parasitemia in which the clearance rate depends on the
regimen, yielded
the best fits. The mean estimates of the elimination
half-life
(
t1/2el) in groups Q7, AQ3, and AQ5 were
8.0 h (95%
CI, 7.5 to 8.3 h), 4.8 h (95% CI, 4.6 to
5.0 h), and 5.3 h (95%
CI, 5.2 to 5.5 h), respectively.
The model estimates and derivatives,
specified for treatment and
outcome, are shown in Table
3. Instead
of
the estimated initial parasitemia (expressed as
A in the
formulas),
lag time (
tlag) is presented. This
was calculated according to
formula 4 in the
Appendix. The elimination
rate has been recalculated
in response to
t1/2el. As a reference value for the observed
data,
the PCT was calculated from the kinetic estimates
(PCT
calc), setting
the detection limit at 6 parasites/µl,
the lowest parasitemia
observed in this study. The kinetic models
yielded the estimates
of
Pterm.
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TABLE 3.
Kinetic parameters in an exponential elimination model of
the parasitemia per treatment group and parasitological outcome
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The parasite elimination half-life was significantly shorter in the
groups that started with artemisinin than the quinine
monotherapy group
and was also significantly shorter for the radical
cure response than
for early and late recrudescence (
P < 0.01
for both
effects; two-factor ANOVA). However, there was a strong
interaction
effect between treatment group and outcome. The CIs
of the estimates in
Table
3 give an indication of the respective
differences. There were
also significant differences between the
treatment groups with respect
to PCT, ET, and the estimated value
of
Pterm.
The outcome, i.e., the occurrence of recrudescence, was fitted in a Cox
proportional hazards model. Since PCT and ET are not
independent of
each other, it is not possible to construct a Cox
model which
adequately describes the hazard function based on
both parameters.
However, the effects of PCT and ET are both reflected
in the value of
Pterm. The same was the case for
P(0)
or the estimated
intercept and the estimates of
k (and thus
t1/2el) and
Pterm.
These
were all entered separately into the Cox model.
Pterm was
shown to be a significant predictor of
recrudescence (
P < 0.001;
relative risk for 1 log
increase of
Pterm, 1.7 [95% CI, 1.4 to
2.1]),
but PCT and ET were also associated with a greater hazard
function of
recrudescence (data not
shown).
To evaluate if the duration of therapy could be individualized, the
chance of recrudescence was estimated in a logistic regression
model.
P(0), PCT, ET, and
Pterm were entered
separately in the
model. No more than 80% of cases were classified
correctly as
recrudescence or radical cure, with no important
differences between
the respective
parameters.
Figure
2 illustrates the simulated time
course of the parasitemia in model C. The figure shows that in regimen
Q, as well
as in regimen AQ3,
Pterm is lower for
the patients with radical
cure than for the patients with
recrudescence. The model did not
discriminate between early and late
recrudescence. In group AQ5,
there was no difference between radical
cure and late recrudescence
with respect to
Pterm.
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FIG. 2.
P. falciparum parasitemia simulated by an
exponential elimination model (see text) during treatment with quinine
monotherapy for 7 days (Q) or a single dose of artemisinin followed by
either 3 days of quinine (AQ3) or 5 days of quinine (AQ5). The arrow
indicates the single dose of 1 g of artemisinin, and the shaded
bar indicates the duration of treatment with quinine. L.d., limit of
detection. , patients with radical cure;
............, patients with late
recrudescence; ······, patients with early recrudescence.
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The mean replication rate by which
Pterm evolves
into recrudescence was 0.03 h
1 on a natural logarithmic
scale, which corresponds to a 0.013-log
increase per h, or a 0.6-log
increase per 48-h cycle. There was
a slight difference in replication
half-life between the subgroups
of
recrudescence.
| |
DISCUSSION |
This study shows that for uncomplicated falciparum malaria in
southern Vietnam the combination of a single dose of artemisinin with 5 days of quinine (AQ5) is as effective as 7 days of quinine monotherapy
(Q) and superior to artemisinin with 3 days of quinine (AQ3). The
standard 7-day quinine treatment is still rather effective, with
initial parasite clearance in most patients, but with a rate of
recrudescence of 17%. Recrudescence (by convention an indicator of
resistance) was associated with a slower parasite clearance.
The study was the continuation of a study in which one of the study
arms had been replaced (3). Although this is an unusual procedure, it is unlikely that this introduced bias. The differences between the three regimens added interesting information to the study.
First, regimen AQ3 was confirmed to be less effective than regimen Q7
in terms of preventing recrudescence. The number of patients included
was larger than at the interim analysis, and this increased the power
of the comparisons enough to detect a significant difference. Second,
the analysis of the population kinetics of the parasitemia yielded new
informationnamely that Pterm is an important
determinant of the chance of recrudescence.
In the parasite kinetic model I, three parameters determine the value
of Pterm: the estimate of the initial
parasitemia, k, and the duration of therapy. P(0)
belonged to the inclusion criteria, and therefore it was within a
relatively narrow range. The decline of the parasitemia started earlier
after the artemisinin regimens than after quinine. This illustrates the
fast antiparasitic activity of artemisinin and the great range of the
parasite development cycle on which it exerts its action, which
confirms in vitro findings (14). The impact of the lag phase
on Pterm is small though. The parasite
elimination rate is more important, and when this is slow, the
eradication time, and thus duration of therapy, becomes critical. A
slower parasite clearance, and thus a higher value of
Pterm, was associated with recrudescence in
groups Q and AQ3. It was also shown that the longer eradication time in
regimen AQ5 lowers Pterm and improves efficacy,
in comparison to those of regimen AQ3. In regimen AQ5 itself, there was
no difference between radical cure and recrudescence with respect to
Pterm. The lack of this difference is not clear,
but it should be noted that a late recrudescence could not be
discriminated from a reinfection. In the low-transmission study area,
reinfection is probably infrequent, and an extra argument is that the
replication rate in the cases of recrudescence attained a realistic
value. A more plausible explanation for the lack of difference in
Pterm between radical cure and recrudescence in
regimen AQ5 is at the same time the Achilles heel of the kinetic model.
During the first 24 to 48 h of therapy, the elimination rate
constant is dominated by the effects of artemisinin. In this period,
the exponential decline is an adequate description of the time course
of the parasitemia. However, later, when the clearance rate slows down
to that of quinine, a second elimination constant should be
incorporated into the model. The effect of a second elimination
constant on the parasitemia was not detected by the model, probably
because by that time the parasitemia has decreased to or is under the detection level in most cases. However, there was a significant difference in elimination rates after artemisinin or quinine. The low
precision of the low parasite counts and the relatively high limit of
detection are important limitations for more refined kinetic modeling.
In regimen Q, the slow parasite clearance in patients with
recrudescence suggests reduced sensitivity, and not therapy that is too
short. Reduced sensitivity to quinine expressed as slower parasite
clearance has been observed in Thailand (10). In Vietnam, this phenomenon has been mentioned, but not confirmed (1,
4). This is the first report which shows that parasite strains
that are less sensitive to quinine circulate in Vietnam. In regimen AQ3, there was a difference in clearance rates between radical cure and
recrudescence. Whether this should be explained by a difference in
sensitivities to artemisinin could not be ascertained. This could be
studied further in a study with artemisinin monotherapy.
The mean replication rate corresponded to a 0.6-log increase per 48-h
cycle. This value is comparable to what has been reported in the
literature (15). However, that the replication rates may
differ for certain parasites and/or their hosts cannot be excluded.
The predictive accuracy of our results was limited. Outcome could be
classified correctly in approximately four of every five patients,
based on either PCT, ET, or Pterm. This does not
provide a satisfactory algorithm with which to predict recrudescence or to individualize the duration of therapy. With our current knowledge, the best advice for an individual patient is to aim at an eradication time of at least 3 days with quinine after a single dose of
artemisinin. A design in which patients would be randomized to
eradication time could give a better idea of the possibilities of
individualization of treatment.
The concept that eradication of a pathogen requires a certain minimum
duration of treatment is not new. In the first half of this century,
when dosing schedules of quinine were not yet uniform, the duration of
quinine treatment was guided by the duration of fever in several
recommended treatment regimens for (mainly tertian) malaria
(11). At present, in the era of antibiotic and antiviral
treatment, the required eradication of the pathogen is still a major
determinant of the duration of therapy. Since eradication occurs beyond
our level of detection, we can only make assumptions based on
extrapolation. The process of extrapolation requires a model that
describes the amount of parasites until below the detection level. Such
models are not easily available. Malaria parasites in blood can be
visualized and counted by simple techniques, but the kinetics of
Plasmodium falciparum are not yet fully understood. However,
White recently presented arguments, based on pharmacodynamic concepts,
explaining how mefloquine resistance developed so quickly in Thailand
(15).
The model of parasite elimination applied in this study confirmed these
concepts and showed that they are also valid for artemisinin and
quinine. The model shows that Pterm is an
important determinant for outcome: radical cure or recrudescence. It
suggests that there is a point of no return the actual value of which
may depend on treatment regimen.
The population kinetics model confirmed and quantified several
pharmacodynamic concepts of antimalarial treatment, which are not yet
common practice. These concepts of duration of treatment, eradication
time, and Pterm could only be studied because of
the short residence time of artemisinin and, to a lesser extent, of quinine. With chloroquine and mefloquine, the extremely long residence times preclude accurate estimation of the eradication time.
Nevertheless, we feel that these concepts of parasite kinetics can be
generalized to other drugs also and that they may provide tools for a
rational design of new antimalarial treatment regimens.
We conclude that a 7-day treatment course of quinine is still effective
in the initial treatment of uncomplicated falciparum malaria in
southern Vietnam. However, the rate of recrudescence is rather high,
and the results suggest that this is caused by reduced sensitivity to
quinine. The addition of a single dose of artemisinin increases the
parasite elimination rate, and this benefits the cure rate. It is
prudent to aim at an eradication time of at least 3 days for
single-dose artemisinin-plus-quinine combinations. This rule of thumb
allows individualizing of the duration of treatment of patients,
provided that the parasitemia is determined regularly and that the
parasite clearance time is known. Otherwise after a single dose of
artemisinin, a minimum of 5 days of quinine treatment should be advised.
| |
APPENDIX |
Population kinetics of parasitemia.
The buildup of the
kinetic models started with inspection of the natural logarithms of the
parasite count, P(t), excluding the negative
blood smears. It appeared that for most individuals the decline of ln
P(t) was more or less constant over all 8-h intervals, with the exception of the first interval. In a plot of the
geometric mean values (Fig. A1), this
is less clear, because the tail of the mean curve is distorted by blood
smears becoming negative. So it seemed rational to start with a simple
log-linear (exponential) decline of the parasitemia as the basic model
and build from this. In the formula
|
(1)
|
or
|
(2)
|
A is the estimated initial parasitemia and
k is the elimination rate constant.
k can be
recalculated into a more conventional
elimination half-life,
t1/2el, according to the formula
In a mixed-effects population kinetics model, parameters can be
entered as fixed, which means that they have a certain value,
or be
nonfixed, which means that they can vary at random with
a mean value of
zero. Parameters can also vary depending on another
factor, for
example, the treatment regimen. The formula of such
an exponential
decline of the parasitemia looks like
|
(3)
|
In this way, several models can be applied to the data from all
patients. Models were compared by using the Bayesian information
criterion (BIC) (
12). The method of maximum likelihoods was
used when different models were to be compared. After choosing
the best
model, restricted maximum likelihood was used to estimate
the
parameters.
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|
FIG. A1.
Geometric mean parasitemia of P. falciparum
during treatment with quinine monotherapy for 7 days (Q []) or a
single dose of artemisinin followed by either 3 days of quinine (AQ3
[]) or 5 days of quinine (AQ5 []). The bars indicate the 95%
CIs. A parasitemia measurement below the detection level (negative
blood smear) was entered as 3 parasites per µl.
|
|
A model with random intercepts and slopes and with independent
residuals was tested as well as a comparable model in which
the
residuals,
, are normal with autocorrelation,
. Autocorrelation
in this context means that the repeated measurements over time
are
correlated; in other words, the value of parasitemia at a
certain time
predicts the following value. A third model, model
I, in which
k was allowed to change per treatment regimen, was
also
constructed, and this model gave the best fit (BIC = 4,720.6).
Negative blood smears, with a value of zero, were not included
in the
models. The three models were also fitted to ln
[
P(
t) +
0.5], with zero values included,
but this did not have a significant
effect on the BIC and estimates. In
further modeling, zero values
were excluded from the data
set.
Although the initial parasite counts were not different among the three
treatment groups, a modification of model I was made
in which the
intercept, ln
A, was allowed to change per regimen.
As
expected (treatment groups were similar with respect to baseline
parasite count), this did not improve the fit, so that the variation
of
this term could be interpreted as a random
effect.
In model I, the estimate of
A was greater than the observed
initial parasitemia,
P(0), or put simply, after drug intake,
it
takes some time before the parasitemia starts to decline. This
time
can conceptually be simplified to a lag phase,
tlag. Although
the lag phase is not readily
explained in biologically plausible
terms, in clinical experience, a
lag phase is usually interpreted
as the time until
P(
t) has decreased to values lower than
P(0).
Moreover, the definitions of the in vivo response to
drug treatment
are based on decrease of the parasite count relative to
the initial
parasitemia, thereby ignoring that, in many patients, the
parasitemia
increases initially and that the lag times may be different
for
individuals. When the lag time is incorporated into the kinetic
models, these have the form
|
(4)
|
From this formula it can easily be seen that in log-linear
models,
A and
tlag are
interdependent, which means that a difference
in
tlag also affects the value of
A.
Nevertheless, the models
were fitted, again incorporating
tlag, and this did not yield
better fits than
model
I.
To investigate further if a mathematical function could give an better
description of the initial part of the curve, irrespective
of
biological interpretation, a quadratic term was added to the
basic
model:
|
(5)
|
This quadratic model was worked out analogously to the simple
(log)linear model with normal residuals
with autocorrelation,
with
c and
k changing per regimen, or with only
k changing per
regimen. The latter two models were also
investigated with
k as
a fixed factor. Model II, the model
with a fixed quadratic term,
c, for every patient and a
linear term,
k, variable per patient,
but depending on
regimen, yielded the best fit (BIC = 4,719.4).
In both models I
and II, the estimates of
k were comparable for
regimens AQ3
and AQ5 and different from those for regimen Q. The
difference in BIC
for models I and II was small, and model II
had 1 df more than model I. Another approach to describe the initial
rise in the parasite count was
to build models in which the logarithm
of
t was factored in.
The basic model of this approach looks like
|
(6)
|
This model did not improve the
fits.
Alternatively, a model with an exponential term added to this logarithm
of
t is described by
|
(7)
|
or written as
|
(8)
|
Model III, with
s fixed for all patients, independent
of treatment regimen, and
k, with random variation, but with
a value
depending on the regimen, yielded the best fits (BIC = 4,640)
of this group of
models.
The problem with this model was that there was no plausible biological
explanation behind it. Since antimalarial drugs are
parasite stage
specific, and since replication may continue in
the lag phase, a term
for parasite stage was incorporated in the
model. For this purpose, we
adopted a model constructed by White,
who assumed a normal distribution
in four patients who failed
to respond to treatment was applied
(
17). It was assumed that
the distribution of the
parasites' age has a mean value, µ, with
a standard deviation (SD).
For the convenience of calculations,
a logistic distribution of the
parasites' age was assumed. This
is a small difference from White's
model. This model, model IV,
which is basically an extension of model
III, but with a biologically
plausible interpretation of the lag phase,
can be described by
![P(t)=e<SUP>A · {&sfgr; · <UP>ln</UP>[1 + e<SUP>(&mgr;−t)/&sfgr;</SUP>]+t−&sfgr;·<UP>ln</UP>(1+e<SUP>&mgr;/&sfgr;</SUP>)}</SUP> · e<SUP>(−k · t)</SUP>](/content/vol44/issue5/fulltext/1302/img010.gif)
|
(9)
|
simplified to
![P(t)=(e<SUP> A · ∫<SUP> t</SUP><SUB>0</SUB> {1+<UP>exp</UP>[<SUP>−(s−&mgr;)/&sfgr;</SUP>]}<SUP>−1</SUP> ds</SUP>) · e<SUP>(−k · t)</SUP>](/content/vol44/issue5/fulltext/1302/img011.gif)
|
(10)
|
where
= (SD ·
)/
However, the fits of model IV were not better than those of model III,
but also were not better than those of model I or II.
In addition, the
lag phase is probably determined not only by
parasite factors, but also
by pharmacokinetic and other factors.
Because model IV did not improve
the fits, and because models
II and III lacked any plausible biological
explanation of the
parameters
c and
s,
respectively, it was decided that the simplest
model, model I, would be
taken as the best description for the
data. In this model, the concept
of
Pterm, fitted by this model,
gave a
plausible explanation of the mechanism of
recrudescence.
| |
ACKNOWLEDGMENT |
This study was part of a research and development program
supported by the Ministry of Development Cooperation of The Netherlands.
| |
FOOTNOTES |
*
Corresponding author. Mailing address: Division of
Infectious Diseases, Tropical Medicine and AIDS, Academic Medical
Center F4.217, P.O. Box 22700, 1100 DE Amsterdam, The Netherlands.
Phone: 31 20 5662170. Fax: 31 20 6972286. E-mail:
p.j.devries{at}amc.uva.nl.
| |
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Antimicrobial Agents and Chemotherapy, May 2000, p. 1302-1308, Vol. 44, No. 5
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Abstract
Introduction
