Medical, Pharma, Engineering, Science, Technology and Business

**Jason JZ Liao ^{1*}, Yifang Li^{2} and Xinhua Jiang^{3}**

^{1}Merck & Co., Inc, North Wales, PA 19454, USA

^{2}Novartis Pharmaceuticals Corporation, Cambridge, MA 02139, USA

^{3}Beijing University of Chemical Technology, Beijing, P.R. China

- *Corresponding Author:
- Liao JJZ

Merck & Co., Inc

North Wales, PA 19454, P.R. China

**Tel:**7175317178

**E-mail:**[email protected]

**Received Date**: April 20, 2017; **Accepted Date:** April 25, 2017; **Published Date**: April 28, 2017

**Citation: **Liao JJZ, Li Y, Jiang X (2017) Comparability of Pharmacodynamics Profiles with an Application to a Biosimilar Study. J Biom Biostat 8: 345. doi: 10.4172/2155-6180.1000345

**Copyright:** © 2017 Liao JJZ, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

**Visit for more related articles at** Journal of Biometrics & Biostatistics

It is often interest of comparing two pharmacodynamics (PD) profiles in drug development. Currently the common practice is borrowing the bioequivalence (BE) rule in pharmacokinetics analysis for pharmacodynamics comparison in terms of the area under the effect curve (AUEC) of the pharmacodynamics profile. However, this may not be a feasible and sensitive enough approach since the bioequivalence approach is based on the summarized parameter of the pharmacodynamics profile rather than on directly comparison of the whole pharmacodynamics profile. In this paper, a simple but efficient and pragmatic pharmacodynamics comparability index is proposed to evaluate the comparability of pharmacodynamics profiles by comparing the whole pharmacodynamics profiles directly. Different biological products have different variability and the CV% can be in a very large range. The PD comparability index can take account of the reference knowledge into consideration in assessment but the AUEC BE type approach ignores the reference variability. The good properties of the proposed approach are illustrated through simulated data and a real dataset.

Comparability; Pharmacodynamics (PD) profile; PD comparability index; Power; Type I error

In pharmaceutical development, pharmacodynamics (PD) markers
are commonly used to understand the compound and speed up the
drug development. For example, in developing biosimilars, the PD
evaluations can provide critical and needed evidence in accumulating
the totality of the evidence for the bio similarity between the proposed
bio similar product and the reference product and providing convincing
evidence for the extrapolation from one indication to other indications
[1-5]. It is quite a challenge for demonstrating the PD comparability.
Unlike pharmacokinetics (PK), there is not much literature on PD
comparison even for the small molecule. Most biologics usually have
multiple indications. A couple of papers used the same bioequivalence
(BE) rule in PK analysis for PD comparison in terms of the area under
the effect curve (AUEC) of the PD profile [6,7]. Recently, FDA [8]
issued guidance for conducting PD comparability study using the
same BE rule. However, this may not be a feasible approach since the
interpretation for AUEC used in PD studies is not the same as for PK
studies since PK describes what the body does to the drug while PD
describes what the drug does to the body. Since AUEC is summarized
before comparing the PD profile directly, having the same AUEC for
a PD profile does not necessarily imply the same PD profile. Note that
the purpose of the comparability of pharmacodynamics is to compare
the entire PD profile. Only one AUEC assessment for the PD profile
may not be sensitive enough. To see this, **Figure 1** shows two different
PD profiles but having very similar AUEC values.

Here is the outline for the rest of the paper. In Section 2, a PD comparability index is proposed to compare the PD profile directly. In Section 3, simulation studies are used to compare the proposed PD comparability index with the AUEC BE approach to demonstrate the advantages of the proposed PD comparability index over the AUEC BE approach. A dataset is used to illustrate the method in Section 4. The summary is followed in Section 5.

There are many advanced statistical approaches in pharmacokinetics analysis besides the classical BE approach. For
example, Dragalin, et al. [9] used Kullback-Leibler divergence for
evaluating bioequivalence; Liao [10,11] compared the pharmacokinetics
profiles directly using a functional linear model. However, to conduct
the PD comparison, the simple but efficient and pragmatic ideas for
assessing the similarity of two dissolution profiles are borrowed here.
Dissolution test in vitro is to ensure the drug product quality. The
similarity of dissolution profiles is to ensure the product performance
in the presence of a change such as scale-up, manufacturing site,
component and composition, equipment and process, both immediaterelease
(IR) and modified-release (MR) dosage formulations. To
demonstrate the similarity of dissolution profiles, there are many
proposed methods such as the simple graphics and summaries and
many other advanced statistical methods. However, instead of using
a more complicated statistical approach, FDA recommends and the
industry commonly uses a relative non-sophisticated single similarity
factor number f_{2} to describe and quantify the difference between two
dissolution profiles (Reference and Test) as:

(1)

Where n is the total number of dissolution time points and wt is the
optional weight factor. The transformation is to scale the factor into (0,
100). A value f_{2}=100 means the two dissolution profiles are exactly the
same. A higher f_{2} number means a better similarity for the dissolution
profiles. The similarity of dissolution profiles is claimed if the lower
95% confidence limit of f_{2}>50, which is about 10% dissolution profile
difference/changes [12-15].

To mimic the evaluation for the similarity of dissolution profiles with a relatively non-sophisticated and pragmatic approach, a PD comparability index to assess the comparability of PD profiles is proposed as follows.

(2)

where n is the total number of time points in the PD profile; and are the PD responses at time tj for the reference and the test product,
respectively; wj is the optional weight. are
the maximum (minimum) profile response for the reference and the
test product, respectively. This PD comparability index is within (0,
1), where 1 indicates the 100% comparability, i.e., the identical PD
profile. A higher f_{PD} number means a better comparability for the two
PD profiles. The PD comparability is claimed if 1) The approximate
lower 95% confidence limit of the PD comparability index f_{PD} for the
test against the reference is greater than a value δ0; and 2) The point
estimate of the index f_{PD} for the test against the reference is greater than
a value δ_{1}.

The two boundaries δ_{0} and δ_{1} used in the PD comparability index
approach can be determined beforehand with the consensus from the
regulatory authorities. The first condition δ0 in the acceptance criteria
takes account of the reference variability and is the acceptable limit.
One way to decide δ_{0} is to use the reference against the reference as
the base to make a comparison between the test and the reference
product. Following Chow, et al. [16] in defining the biosimilarity limit,
a discounting (say, 0.9) of the approximate lower 95% confidence
limit of the PD comparability index using only the reference against
the reference information can be provided as a way of selecting the δ_{0},
the threshold for accepting the test against the reference. The second
condition in the acceptance criteria is to ensure no major PD profile
difference for the test product passed the comparability due to a large
variability for the reference product [17,18] which is usually the case
for a biological product. Toward this, a value of δ_{1}=0.9, which is about
10% of the mean difference could be a reasonable value for use.

Note that in assessing the similarity of the dissolution profiles, a
fixed boundary 50 in the acceptance criterion was used as the lower
boundary of f_{2} and the amount 50 is the f_{2} value when there is a
10% dissolution profile difference. To mimic this and simplify the
acceptance criteria, then δ_{0} can also be set as a fixed value regardless
of the reference variability, say, 0.77, which accounts for about 30%
PD profile difference/changes relative to the response range when the
maximum (minimum) response is the same for both the test product
and the reference product. The third choice of the δ_{0} can also be set as
the maximum of a fixed value and the lower confidence limit of the
PD comparability index from the reference against the reference itself.
In summary, to select an appropriate δ_{0} in the first condition, three
methods can be used.

1) For simplicity, δ_{0} can be set at a fixed value regardless of the
reference variability. For example, δ_{0} could be set at 0.77 to account
for 30% PD profile difference/changes when the maximum (minimum)
response is the same for both the test biologics and the reference
product.

2) To consider the reference variability, δ_{0} can be set at the lower
boundary of the 95% one-sided confidence interval of the reference
against reference multiplied by a discount constant factor c(0 < c < 1)
say, c=0.9.

3) δ_{0} can be set as the maximum of the values obtained from the
previous two methods.

To estimate the value of f_{PD} in eqn. (2), the corresponding
parameters can be obtained by fitting a model such as the Emax model
or the extended Emax model [19], or from a smooth curve of the PD
profile using a non-parametric method such as the smooth spline and
the confidence bands of the smooth spline can be constructed using the
method [20] in which can be used to derive the lower 95% confidence
limit of f_{PD} as follows

(3)

Where , is the residual variance for the reference and the
test product, respectively, and are the predicted PD responses
at time tj for the reference and the test product, respectively; and are the predicted maximum (minimum) profile
response for the reference and the test product, respectively. If possible,
the pharmacokinetics and pharmacodynamics (PK/PD) is preferably
evaluated in the same subjects to obtain information on the PK-PD
relationship. To construct the confidence interval of f_{PD} for reference
against the reference, a bootstrap method is recommended to construct
the approximate lower 95% confidence limit. The bootstrapping is to
resample from the subjects with replacement twice to form two data
sets with each having sample size n, then to extract the corresponding
responses to refit the PD profile curves using smoothing splines and
compute the confidence interval limit using eqn. (3) based on the
estimated results of the two resampled data sets. The bootstrapping
steps were repeated for N times and the lower 2.5% percentile of the
PD comparability index is then used as the approximate 95% lower
confidence limit.

In this section, the simulation study is used to compare the performance of the BE approach using the AUEC under the PD profile and the proposed PD comparability index in terms of the type I error and power. The data were generated from the PD profile. The following two PD profiles are considered in this simulation study:

and

Where PD1 is considered as the reference product. When the PD
profiles from the reference and the test product are different as shown
in **Figure 2**, the type I errors of the two approaches are compared.
When the test product also takes the same PD profile of the reference,
the powers of the two approaches are compared. It is a well-known fact
that the variability varies from the time points and thus, a heterogeneity error term is used in generating the data. In detail, the PD is evaluated
at the following time points: 0, 0.25, 0.50, 1, 2, 3, 4, 5, 6, 8, 12, 18, 24,
30, 36, 42, 48, 60, and 72 hours after dosing with a heterogeneity error
0.4 exp(0.1y) × ε, where y is the true PD value and ε is from a standard
normal distribution. Three different sample sizes n=30, 40, and 60 for
each product were used for the simulation. At each setting, the same
experiment was repeated 1000 times.

To determine the comparability between the reference and the test
product, the AUEC BE approach and the proposed PD comparability index approach were used. For the AUEC BE approach, the BE 0.8-1.25
criterion was used. For the proposed PD comparability index approach,
the cubic smoothing spline was used for estimating the PD curve. The
comparability index and the 95% confidence interval limit of reference
against test were estimated using eqns. (2) and (3), where the optional
weight was not used. In the PD comparability index approach criteria,
two values of δ_{0} were used: δ_{1}=0.9 for 10% mean difference and ��1=0.83
for 20% mean difference. For δ_{0} in the first criterion, all three different
methods were used in this simulation. For the reasonable fixed constant,
two constant values were considered: 0.77 (accounting for 30% PD
difference), and 0.8 (accounting for 25% PD difference). The reference
against reference confidence interval boundary was computed using the
bootstrap method. For each method, the bootstrapping was done 1000
times. The rate of passing PD comparability from the 1000 simulations
is shown in **Table 1**.

SampleSizePer Arm | AUEC BE | PD Comparability Index | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

𝛿1=0.9 | 𝛿1=0.83 | 𝛿1=0.83 | ||||||||||

𝛿0 | 0.77 | 90Ref | Max | 0.77 | 90Ref | Max | 0.8 | 90Ref | Max | |||

Power | N=30 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |

N=40 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ||

N=60 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ||

Type IError | N=30 | 1 | 0 | 0 | 0 | 1 | 0.044 | 0.044 | 0.295 | 0.044 | 0.044 | |

N=40 | 1 | 0 | 0 | 0 | 0.999 | 0.022 | 0.022 | 0.232 | 0.022 | 0.022 | ||

N=60 | 1 | 0 | 0 | 0 | 1 | 0.004 | 0.004 | 0.178 | 0.004 | 0.004 |

**Table 1:** Rate of passing PD comparability from simulation studies.

When there is no PD profile difference, **Table 1** indicates that
both AUEC BE type approach and the proposed PD comparability
index approach have good powers. However, when the reference
curve and the test curve are different given as PD1 and PD2 shown in **Figure 2**, respectively, the AUEC BE criterion tends to claim them to
be comparable and leads to a large type I error. However, the newly
proposed PD comparability index approach can give satisfactory
results when δ_{0} and δ_{1} are chosen properly, with a well-controlled type
I error under or around 0.05. Larger δ_{1} has a better control on the type
I error. Note that the choice of δ_{0} as the maximum of a fixed and a
reference variability based has exactly the same results as the reference
variability based because in the simulation settings, the “max” always
picks up the “90ref” value as the “90ref” is always greater than the
fixed boundary. This may not be the case when reference variability is
large, which can be seen in the illustration example. To achieve a better
control of the type I error, the maximum value of a fixed value and the
reference variability dependent value is recommended. The simulation
results also show that the type I error is also better controlled when the
sample size is relatively large, as expected.

It is a well-known fact that the sampling time points may have a
big effect in the assessment. Toward this, two more different sampling
schemes were used in the simulation studies. One was with less
sampling time points: 0, 0.50, 2, 4, 8, 12, 18, 24, 36, 48, 60, and 72. The
other was with much less sampling time points: 0, 0.50, 4, 8, 12, 18,
48, and 72. For these two extra sampling schemes, the AUEC BE type
approach and the PD comparability index approach generated similar
results (not shown here) and had similar conclusions in terms of the
type I error and the power as shown in **Table 1**.

In summary, the PD comparability index compares the whole PD profile directly and provides more sensitive and the type I error controlled assessment comparing to the AUEC BE type approach. The proposed PD comparability index can take account of the reference variability and reference knowledge into consideration while the AUEC BE type approach does not.

Consider a study for a proposed biosimilar cancer drug to a
marketed innovator cancer drug. A parallel-design study was conducted
to assess the PK/PD comparability of the biosimilar biologics to the
marketed innovator at two different dose levels 0.1 mg/kg and 0.3 mg/
kg [21-23]. At the dose level 0.1 mg/kg, twenty eight (28) subjects were
allocated to both the marketed innovator and the proposed biosimilar
biologics. The blood for pharmacokinetics was drawn at baseline and 4,
10, 24, 34, 48, 72, and 96 hours after drug administration; and the PD
was evaluated at the baseline and 4, 24, 48, 72, and 96 hours after drug
administration. However, there was only one reading for one subject for
both the biosimilar biologics and the reference product, and thus, this
subject were not included in this evaluation. The raw data for the PD
endpoint absolute neutrophil count (Neut) are plotted against the time
to generate the PD profile in **Figure 3**, in which much higher variability
is shown in the middle range of the PD profile. Before the formal
analyses, the summary statistics in terms of the mean and the standard
deviation at each time point are listed in **Table 2**. The comparison
for the PD endpoint absolute neutrophil count (Neut) at each time
point was conducted. The 95% confidence interval of the difference
between the biosimilar and the reference and the p-value testing the
mean difference between the test and reference are also listed in **Table
2**, which indicates that there are no statistically significant differences at all the sampled time points and the confidence interval indicates the
two products are comparable at all the sampled time points.

Time (hr) | Mean (Standard Deviation) | ||||||
---|---|---|---|---|---|---|---|

0 | 4 | 24 | 48 | 72 | 96 | ||

PD | Reference (R) | 1.837 (0.463) | 3.919 (0.750) | 20.960 (3.455) | 20.793 (3.223) | 7.375 (1.995) | 2.353 (1.344) |

Test (T) | 1.763 (0.572) | 4.368 (0.894) | 20.753 (3.272) | 19.728 (4.329) | 7.124 (2.288) | 2.030 (0.983) | |

95% CI(T-R) | (-0.207, 0.355) | (-0.915, 0.016) | (-1.734, 2.147) | (-1.035, 3.164) | (-0.975, 1.475) | (-0.329, 0.973) | |

p-value* | 0.599 | 0.058 | 0.831 | 0.313 | 0.683 | 0.325 |

*Testingthe mean difference between the reference and test.

**Table 2:** Summary statistics at each time point.

As the first formal analysis, the AUEC of the PD profile for each
subject was calculated and the BE approach was used to assess the
PD comparability of the proposed biosimilar and the reference. The
estimated GMR of the biosimilar against the reference is 0.897 with the
90% confidence interval (0.875, 1.026). Thus, the proposed biosimilar
and the reference are bioequivalence in terms of area under the PD
profile using the BE criteria. Since the goal of the PD comparability is
to compare the whole PD profile, it may not be good enough to just
compare the PD responses at each observed time points as shown in **Table 2**. For this purpose, the proposed PD comparability index defined
in eqn. (2) was also used. The data are plotted together with the fitted
PD interpolation profiles for both the reference and the test in **Figure 4**.

To quantify the similarity of PD profiles between the test and
the innovator product, the proposed PD comparability index was
calculated. The estimated PD comparability index is 0.975, and the
lower 95% confidence interval limit is 0.767. To compute the reference
against the reference confidence interval, 1000 bootstrap replications
were used, and in each bootstrap replication, the reference data set
was resampled twice to form two data sets. The average of the 1000
lower confidence interval limits is 0.723, which indicates that there is
a considerable variability for the reference product itself and this value
0.723 can account for 38% PD profile difference/changes. The results of the PD comparability index approach using different δ_{0} and δ_{1} are
summarized in **Table 3**.

AUEC BE | PD Comparability Index | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

𝛿1=0.9 | 𝛿1=0.9 | 𝛿1=0.83 | ||||||||

𝛿0 | 0.74 | 90Ref | Max | 0.77 | 90Ref | Max | 0.77 | 90Ref | Max | |

Pass | Pass | Pass | Pass | Fail | Pass | Fail | Fail | Pass | Fail |

**Table 3:** Data analysis results for the example dataset.

**Table 3** indicates that the conclusion depends on the choice of δ_{0} and δ_{1}. The estimated PD comparability index of the test against the
reference is large, and greater than both the selected δ_{1} values, thus
the δ_{1} criteria passed. Since the estimated lower confidence interval
limit for the PD comparability index of the test against the reference
is 0.767 but the estimated confidence interval lower limit for the PD
comparability index of the reference against the reference is 0.723,
thus, the maximum value always picks up the constant δ_{0} as 0.74, or
0.77. If only the reference against reference PD comparability index
information is used, then PD comparability conclusion can be claimed
on all parameter choices. The choice of a fixed boundary or the
maximum of the fixed and the reference variability based (this leads
to the same as the fixed boundary in this example) will impact the final
conclusion. The PD comparability only passes for the choice of 0.74 but
fails the choice of 0.77.

Although more advanced statistical techniques can be developed,
a simple but efficient and pragmatic PD comparability index f_{PD} was
proposed to demonstrate the comparability of PD profiles between
the test biologics and the reference product directly in this paper.
This PD comparability index compares the two PD profiles directly
while the AUEC is only a summary of the PD profile which may be
not sensitive enough. Much more confident conclusion can be drawn
using this PD comparability index than using the only summarized
parameter AUEC of the PD profile. Different biological products have
different variability and the CV% can be in a very large range. The PD
comparability index can take account of the reference knowledge into
consideration in assessment but the AUEC BE type approach ignores
the reference variability.

The two boundaries δ_{0} and δ_{1} used in the PD comparability index
approach can be determined beforehand with the consensus from the regulatory authorities. Different choices of the acceptance criterion
for the PD comparability were discussed in this paper. One of the
choices for δ_{0} was based on the comparison of the reference against
the reference itself. The PD comparability index of the test against the
reference is compared to the PD comparability index of the reference
against itself. In this case, the variability of the reference product plays
an important role and the acceptance boundary is a reference-scaled
based. With that said the acceptance criteria may vary from product
to product. A simpler acceptance criterion was also proposed. For
example, the approximate lower 95% confidence limit of the PD
comparability index for the test against the reference can be compared
to a fixed value, say, 0.77, which allows for 30% PD profile changes
when the maximum (minimum) response is the same for both the test
and the reference product. This acceptance boundary is for all reference
products regardless the reference variability, thus, it is not a referencescaled
based but is used as the presumed most tolerable difference.
Other fixed value after the discussion with regulatory authorities can
also be used. However, from the simulation and the example, in order
to achieve a better control of type I error, the maximum of the reference
scaled boundary and a fixed boundary is recommended.

As evidenced in **Figure 1**, the sampling time points and the number
of time points can be very critical toward the final conclusion of the
PD comparability assessment. The influence factors can from the PK
mechanism, the PD mechanism, and the shape of the PD time profile.
It is the goal to design a small but yet very efficient PD comparability
study and this can be very challenging.

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