Full text of DOI:10.1359/jbmr.2002.17.9.1662

JOURNAL OF BONE AND MINERAL RESEARCH
Volume 17, Number 9, 2002
©
2002 American Society for Bone and Mineral Research
Long-Term Predictions of the Therapeutic Equivalence of
Daily and Less Than Daily Alendronate Dosing*
1
2,3
4
2,3
´
C.J. HERNANDEZ, G.S. BEAUPRE, R. MARCUS, and D.R. CARTER
ABSTRACT
Less than daily alendronate dosing has been identified as an attractive alternative to daily dosing for patients
and physicians. A recent 2-year study found bone mineral density (BMD) changes caused by weekly
alendronate dosing therapeutically equivalent to that caused by daily dosing. There are no methods that can
be used to predict how long therapeutic equivalence will be maintained after the first 2 years of treatment. In
addition, it is unclear if dosing less frequently than weekly also might be therapeutically equivalent to daily
dosing. In this study we use a computer simulation to develop predictions of the therapeutic equivalence of
daily and less than daily dosing over time periods as long as a decade. The computer simulation uses a
cell-based computer model of bone remodeling and a quantitative description of alendronate
pharmacokinetics/pharmacodynamics (PK/PD). The analyses suggest that less than daily dosing regimens do
not increase BMD as much as daily dosing. However, model predictions suggest that dosing as frequent as
weekly still may be therapeutically equivalent to daily dosing over periods as long as 10 years. In addition, the
simulations predict dosing less frequently than weekly may be therapeutically equivalent to daily dosing within
the first year of treatment but may not be therapeutically equivalent after 10 years. Hypotheses based on these
simulations may be useful for determining which dosing regimen may be most attractive for clinical trials. (J
Bone Miner Res 2002;17:1662–1666)
Key words: bone remodeling, alendronate, osteoporosis, bone mineral density, drug dosing
INTRODUCTION
combined with the requirements of other drugs used by the
elderly population. Less frequent dosing (less than daily)
AILY ALENDRONATE treatment has been shown to in- would simplify the treatment process and may improve
(
2)
D
crease areal bone mineral density (BMD) and reduce patient compliance. A recent 2 year study found the BMD
(1)
fracture risk in patients with osteoporosis. However, this increases caused by weekly and twice-weekly dosing regi-
manner of administering alendronate is associated with a mens therapeutically equivalent to those caused by daily
number of dosing requirements that include fasting and treatment. It is not known how the results of daily and
limitations on activity for a one-half hour after the dose is less than daily dosing would compare over longer periods of
administered. When administered daily, the dosing re- time (10 years). If weekly dosing is therapeutically equiv-
quirements can be a substantial burden, especially when alent to daily dosing over long time periods, there is the
possibility that even less frequent treatments (twice monthly
(3,4)
(
2)
or monthly) also might be therapeutically equivalent to
daily treatment.
Predicting the long-term results of a new alendronate
dosing strategy is difficult because clinical results depend
on the pharmacokinetics of alendronate (PK; the distribu-
*
Presented at the 23rd Annual Meeting of the American Society
of Bone and Mineral Research, Phoenix, Arizona, USA, October
2–16, 2001.
Dr. Marcus is a full-time employee of Eli Lilly and Company.
The other authors have no conflict of interest.
1
1
Department of Orthopedics, The Mount Sinai School of Medicine, New York, New York, USA.
Rehabilitation Research and Development Center, Veterans Affairs Palo Alto Health Care System, Palo Alto, California, USA.
Division of Biomechanical Engineering, Department of Mechanical Engineering, Stanford University, Stanford, California, USA.
Eli Lilly and Company, Indianapolis, Indiana, USA.
2
3
4
1
662

PREDICTING INTERMITTENT ALENDRONATE RESULTS
1663
tion and elimination of the drug in the body), the pharma-
codynamics of alendronate (PD; the relationship between
drug concentration and physiological response), and the
relationship between alendronate’s primary effect (a change
in bone-remodeling activity) and changes in BMD. A quan-
titative method that combines the PK/PD data with a de-
scription of alendronate’s effects on bone remodeling and
BMD could be used to predict the benefits of less frequent
treatment strategies over short or long time periods and help
provide new hypotheses regarding the relative effectiveness
of different dosing strategies. Recently, we established a
computational method of relating the changes in bone-
remodeling activity caused by alendronate to changes in
(
5)
BMD. The computer model used was only capable of
simulating daily dosing because it did not detail the PK/PD
of alendronate. However, if combined with existing quan-
titative data describing the pharmacokinetics and pharma-
codynamics of alendronate, our model of bone remodel-
ing could be used to predict the long-term effects and
therapeutic equivalence of less than daily dosing.
FIG. 1. Changes in alendronate concentration in bone are described.
(11)
Data points are taken from clinical measurements
and are normal-
(6)
ized by the amount of each dose remaining in the body 2 days after
administration (assumed here to represent the total portion sequestered
in the bone). The solid line represents Eq. (1) and is highly predictive
2
of the rate of alendronate elimination over this time period (r Ͼ 0.99).
In this analysis we develop a simple PK/PD model of
alendronate and integrate it with a simulation of bone re-
modeling to predict the therapeutic equivalence of less than
daily and daily alendronate dosing regimens. Predictions are
made over short-term (1 year) and long-term (10 year)
periods of treatment. New hypotheses regarding the thera-
peutic equivalence of daily and less than daily alendronate
treatments are developed based on these predictions.
In the current analysis the simulation of bone remodeling
is combined with a simple PK/PD model. Because studies
have suggested that the physiological response is related
directly to the concentration of alendronate present in the
(6)
bone tissue, the PK/PD model is dominated by the char-
acteristics of alendronate that influence drug concentration
in the bone. Studies of alendronate absorption suggest that
the fraction of an oral dose that is absorbed into bone tissue
is not influenced by the size of the dose and that the rate of
absorption of alendronate into the bone is very fast when
MATERIALS AND METHODS
(6)
A description of the computer model used to simulate
daily alendronate treatment has been presented previ-
compared with the remodeling process. Based on these
pharmacokinetic and pharmacodynamic characteristics of
alendronate, we assume that the maximum BMU response
(
5,7)
ously
and will be discussed briefly here. The model
describes the activity of basic multicellular units (BMUs) in
a manner based on that used by Hazelwood and col-
(
Rmax, the change in BMU activity caused by daily treat-
ment) is based on the cumulative dose of the drug rather
than the size of each individual dose. This simplification
implies that with regard to absorption into the bone, there is
little difference between daily and less than daily regimens
of the same cumulative dose. Therefore, the differences
between daily and less than daily dosing are considered to
be dependent on the rate of alendronate elimination from the
bone. A knowledge of the rate of alendronate elimination is
therefore essential to the model.
(
8,9)
leagues.
BMUs are organized groups of osteoclasts and
osteoblasts that are responsible for bone resorption and
formation at remodeling sites. The model calculates the rate
of appearance of BMUs and the volume of bone resorbed
and formed by all active BMUs in a volume of cancellous
bone. The output from the computer model includes bone
volume fraction and degree of mineralization (ash fraction).
The bone volume fraction and degree of mineralization can
be used to calculate total mineral content in a simulated
bone sample and thereby determine BMD. Predicted
changes in BMD are compared with those found clinically
in the lumbar spine. Numerical parameters used in the
model are derived from bone histomorphometry measure-
ments in humans. Daily alendronate treatment is simulated
by reducing the origination frequency (birthrate) of new
BMUs by the same factor that has been observed clinically
Alendronate elimination occurs in the model at an expo-
nentially decreasing rate where 66% of the total dose re-
(11)
mains 6 months after treatment is stopped. A logarithmic
function is used to express both the fraction of each alen-
dronate dose that remains sequestered in the bone after
administration and the response (R ) that remains t days
f
afterward:
(
an 87% reduction in BMU origination frequency for 10
R ϭ 1 Ϫ m ϫ ln͑t ϩ 1͒,
f
(1)
(10)
mg/day of alendronate).
The decrease in BMU origina-
tion frequency results in increased BMD due to a reduction where m is a constant equal to 0.065 that is determined by
in the remodeling space (the resorption cavities formed fitting the equation to clinical data (Fig. 1).
during bone remodeling) and an increase in the degree of
mineralization of the bone tissue.
The cumulative dose simulated in this study is the equiv-
alent of a 10-mg/day oral dose (i.e., 10 mg/day oral, 70
(5)

1
664
HERNANDEZ ET AL.
FIG. 3. The predicted changes in BMD in response to alendronate are
depicted. Each line represents a different frequency of alendronate
administration.
FIG. 2. The percent reduction in BMU origination frequency is
presented for daily, weekly, and monthly alendronate treatment regi-
men. The same maximum response is used for each regimen because
they all use the same cumulative dose. Time steps of 1 day are used.
TABLE 1. THE PREDICTED CHANGES IN BMD FOR EACH OF
THE DOSING REGIMENS
mg/week oral, etc.). The change in BMU origination fre-
quency associated with this dosage clinically (87% reduc-
Predicted
BMD increase
after 1 year
Predicted
BMD increase
after 10 years
(10)
tion from pretreatment levels)
is used as the value for
Treatment
Daily
Twice weekly
Weekly
Twice monthly
Monthly
Rmax. For less than daily dosing, the total response to
alendronate (R) is reduced from the value of Rmax at the
same rate that alendronate is eliminated from the body
between doses [see Eq. (1)]. The total percent decrease in
origination frequency caused by alendronate can be ex-
pressed as a function of the number of days t since the last
treatment:
5.37%
5.12%
4.94%
4.73%
4.49%
11.98%
11.38%
10.96%
10.47%
9.90%
RESULTS
R ϭ Rmax ϫ R ϭ R ϫ ͑1 Ϫ m ϫ ln͑t ϩ 1͒͒,
(2)
f
max
The predicted increase in BMD was reduced when the
where R is the percent decrease in origination frequency, treatment was administered less frequently (Fig. 3). The
Rmax is the response for daily dosing (determined by the BMD change caused by daily treatment was 5.37% after 1
cumulative dose), and R is the fraction of the response that year and 11.98% after 10 years. The differences between
f
remains after treatment ends [see Eq. (1)]. The percent daily and less than daily treatment methods became more
pronounced with time. After 1 year the increase caused by
daily treatment was predicted to be 0.88% greater than that
predicted for monthly treatment but after 10 years the dif-
ference was 2.08% (Table 1). After 1 simulated year the
difference in predicted BMD increase between less than
daily dosing and daily dosing is predicted to be Ͻ1.5%
decrease in origination frequency caused by daily and less
than daily regimens over time can be compared (Fig. 2).
Daily, twice weekly, weekly, twice monthly, and monthly
dosing regimens of the same cumulative dose are simulated.
Computer simulations are performed on an SGI O2 work-
station (Silicon Graphics Inc., Mountain View, CA, USA).
Simulation results are presented in terms of the percent
changes in BMD and therapeutic equivalence to daily treat-
ment. Therapeutic equivalence is determined in a manner
similar to that used by Schnitzer et al. : a dosing regimen
is considered therapeutically equivalent to daily if the per-
cent BMD increase is within 1.5% (relative to the pretreat-
ment level) of that predicted for daily dosing. Dosing reg-
imens are compared after 1 year (short term) and 10 years
(
relative to pretreatment), suggesting that any of the less
than daily dosing regimens simulated may be therapeuti-
cally equivalent to daily dosing. However, after 10 years of
simulated treatment, the twice weekly and weekly regimens
were predicted to be therapeutically equivalent to daily
dosing and twice monthly and monthly dosing were not.
(3)
DISCUSSION
(long-term) of simulated treatment assuming that no influ-
ences other than alendronate are actively changing the bone-
remodeling process.
The objective of this analysis was to compare the BMD
increases predicted from daily and less than daily alendro-

PREDICTING INTERMITTENT ALENDRONATE RESULTS
1665
(3,4)
nate administration. Simulations of less than daily alendro- 0.4% after 2 years.
The changes predicted in this study
nate treatment suggest that the improvements in BMD are (5.12% and 4.94% at 1 year and 6.86% and 6.61% at 2
reduced as the frequency of dosage is reduced, even if the years) are within the 95% CIs of the clinical data, showing
total cumulative dose of alendronate is maintained constant. that the computer predictions are similar to those seen
Although less than daily treatment was not predicted to
increase BMD as much as daily treatment, some less than
daily treatments could be considered therapeutically equiv-
alent to daily treatments. Based on the definition of thera-
peutic equivalence used in our study, twice weekly and
weekly dosing were predicted to be therapeutically equiva-
lent to daily dosing during the first 10 years of treatment.
It is important to address the limitations of the predictive
model when assessing the results. First, the predictions are
based on an implementation of the bone-remodeling model
clinically. No other clinical studies of less than daily alen-
dronate dosing for the same cumulative dose are available in
the literature for comparison.
Our predictions suggest that, according to BMD in-
creases, twice weekly and weekly alendronate dosing may
be therapeutically equivalent to daily dosing, supporting the
(3,4)
conclusions of recent clinical studies.
In addition, our
predictions suggest that twice weekly and weekly alendro-
nate dosing will continue to be therapeutically equivalent to
daily dosing for as long as 10 years after the start of
treatment. However, we also predict that administration of
alendronate at monthly or twice monthly frequencies may
appear therapeutically equivalent to daily dosing after 1
year but may not after 10 years. Therefore, we suggest that
using the current definition of therapeutic equivalence, the
length of an equivalence study may be a factor that can
influence whether or not two treatment methods are consid-
ered equivalent. Consequently, future equivalence studies of
bisphosphonates (and possibly other drugs influencing bone
metabolism) should either use a definition of therapeutic
equivalence relative to daily dosing or specify the time
(5)
developed previously. Although we refer the reader to the
original publication for a thorough discussion of the limi-
tations of that model, it is important to note that it is based
on bone histology measurements and therefore takes on the
assumptions used in dynamic bone histomorphometry. In
addition, the simulation only takes into account the changes
in the remodeling process caused by alendronate and does
not consider cellular processes that may account for changes
in the remodeling process (osteoclast or osteocyte apopto-
(
12)
sis)
or modifications to mineral structure or crystallinity
caused by the drug (although overall degree of mineraliza-
tion is considered).
The predictions based on this model are useful for com- associated with equivalency conclusions.
paring different treatment regimens used in a general pop-
The model used in this analysis was based on alendronate
ulation but are not meant to describe the changes in BMD in and did not explicitly address other bisphosphonates. The
an individual. In addition, some of the simulations per- results would apply to other bisphosphonates that have
formed in this analysis considered the possibility of very similar PK/PD properties to alendronate. In particular, other
large doses of alendronate (the equivalent of a 300-mg or bisphosphonates that cause similar changes in bone remod-
1
50-mg oral dose for monthly or twice monthly dosing). eling and display similar rates of elimination as alendronate
Such large oral doses are not considered appropriate for use may show results consistent with our predictions. We expect
in humans. However, because the pharmacodynamics of our
model are based on total alendronate sequestered in the
bone, the predictions also would be consistent with any
other method of administration (such as intravenous injec-
tion) that deposits the same amount of alendronate into the
bone per dose.
the differences between dosing methods to be greater for a
bisphosphonate that has a larger influence on the remodel-
ing process (a larger R ) and smaller for a bisphosphonate
f
with a slower rate of elimination. As opposed to all other
bisphosphonates developed for clinical use, etidronate
uniquely modifies the mineralization process that may lead
In comparing antiresorptive drug treatments, greater in-
creases in lumbar spine BMD have been shown to cause
(15)
to frank undermineralization and osteomalacia.
reason, our results may not apply to that agent.
For this
(13)
larger reductions in vertebral fracture risk.
that dosing methods that generate larger increases in BMD
such as daily) may provide greater reductions in fracture
This implies
Less frequent treatment methods are attractive to clini-
cians because they often result in increased patient compli-
ance and a resulting improvement in treatment outcome.
Clinical studies of new less frequent treatment methods for
osteoporosis drugs often are long and require large commit-
ments of resources. Identifying those treatment methods
that are most likely to give the desired result could give
researchers more confidence when developing clinical stud-
ies. In this analysis we have identified twice weekly and
weekly alendronate treatments as those most likely to have
similar benefits to daily treatment after a 10 years of ad-
ministration. Although further validation would be needed
to use this model to predict BMD changes in individual
(
incidence than other dosing methods (such as less than
daily). However, a significant portion of the reduction in
fracture risk caused by alendronate is not explained by
(
14)
BMD. The unexplained portion of fracture risk reduction
could reflect the reduction in stress riser prevalence associ-
ated with decreasing the surface prevalence of remodeling
sites, or it could reflect other changes in microarchitecture
or tissue properties that influence biomechanics. Without a
good description of the unexplained portion, numerical pre-
dictions of fracture risk based on BMD during alendronate
treatment may be limited.
The predictions made in this model are consistent with patients, it is useful for comparing different treatment meth-
clinical studies that found the increases in BMD from twice ods and could be an important tool during the development
weekly and weekly treatment to be 5.2 Ϯ 0.3% and 5.1 Ϯ of large clinical studies of a variety of pharmaceuticals that
0
.3% (mean Ϯ 2 SE) after 1 year and 7.0 Ϯ 0.4% and 6.8 Ϯ affect bone metabolism.

1
666
HERNANDEZ ET AL.
ACKNOWLEDGMENTS
The authors thank Mitchell B. Schaffler for his encour-
agement. This work was supported by the Department of
Veterans Affairs (A2424P), a fellowship from the Ford
Foundation, and a scholarship from the Society of Profes-
sional Engineers foundation.
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Address reprint requests to:
Christopher J. Hernandez, Ph.D.
The Mt. Sinai School of Medicine
One Gustave L. Levy Place, Box 1188
New York, NY 10029, USA
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