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{\bf {\large Adaptive design methods in clinical trials - a review}}\\[0pt]
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Shein-Chung Chow$^{1}$ and Mark Chang$^{2}$

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$^{1}$Duke University School of Medicine, Durham, North Carolina, USA

$^{2}$Millennium Pharmaceuticals, Inc., Cambridge, Massachusetts, USA
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$^{1}$Corresponding author.

E-mail addresses: SCC: sheinchung.chow@duke.edu, MC: mark.chang@mpi.com

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Abstract
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In recent years, the use of adaptive design methods in clinical research and
development based on accrued data has become very popular due to its
flexibility and efficiency. Based on adaptations applied, adaptive designs
can be classified into three categories: prospective, concurrent (ad hoc),
and retrospective adaptive designs. An adaptive design allows modifications
made to trial and/or statistical procedures of on-going clinical trials.
However, it is a concern that the actual patient population after the
adaptations could deviate from the originally target patient population and
consequently the overall type I\ error (to erroneously claim efficacy for an
infective drug) rate may not be controlled. In addition, major adaptations
of trial and/or statistical procedures of on-going trials may result in a
totally different trial that is unable to address the scientific/medical
questions the trial intends to answer. In this article, several commonly
considered adaptive designs in clinical trials are reviewed. Impacts of ad
hoc adaptations (protocol amendments), challenges in {\it by design}
(prospective) adaptations, and obstacles of retrospective adaptations are
described. Strategies for the use of adaptive design in clinical development
of rare diseases are discussed. Some examples concerning the development of
Velcade intended for multiple myeloma and non-Hodgkin's lymphoma are given.
Practical issues that are commonly encountered when implementing adaptive
design methods in clinical trials are also discussed.

\section{Introduction}

In the past several decades, it is recognized that increasing spending of
biomedical research does not reflect an increase of the success rate of
pharmaceutical (clinical) development. Woodcock (2005) indicated that the
low success rate of pharmaceutical development could be due to (i) a
diminished margin for improvement that escalates the level of difficulty in
proving drug benefits, (ii) genomics and other new science have not yet
reached their full potential, (iii) mergers and other business arrangements
have decreased candidates, (iv) easy targets are the focus as chronic
diseases are harder to study, (v) failure rates have not improved, (vi)
rapidly escalating costs and complexity decreases willingness/ability to
bring many candidates forward into the clinic [1]. As a result, the United
States Food and Drug Administration (FDA) kicked off a {\it Critical Path
Initiative} to assist the sponsors in identifying the scientific challenges
underlying the medical product pipeline problems. In 2006, the FDA released
a {\it Critical Path Opportunities List} that calls for advancing innovative
trial designs, especially for the use of prior experience or accumulated
information in trial design. The {\it Critical Path Opportunities List}
interprets it as the encouragement for the use of innovative adaptive design
methods in clinical trials and the potential use of Bayesian approach in
clinical research and development. The purpose of adaptive design methods in
clinical trials is to give the investigator the flexibility for identifying
best (optimal) clinical benefit of the test treatment under study without
undermining the validity and integrity of the intended study.

The concept of adaptive design can be traced back to 1970s when the adaptive
randomization and a class of designs for sequential clinical trials were
introduced [2]. As a result, most adaptive design methods in clinical
research are referred to as adaptive randomization [3-6], group sequential
designs with the flexibility for stopping a trial early due to safety,
futility and/or efficacy [7-13], and sample size re-estimation at interim
for achieving the desired statistical power [14-16]. The use of adaptive
design methods for modifying the trial and/or statistical procedures of
on-going clinical trials based on accrued data has been practiced for years
in clinical research. Adaptive design methods in clinical research are very
attractive to clinical scientists due to the following reasons. First, it
reflects medical practice in real world. Second, it is ethical with respect
to both efficacy and safety (toxicity) of the test treatment under
investigation. Third, it is not only flexible, but also efficient in the
early and late phase of clinical development. However, it is a concern
whether the p-value or confidence interval regarding the treatment effect
obtained after the modification is reliable or correct. In addition, it is
also a concern that the use of adaptive design methods in a clinical trial
may lead to a totally different trial that is unable to address
scientific/medical questions that the trial is intended to answer [17-18].

In recent years, the potential use of adaptive design methods in clinical
trials have attracted much attention. The Pharmaceutical Research and
Manufacturers of America (PhRMA) and Biotechnology Industry Organization
(BIO) have established adaptive design working groups and proposed
strategies, methodologies, and implementations for regulatory consideration
[19]. However, there are no universal agreement in terms of definition,
methodologies, and applications. Many journals have published special
sections and/or issues on adaptive design. These journals included, but are
not limited to, Biometrics (Vol. 62, No. 3), Statistics in Medicine (Vol.
25, No. 19), Journal of Biopharmaceutical Statistics (Vol. 15, No. 4 and
Vol. 17, No. 6), Biometrical Journal (Vol. 48, No. 4), and Pharmaceutical
Statistics (Vol. 5, No. 2). For a comprehensive summarization of the issues
and recommendations for the use of adaptive design methods, readers many
consult with [18] and [20].

The purpose of this article is multi-fold. First, it is to provide a
comprehensive review of adaptive design methods in clinical research and
development. Second, it is not only to outline challenges in prospective
adaptations, impact on concurrent adaptations, and obstacles of
retrospective adaptations being made of on-going trials, but also to discuss
issues that are commonly encountered when implementing adaptive design
methods in clinical trials. Third, it is to discuss strategies for clinical
development of rare diseases using adaptive design methods. In the next
section, commonly employed adaptations and the resultant adaptive designs
are briefly described. Also included in this section are regulatory and
statistical perspectives regarding the use of adaptive design methods in
clinical trials. The impact of protocol amendments, challenges of by design
adaptations, and obstacles of retrospective adaptations when applying
adaptive design methods in clinical trials are discussed in Section 3. In
Section 4, strategies for the use of adaptive design in clinical development
of rare diseases are discussed. Also included in this section are some trial
examples concerning the development of Velcade (intended for multiple
myeloma and non-Hodgkin's lymphoma). Practical issues that are commonly
encountered when implementing adaptive design methods in clinical trials are
discussed in Section 5. Some concluding remarks are given in the last
section.

\section{What is adaptive design?}

In clinical trials, it is not uncommon to modify trial and/or statistical
procedures during the conduct of clinical trials based on the review of
interim data. The purpose is not only to efficiently identify clinical
benefits of the test treatment under investigation, but also to increase the
probability of success of clinical development. Trial procedures are
referred to as the eligibility criteria, study dose, treatment duration,
study endpoints, laboratory testing procedures, diagnostic procedures,
criteria for evaluability, and assessment of clinical responses. Statistical
procedures include randomization, study design, study objectives/hypotheses,
sample size, data monitoring and interim analysis, statistical analysis
plan, and/or methods for data analysis. In this article, we will refer to
the adaptations (or modifications) made to the trial and/or statistical
procedures as the adaptive design methods. Thus, an adaptive design is
defined as a design that allows adaptations to trial and/or statistical
procedures of the trial after its initiation without undermining the
validity and integrity of the trial [21]. In their recent publication, with
the emphasis of the feature of by design adaptations only (rather than ad
hoc adaptations), the PhRMA Working Group on Adaptive Design refers to an
adaptive design as a clinical trial design that uses accumulating data to
decide on how to modify aspects of the study as it continues, without
undermining the validity and integrity of the trial [19]. In many cases, an
adaptive design is also known as a flexible design.

\subsection{Adaptations}

An adaptation is referred to a modification or a change made to trial and/or
statistical procedure during the conduct of a clinical trial. By definition,
adaptations that are commonly employed in clinical trials can be classified
into the categories of prospective adaptation, concurrent (or ad hoc)
adaptation, and retrospective adaptation. Prospective adaptations include,
but are not limited to, adaptive randomization, stopping a trial early due
to safety, futility or efficacy at interim analysis, dropping the losers (or
inferior treatment groups), sample size re-estimation, and etc. Thus,
prospective adaptations are usually referred to as by design adaptations as
described in the PhRMA white paper [19]. Concurrent adaptations are usually
referred to as any ad hoc modifications or changes made as the trial
continues. Concurrent adaptations include, but are not limited to,
modifications in inclusion/exclusion criteria, evaluability criteria,
dose/regimen and treatment duration, changes in hypotheses and/or study
endpoints, and etc. Note that concurrent adaptations are generally not
envisioned as candidates for change initially but their needs become
apparent as the trial continues. Retrospective adaptations are usually
referred to as modifications and/or changes made to statistical analysis
plan prior to database lock or unblinding of treatment codes. In practice,
prospective, ad hoc, and retrospective adaptations are implemented by study
protocol, protocol amendments, and regulatory reviewer's consensus,
respectively.

\subsection{Type of adaptive designs}

Based on (primarily prospective) adaptations employed, commonly considered
adaptive design methods in clinical trials include, but are not limited to:
(i) an adaptive randomization design, (ii) a group sequential design, (iii)
a sample size re-estimation design, (iv) a drop-the-loser design, (v) an
adaptive dose finding (e.g., dose escalation) design, (vi) a
biomarker-adaptive design, (vii) an adaptive treatment-switching design,
(viii) a hypothesis-adaptive design, (ix) an adaptive seamless phase II/III
trial design, and (x) a multiple adaptive design. These adaptive design
methods are briefly described below.

\paragraph{Adaptive randomization design}

An adaptive randomization design is a design that allows modification of
randomization schedules based on varied and/or unequal probabilities of
treatment assignment in order to increase the probability of success (Figure
1) [See Additional file 1]. Commonly applied adaptive randomization
procedures include treatment-adaptive randomization [3-4],
covariate-adaptive randomization, and response-adaptive randomization [5-6].
Although an adaptive randomization design could increase the probability of
success (so-called play-the-winner), it may not be feasible for a large
trial or a trial with a relatively long treatment duration because the
randomization of a given subject depends on the response of the previous
subject. A large trial or a trial with a relatively long treatment duration
utilizing adaptive randomization design will take a much longer time to
complete. Besides, randomization schedule may not be available prior to the
conduct of the study. Moreover, statistical inference on treatment effect is
often difficult to obtain if it is not impossible due to complicated
probability structure as the result of adaptive randomization.

\paragraph{Group sequential design}

A group sequential design is a design that allows for prematurely stopping a
trial due to safety, futility/efficacy or both with options of additional
adaptations based on results of interim analysis. Various stopping
boundaries based on different boundary functions for controlling an overall
type I error rate are available in the literature (see, e.g., Lan and
DeMets, 1987; Wang and Tsiatis, 1987; Rosenberger et al., 2001; Jennison and
Turnbull, 2000, 2005; Chow and Chang, 2006). In recent years, the concept of
two-stage adaptive design has led to the development of the adaptive group
sequential design (e.g., Cui, Hung, and Wang, 1999; Posch and Bauer, 1999;
Lehmacher and Wassmer, 1999; Liu, Proschan, and Pledger, 2002). It should be
noted that the standard methods for group sequential design may not be
appropriate (i.e., it may not be able to control the overall type I error
rate at the desired level of 5\%) if there is a shift in target patient
population due to additional adaptations or protocol amendments.

\paragraph{Sample size re-estimation design}

A sample size re-estimation design is referred to as an adaptive design that
allows for sample size adjustment or re-estimation based on the observed
data at interim (Figure 2) [See Additional file 2]. Sample size adjustment
or re-estimation could be done in either a blinding or unblinding fashion
based on the criteria of treatment effect-size, conditional power, and/or
reproducibility probability (see, e.g., [9], [14-16], and [22-26]). Sample
size re-estimation suffers from the same disadvantage as the original power
analysis for sample size calculation prior to the conduct of the study
because it is performed by treating estimates of the study parameters, which
are obtained based on data observed at interim, as true values. It is not a
good clinical/statistical practice to start with a small number and then
perform sample size re-estimation (adjustment) at interim by ignoring the
clinically meaningful difference that one wished to detect for the intended
clinical trial. It should be noted that the observed difference at interim
based on a small number of subjects may not be of statistically significance
(i.e., it may be observed by chance alone). Thus, standard methods for
sample size re-estimation based on the observed difference with a limited
number of subjects may be biased and misleading.

\paragraph{Drop-the-losers design}

A drop-the-losers design is a design that allows dropping the inferior
treatment groups. A drop-the-losers design also allows adding additional
arms. A drop-the-losers design is useful in phase II clinical development
especially when there are uncertainties regarding the dose levels [27-30].
The selection criteria and decision rules play important roles for
drop-the-loser designs. Dose groups that are dropped may contain valuable
information regarding dose response of the treatment under study. Typically,
drop-the-loser design is a two-stage design. At the end of the first stage,
the inferior arms will be dropped based on some pre-specified criteria. The
winners will then proceed to the next stage. In practice, the study is often
powered for achieving a desired power at the end of the second stage (or at
the end of the study). In other words, there may not be any statistical
power for the analysis at the end of the first stage for dropping the losers
(or picking up the winners). In this case, it is a common practice to drop
the losers or pick up the winners based on so-called precision analysis,
i.e., an approach for determining the confidence level for achieving a
statistical significance. Note that some clinical scientists prefer the term 
{\it pick-the-winner designs}.

\paragraph{Adaptive dose finding design}

An adaptive dose finding (e.g., escalation) design is often used in early
phase clinical development to identify the minimum effective dose (MED)
and/or the maximum tolerable dose (MTD), which is used to determine the dose
level for the next phase clinical trials [31-33]. For adaptive dose finding
design, the method of continual re-assessment method (CRM) in conjunction
with Bayesian approach is usually considered [34-36]. Mugno et al. (2004)
introduced a nonparametric adaptive urn design approach for estimating a
dose-response curve [37]. More details regarding PhRMA's current position
and proposed statistical methods, the reader should consult with a special
issue recently published at the {\it Journal of Biopharmaceutical Statistics}%
, Vol. 17, No. 6.

\paragraph{Biomarker-adaptive design}

A biomarker-adaptive design is a design that allows for adaptations based on
the response of biomarkers such as genomic markers. An-adaptive biomarker
design involves biomarker qualification and standard, optimal screening
design, and model selection and validation. It should be noted that there is
a gap between identifying biomarkers that associated with clinical outcomes
and establising a predictive model between relevant biomarkers and clinical
outcomes in clinical development. For example, correlation between biomarker
and true clinical endpoint makes a prognostic marker. However, correlation
between biomarker and true clinical endpoint does not make a predictive
biomarker.

{\it A prognostic biomarker} informs the clinical outcomes, independent of
treatment. They provide information about the natural course of the disease
in individuals who have or have not received the treatment under study.
Prognostic markers can be used to separate good- and poor-prognosis patients
at the time of diagnosis. {\it A predictive biomarker} informs the treatment
effect on the clinical endpoint ([20]).

A biomarker-adaptive design can be used to (i) select right patient
population (e.g., enrichment process for selection of a better target
patient population), (ii) identify nature course of disease, (iii) early
detection of disease, and (iv) help in developing personalized medicine
(see, e.g., [20] and [38-39]).

\paragraph{Adaptive treatment-switching design}

An adaptive treatment-switching design is a design that allows the
investigator to switch a patient's treatment from an initial assignment to
an alternative treatment if there is evidence of lack of efficacy or safety
of the initial treatment (see, e.g., [36] and [40]). In oncology clinical
trials, estimation of survival is a challenge when treatment-switching has
occurred in some patients. A high percentage of subjects who switched due to
disease progression could lead to change in hypotheses to be tested. In this
case, sample size adjustment for achieving a desired power is necessary.

\paragraph{Adaptive-hypotheses design}

An adaptive-hypotheses design refers to a design that allows modifications
or changes in hypotheses based on interim analysis results [41].
Adaptive-hypotheses designs often considered before database lock and/or
prior to data unblinding. Some examples include the switch from a
superiority hypothesis to a non-inferiority hypothesis and the switch
between the primary study endpoint and the secondary endpoints. For the
switch from a superiority hypothesis to a non-inferiority hypothesis, the
selection of non-inferiority margin is critical which has an impact on
sample size adjustment for achieving the desired power. According to the ICH
guideline, the selected non-inferiority margin should be both clinical and
statistical justifiable.

\paragraph{Adaptive seamless phase II/III design}

An adaptive seamless phase II/III trial design is referred to a program that
addresses within single trial objectives that are normally achieved through
separate trials in phase IIb and phase III of clinical development. An
adaptive seamless phase II/III design (Figure 3) [See Additional file 3] is
an adaptive seamless phase II/III trial design that would use data from
patients enrolled before and after the adaptation in the final analysis
[42-43]. An adaptive seamless phase II/III design is a two-stage design
consisting of a so-called learning stage (phase IIb) and a confirmatory
stage (phase III). A typical approach is to power the study for the phase
III confirmatory phase and obtain valuable information with certain
assurance using confidence interval approach at the phase II learning stage.
Its validity and efficiency, however, has been challenged [44]. Moreover, it
is not clear how to perform a combined analysis if the study objectives (or
endpoints) are similar but different at different phases [45]. More research
is needed.

\paragraph{Multiple adaptive design}

Finally, a multiple-adaptive design is any combinations of the above
adaptive designs. Commonly considered multiple-adaptation designs include
(i) the combination of adaptive group sequential design, drop-the-losers
design, and adaptive seamless trial design and (ii) adaptive dose-escalation
design with adaptive randomization [18]. In practice, since statistical
inference for a multiple-adaptation design is often difficult, it is
suggested that a clinical trial simulation be conducted to evaluate the
performance of the resultant multiple adaptive design at the planning stage.

\subsection{Statistical and regulatory perspectives}

From regulatory point of view, the use of adaptive design methods based on
accrued data in clinical trials may introduce operational bias such as
selection bias, or bias that results from the method of evaluation, early
withdrawal, and modification of treatment. Consequently, it may not be able
to preserve the overall type I error rate at the pre-specified level of
significance. In addition, the naive p-values may not be correct and the
corresponding confidence intervals for the treatment effect may not be
reliable. Moreover, it may result in a totally different trial that is
unable to address the medical questions that original study intended to
answer. In practice, commonly seen adaptations include, but are not limited
to, (i) sample size adjustment at interim, (ii) sample size allocation to
treatments, (iii) delete, add, or change treatment arms, (iv) shift in
target patient population such as changes in inclusion/exclusion criteria,
(v) change in statistical test strategy, (vi) change in study endpoints, and
(vii) change in study objectives such as the switch from a superiority trial
to a non-inferiority trial. One of the drawbacks of adaptive designs is that
interpretation of trial results is difficult, such as the clinically
meaningful effect size for the treatments under study [46].

From statistical point of view, major (or significant) adaptations to trial
and/or statistical procedures could (i) introduce bias/variation to data
collection, (ii) result in a shift in location and scale of the target
patient population, and (iii) lead to inconsistency between hypotheses to be
tested and the corresponding statistical tests. These concerns will not only
have an impact on the accuracy and reliability of statistical inference
drawn on the treatment effect, but also present challenges to
biostatisticians for development of appropriate statistical methodology for
an unbiased and fair assessment of the treatment effect.

Note that although the flexibility of modifying study parameters is very
attractive to clinical scientists, several regulatory questions/concerns
arise. First, what level of modifications to the trial procedures and/or
statistical procedures would be acceptable to the regulatory authorities?
Second, what are the regulatory requirements and standards for review and
approval process of clinical data obtained from adaptive clinical trials
with different levels of modifications to trial procedures and/or
statistical procedures of on-going clinical trials? Third, has the clinical
trial become a totally different clinical trial after the modifications to
the trial procedures and/or statistical procedures for addressing the study
objectives of the originally planned clinical trial? These concerns should
be addressed by the regulatory authorities before the adaptive design
methods can be widely accepted in clinical research and development.

\section{Impact, challenges, and obstacles}

\subsection{Impact of protocol amendments}

In practice, for a given clinical trial, it is not uncommon to have 3-5
protocol amendments after the initiation of the clinical trial. One of the
major impacts of many protocol amendments is that the target patient
population may have been shifted during the process, which may have resulted
in a totally different target patient population at the end of the trial. A
typical example is the case when significant modifications are applied to
inclusion/exclusion criteria of the study protocol. As a result, the
resultant actual patient population following certain modifications to the
trial procedures is a {\it moving} target patient population rather than a
fixed target patient population. As indicated in [18], the impact of
protocol amendments on statistical inference due to shift in target patient
population (moving target patient population) can be studied through a model
that link the moving population means with some covariates [47]. Chow and
Shao (2005) derived statistical inference for the original target patient
population for simple cases [46].

\subsection{\noindent Challenges in \noindent {\it by design} adaptations}

In clinical trials, commonly employed prospective (by design) adaptations
include stopping the trial early due to safety, futility, and/or efficacy,
sample size re-estimation (adaptive group sequential design), dropping the
losers (adaptive dose finding design), and combining two separate trials
into a single trial (adaptive seamless design). These designs are typical
multiple-stage designs with different adaptations. In this section, major
challenges in analysis and design are described. Recommendations and future
development for resolution are provided whenever possible.

The major difference between a classic multiple-stage design and an adaptive
multiple-stage design is that an adaptive design allows adaptations after
the review of interim analysis results. These {\it by design} adaptations
include sample size adjustment (re-assessment or re-estimation), stopping
the trials due to safety, efficacy/futility, or dropping the losers (picking
the winners). Note that commonly considered adaptive group sequential
design, adaptive dose finding design, and adaptive seamless trial design are
special cases of multiple-stage designs with different adaptations. In this
section, we will discuss major challenges in design (e.g., sample size
calculation) and analysis (controlling type I error rate under moving target
patient population) of an adaptive multiple-stage design with $K-1$ interim
analyses.

A multiple-stage adaptive group sequential design is very attractive to
sponsors in clinical development. However, major (or significant)
adaptations such as modification of doses and/or change in study endpoints
may introduce bias/variation to data collection as the trial continues. To
account for these (expected and/or unexpected) biases/variation, statistical
tests are necessary adjusted to maintain the overall type I error and the
related sample size calculation formulas have to be modified for achieving
the desired power. In addition, the impact on statistical inference is not
negligible if the target patient population has been shifted due to major or
significant adaptations and/or protocol amendments. This has presented
challenges to biostatisticians in clinical research when applying a
multiple-stage adaptive design. In practice, thus, it is worthy pursuing the
following specific directions that (i) deriving valid statistical test
procedures for adaptive group sequential designs assuming model, which
relates the data from different interim analyses, (ii) deriving valid
statistical test procedures for adaptive group sequential designs assuming
the random-deviation model, (iii) deriving valid Bayesian methods for
adaptive group sequential designs, and (iv) deriving sample size calculation
formulas for various situations. Tsiatis and Mehta (2003) showed that there
exists an optimal (i.e., uniformly more powerful) design for any class of
sequential design with a specified error spending function. It should be
noted that adaptive designs do not require in general a fixed error spending
function [44]. One of major challenges for an adaptive group sequential
design is that the overall type I error rate may be inflated when there is a
shift in target patient population [48].

For adaptive dose finding design, Chang and Chow's method can be improved by
the following specific directions that (i) studying the relative merits and
disadvantage of their method under various adaptive methods, (ii) examining
the performance of an alternative method by forming the utility first with
different weights to the response levels and then modeling the utility, and
(iii) deriving sample size calculation formulas for various situations. An
adaptive seamless phase II/III design is a two-stage design that consists of
two phases namely a learning (or exploratory) phase and a confirmatory
phase. One of the major challenges for designs of this kind is that
different study endpoints are often considered at different stages for
achieving different study objectives. In this case, the standard statistical
methodology for assessment of treatment effect and for sample size
calculation cannot be applied.

For a two-stage adaptive design, the above described method by Chang (2007b)
can be applied [49]. Chang's method, however like other stage-wise
combination methods, is valid under the assumption of constancy of the
target patient populations, study objectives, and study endpoints at
different stages.

\subsection{Obstacles of retrospective adaptations}

In practice, retrospective adaptations such as adaptive-hypotheses may
encounter prior to database lock (or unblinding) and implemented through the
development of statistical analysis plan. To illustrate the impact of
retrospective adaptations, we consider the situation where switching
hypotheses between a superiority hypothesis and a non-inferiority
hypothesis. For a promising test drug, the sponsor would prefer an
aggressive approach for planning a superiority study. The study is usually
powered to compare the promising test drug with an active control agent.

However, the collected data may not support superiority. Instead of
declaring the failure of the superiority trial, the sponsor may switch from
testing superiority to testing the following non-inferiority hypotheses. The
margin is carefully chosen to ensure that the treatment of the test drug is
larger than the placebo effect and, thus, declaring non-inferiority to the
active control agent means that the test drug is superior to the placebo
effect. The switch from a superiority hypothesis to a non-inferiority
hypothesis will certainly increase the probability of success of the trial
because the study objective has been modified to establishing
non-inferiority rather than showing superiority. This type of switching
hypotheses is recommended provided that the impact of the switch on
statistical issues and inference (e.g., appropriate statistical methods) on
the assessment of treatment effect is well justified.

\section{Strategies for clinical development of rare diseases}

\subsection{Adaptive design strategies}

Clinical development of a new drug product is a lengthy and costly process,
which includes phases I to III clinical development (prior to regulatory
review and approval) and phase IV clinical development (post-approval). For
life-threatening diseases or diseases with unmet medical need (rare
diseases), this lengthy clinical development process is not acceptable.
Thus, the use of adaptive design methods in clinical trials is called for.
The purpose is to shorten the development process (speed) without
compromising the safety and efficacy of the drug product under investigation
(validity) by maximizing the power for identify best clinical benefit of the
drug product under investigation with limited number of subjects
(efficiacy). As a result, many adaptive design methods are developed for
archiving the ultimate goals of validity, efficiency, and speed in clinical
development. In practice, it however should be noted that many other
important factors beyond statistical components may have an impact on the
development process. These factors include, but are not limited to, patient
enrollment, treatment durations, and time required for regulatory
review/approval.

Commonly considered strategies for the use of adaptive design methods in
clinical development include, but are not limited to, adaptive dose finding,
adaptive seamless phase I/II in early clinical development, and adaptive
seamless phase II/III in late phase clinical development. These strategies
help in not only shortening the development time in a more efficient way but
also increasing the probability of success in clinical development. As an
example, let us consider the development of a new drug product for a rare
disease of multiple myeloma (MM) with unmet medical need. A traditional
approach is to conduct a typical phase I study for identifying the maximum
tolerated dose (MTD), which is often considered as the optimal dose for the
late phase of clinical development. In practice, there are several options
that we can run this study with several doses or dose schedules. For
example, this trial can be run with parallel dose groups or sequentially
with the test drug as a single or add-on agent. The traditional approach
will not be able to provide the entire spectrum of the dose response of the
test drug. On the other hand, if we consider an adaptive approach, it allows
us to use more options at the beginning and drop some of the arms (options)
if they are either too toxic or ineffective (activity too low or requires
very high dose that makes the treatment very costly -- biologic product may
be very costly). In addition, since the treatment arms are often correlated,
the information such as dose limiting toxicity (DLT) from different arms can
be synchronized using methods such as Bayesian model [36].

Similar approaches can be used for phase II trials, phase I/II, or phase
II/III adaptive seamless design. In this approach, the interim endpoint may
be a marker such as response rate or time to disease progression. Some of
the inferior arms can be dropped at interim. If some of the arms are
promising, we can apply different randomization scheme to assign more
patients to the superior arms (play-the-winner). In this case, not only the
total cost will not increase, but also we will increase the chance of
success because the increase of sample size for the superior treatment arms
are most promising. In addition, the schedules for the trial are similar
because the total number of patients remains unchanged. This adaptive design
strategy can be applied to phase III trials, but with much less arms. For
phase IV studies, the adaptive design can also be applied. However, the
situation is different because the drug has been approved during phase IV
clinical development. The focus of phase IV clinical development will be the
safety rather than efficacy.

In what follows, adaptive design strategies are illustrated through some
trial examples regarding the development of the drug product intended for
the rare disease of multiple myeloma. Without loss of generality, data are
modified from actual trials for the illustration purpose.

\subsection{Some trial examples}

\paragraph{\bf Example 1: Dose-finding (escalation) design }

In a phase I oncology trial, suppose that the primary objective is to
identify the maximum tolerated dose (MTD) for a new test drug. Based on the
animal studies, it is estimated that the toxicity (dose limiting toxicity
rate) is 1\% for the starting dose 25 mg/m$^{2}$ (1/10 of the lethal dose).
The dose limiting toxicity (DLT) rate at MTD is defined as 0.25 and the MTD
is estimated to be 150 mg/m$^{2}$. A typical approach is to consider
so-called 3+3 traditional escalation rule (TER). On the other hand, an
adaptive type approach is to apply the continual re-assessment method (CRM)
in conjunction with a Bayesian approach. We can compare the 3+3 TER approach
and the Bayesian CRM adaptive method through simulations. A logistic
toxicity model is chosen for the simulations. The dose interval sequence is
chosen to be the customized dose increment sequence (Increment factors = 2,
1.67, 1.33, 1.33, 1.33, 1.33, 1.33, 1.33, 1.33). The evaluations of the
escalation designs are based on the criteria of safety, accuracy, and
efficiency. Simulation results for all three methods for three different MTD
scenarios are summarized in Table 1.

\begin{center}
\qquad 
\end{center}

In this example, as it can be seen that if the true MTD is 150 mg/m$^{2},$
the TER approach underestimates MTD (125mg/m$^{2}$), while the Baysian CRM
adaptive method also slightly underestimates the MTD (141mg/m$^{2}$). The
average number of patients required is 19.4 and 15.5 for the TER approach
and the Bayesian CRM adaptive method, respectively. From a safety
perspective, the average number of DLTs is 2.9 and 2.5 per trial for the TER
approach and the Bayesian CRM, respectively. As a result, the Bayesian CRM
adaptive method is preferable.

\bigskip

\paragraph{{\bf Example 2:} {\bf Three-stage adaptive design for NHL trial}}

A phase III two parallel group Non-Hodgkin's Lymphoma trial was designed
with three analyses. The primary endpoint is progression-free survival
(PFS), the secondary endpoints are (1) overall response rate (ORR) including
complete and partial response and (2) complete response rate (CRR). The
estimated median PFS is 7.8 months and 10 months for the control and test
groups, respectively. Assume a uniform enrollment with an accrual period of
9 months and a total study duration of 23 months. The estimated ORR is 16\%
for the control group and 45\% for the test group. The classic design with a
fixed sample-size of 375 subjects per group will allow for detecting a
3-month difference in median PFS with 82\% power at a one-sided significance
level of $\alpha =0.025.$ The first interim analysis (IA) will be conducted
on the first 125 patients/group (or total $N_{1}=250$) based on ORR. The
objective of the first IA is to modify the randomization. Specifically, if
the difference in ORR (test-control), $\Delta _{ORR}>0$, the enrollment will
continue. If $\Delta _{ORR}\leq 0$, then the enrollment will stop. If the
enrollment is terminated prematurely, there will be one final analysis for
efficacy based on PFS and possible efficacy claimed on the secondary
endpoints. If the enrollment continues, there will be an second interim
analysis based on PFS. The second interim analysis will could lead to either
claim efficacy or futility, or continue to the next stage with possible
sample-size reestimation. The final analysis of PFS. When the primary
endpoint (PFS) is significant, the analyses for the secondary endpoints will
be performed for the potential claim on the secondary endpoints. During the
interim analyses, the patient enrollment will not stop. This example is
modified slightly from an ongoing adaptive trial (Figure 4) [See Additional
file 4].

\bigskip 

\paragraph{\bf Example 3: Two-stage drop-loser adaptive design for optimal
treatment in a phase IV trial }

For phase IV study, the adaptive design can also work well. For example,
after a year since an oncology drug in the market, physicians have used the
drug with different combinations for treating patients with MM. However,
there is a strong desire to know which combination is the best for the
patient populations. Many physicians have their own experiences, no one has
convincing data. Therefore, the sponsor is planned a trial to investigate
the optimal combination for the drug. In this scenario, we can use much
smaller sample size than phase III trials because the issue is focused on
the type-I control as the drug is approved. The issue is that given a
minimum clinically meaningful difference (e.g., two weeks in survival), what
is the probability of the trial will be able to identify the optimal
combination. Again this can be done through simulations, the strategy is to
start with about five combinations, drop inferior arms and calculate the
probability of selecting the best arm under different combinations of sample
size at the interim and final stages. In this adaptive design, we will drop
2 arms based on the observed response rate, i.e., the two arms with lowest
observed response rates will be dropped at interim analysis and the rest
three arms will be carried forward to the second stage. The characteristics
of the design are presented in Table 2 for different sample sizes.

Table 2: Simulation results of Phase IV drop-loser design

\begin{tabular}{lll}
\hline
Interim sample size & Final sample size & Probability of identifying \\ 
\hline
per group & per group & the optimal arm \\ 
25 & 50 & 80.3\% \\ 
50 & 100 & 91.3\% \\ \hline
\end{tabular}%
\qquad \qquad

Note: response rate for the five arms: 0.4, 0.45, 0.45, 0.5, and 0.6.

\bigskip

Given the response rate 0.4, 0.45, 0.45, 0.5, and 0.6 for the five arms and
91\% power, if a traditional design is used, there will be 9 multiple
comparisons (adjusted alpha = 0.0055 using Bonferroni method). The required
sample size for the traditional design is 209 per group or a total of 1045
subjects comparing a total of 500 subjects for the adaptive trial (250 at
the first stage and 150 at the second stage). \ In the case when the null
hypothesis is true (the response rates are the same for all the arms), it
doesn't matter too much which arm is choose as the optimal.

\bigskip

\section{Implementation of adaptive design in clinical trials}

As indicated earlier, the use of adaptive design methods in clinical trials
is very attractive due to its flexibility and efficiency for identifying
best clinical benefits of the treatment under investigation. The
flexibility, however, may introduce possible operational biases and
consequently have an impact on the overall type I error rate. Thus, some
practical issues that are commonly encountered when implementing adaptive
design methods in clinical trials are necessarily considered to ensure the
validity and integrity of the clinical trials. These practical issues are
key to the success of the clinical trials utilizing adaptive design methods.

\subsection{Study planning}

Before the implementation of an adaptive design in clinical trials, the
following practical issues are necessarily considered. First, the following
questions should be addressed in order for determining whether an adaptive
design is feasible for the intended trial:

\begin{itemize}
\item Will the adaptive design require extraordinary efforts for
implementation?

\item Are the level of difficulty and the associated cost justifiable for
the gain from the adaptive design?

\item Will the implementation of the adaptive design delay patient
recruitment and prolong the duration of the study?

\item Would delayed responses diminish the advantage of the adaptive design?

\item How often will the unblinded analyses be practical, and to whom should
the data be unblinded?

\item How should the impact of a Data Monitoring Committee's (DMC's)
decisions regarding the trial (e.g., recommending early stopping or other
adaptations due to safety concerns) be considered at the design stage?
\end{itemize}

Second, the following questions should be addressed to ensure the validity
of the adaptive design for the intended trial:

\begin{itemize}
\item Will the unblinding cause potential bias in treatment assessment?

\item Will the implementation of the adaptive design destroy the randomness?
\end{itemize}

Third, the following questions regarding the degree of flexibility (e.g.,
sensitivity or robustness) are necessarily considered:

\begin{itemize}
\item Will protocol deviations or violations invalidate the adaptive method?

\item How might an unexpected DMC action affect the power and validity of
the design?
\end{itemize}

When designing a trial, we should also consider how to prevent premature
release of the interim results to the general public using information masks
because releasing information it could affect the rest of the trial and
endanger the integrity of the trial. Regarding study design, and we strongly
suggest early communication with the regulatory agency and DMC regarding the
study protocol and the DMC charter. For broader discussions of planning
different adaptive designs, please see the PhRMA full white papers on
adaptive design (see, e.g., [16], [19], [43], [46], and [50-52])

\subsection{Communication with regulatory agency}

As indicated earlier, the primary concern when implementing adaptive design
methods in clinical trials is its validity and integrity from regulatory
perspective. It is a concern whether the application of adaptive design
methods may have introduced some unexpected operational bias, which may have
an impact on accuracy and reliability of the obtained statistical inference.
It is also a concern whether the application of adaptive design methods is
able to control the overall type I error rate at the pre-specified level of
significance. As a result, regulatory agencies such as the US FDA request
strategies or plans for preventing possible operation biases and for
controlling the overall type I error rate be developed. In addition, the
sponsors are encourage to begin a dialogue about adaptive designs with
medical reviewers and/or statistical reviewers from the regulatory agencies
as early as possible (preferably at least a year) before the planning of a
trial. In a adaptive design conference, an statistician from US FDA office
for adaptive design addresses some of the expectations for regulatory
submissions utilizing adaptive design([53]). These expectations regarding a
clinical trial utilizing adaptive design methods are summarized below:

\begin{itemize}
\item It should be prospectively planned;

\item It should have valid statistical approaches on modification of design
elements that have alpha control and can be defined in terms of ICH E-9
standard;

\item It should have valid point estimates and confidence interval estimates;

\item It should build on experience from external trials;

\item It should takes a {\it learn} and {\it confirm} approach;

\item It should have standard operating procedures (SOPs) and infrastructure
for adaptive process monitoring to avoid bias;

\item It should have SOPs on adaptive design decisions; and

\item It should includes documentation of actual monitoring process, extent
of compliance, and potential effect on study results.
\end{itemize}

In order to meet the above expectations, it is critical to communicate with
the agency. The advantage for communicating with the regulatory agency early
is that the regulatory agency could be of assistance in sharing the data or
at least the disease information or models available within the agency.
Building off external data and experience is sometimes a crucial element of
adaptive design. As indicated in {\it The Pink Sheet} (December 18 issue,
2006, p. 24), drug development is a knowledge-creating business and the
access to external data and experience is extremely helpful when
implementing adaptive design methods in clinical trials.

\subsection{Trial monitoring}

In practice, it is recognized that there are often deviations from the study
protocol when conducting a clinical trial. It is ethical to monitor the
trials to ensure that individual subjects are not exposed, or have limited
exposure, to unsafe or ineffective treatment regimens. For this purpose, an
independent DMC is usually established. The DMC plays a critical role in
monitoring clinical trials. There are common issues that affect a DMC's
decision, such as short-term versus long-term treatment effects, early
termination philosophies, response to early beneficial trends, response to
early unfavorable trends, and response where there are no apparent trends
[52-53]. It is recommended that a DMC be established to monitor the trial
when an adaptive design is employed in clinical trials, especially when many
adaptations are considered for allowing greater flexibility.

\paragraph{Stopping rules}

The stopping rule chosen in the design phase serves as a (statistical)
guideline to the DMC, which will make a decision regarding whether to
continue or stop the trial early due to safety, efficacy, or futility [51].
If all aspects of the conduct of the clinical trial adhered exactly to the
conditions stipulated during the design phase, the stopping rule obtained
during the design phase could be used directly. However, there are usually
complicated factors that must be dealt with during the conduct of the trial.

\paragraph{Deviation of analysis schedule}

DMC meetings are typically based on the availability of its members, which
may be different from the schedules set at the design phase. The enrollment
may be different from the assumption made at the design phase. Deviation in
the analysis schedule will affect the stopping boundaries; therefore, the
boundaries should be recalculated based on the actual schedules.

\paragraph{Deviation of efficacy variable estimation}

The true variability of the response variable is never known, but the actual
data collected at interim analysis may show that the initial estimates in
the design phase are inaccurate. Deviation in the variability could affect
the stopping boundaries. In this case, we may want to know the likelihood of
success of the trial based on current data, which is known as conditional
and predictive power, and repeated confidence intervals. Similarly, the
estimation of treatment difference in response could be different from the
initial estimation in the design phase. This could lead to an adaptive
design or sample-size re-estimation [12].

\paragraph{Safety factors}

Efficacy is not the only factor that will affect a DMC's decision. Safety
factors are critical for the DMC to make an appropriate recommendation to
stop or continue the trial. The term \textquotedblleft benefit-risk
ratio\textquotedblright\ is a most commonly used composite criterion to
assist in decision-making. In this respect, it is desirable to know the
likelihood of success of the trial based on current data, i.e., the
conditional power or predictive power. The DMC may also weight the
short-term and long-term treatment effects in its recommendations.

Note that the commonly used tools for monitoring a group sequential design
are stopping boundaries, conditional and predictive powers, futility index,
and repeated confidence interval. These tools can be used in other adaptive
designs. Bayesian monitoring tools are appreciated for different adaptive
designs.

\section{\noindent Concluding remarks}

As indicated earlier, although the use of adaptive design methods in
clinical trials is motivated by its flexibility and efficiency, there are
still some challenge in implementation. Recently, there are many discussions
are around the flexibility, efficiency, validity, integrity, and
implementations of various types of adaptive designs. When implementing an
adaptive design in a clinical trial, In practice, it is recommended that a
couple of principles that (i) adaptation should not alter the quality of
trial conduct and (ii) type I error should be preserved must be followed
when implementing the adaptive design methods in phase III clinical trials.
Following these principles, some basic considerations such as dose/dose
regimen, study endpoints, treatment duration, and logistics should be
carefully evaluated for feasibility [46]. To maintain the validity and
integrity of an adaptive design with complicated adaptations, it is strongly
suggested that an independent data monitoring committee (IDMC) should be
established. In practice, IDMC has been widely used in group sequential
design with adaptations of stopping a trial early and sample size
re-estimation. The role and responsibility of an IDMC for a clinical trial
using adaptive design should clearly defined. IDMC usually convey very
limited information to investigators or sponsors about treatment effects,
procedural conventions, and statistical methods with recommendations in
order to maintain the validity and integrity of the study.

When applying adaptive design methods in clinical trials, it is suggested
that the feasibility of certain adaptations such as changes in study
endpoints/hypotheses be carefully evaluated to prevent from any possible
misuse and abuse of the adaptive design methods. It should also be noted
that although clinical trial simulation does provide "$a$" solution not "$%
the $" solution for a complicated multiple adaptive design. In practice,
\textquotedblleft how to validate the assumed predictive model for clinical
trial simulation?\textquotedblright\ is a major challenge to both
investigators and biostatisticians.

For a fair and unbiased assessment of treatment effect, the impact of
protocol amendments, the major challenges of by design adaptations, and the
obstacles of retrospective adaptations prior to database lock and/or
unblinding must be carefully evaluated. However, thus far, statistical
methodology for addressing these issues (difficulties) are not fully
understood and well established, especially under the framework of moving
target patient \ population as the result of protocol amendments. In a
recent FDA/PhRMA Workshop on adaptive design held November 2006, the FDA has
announced to slow the escalating momentum behind adaptive clinical trial
designs to allow time to craft better working definitions of the new models
and build a better base before moving forward. As a result, it is suggested
that effort should be directed to current issues such as the impact of
protocol amendments, challenges in by design adaptations, and obstacles of
retrospective adaptations as described in the previous sections.

In summary, from the clinical point of view, adaptive design methods reflect
real clinical practice in clinical development. Adaptive design methods are
very attractive due to their flexibility and are very useful especially in
early clinical development. From the statistical point of view, the use of
adaptive methods in clinical trials makes current good statistics practice
even more complicated. The validity of the use of adaptive design methods is
not well established and fully understood. Guidelines regarding the use of
adaptive design methods must be developed so that appropriate statistical
methods and statistical software packages can be developed accordingly.
Regulatory guidelines can not only prevent possible misuse and/or abuse of
adaptive design methods in clinical trials, but also maintain the validity
and integrity of the trial.

\section{Acknowledgements}

The authors wish to thank Orphanet for the kind invitation and valuable
suggestions and comments that led to significant improvement of the article.
The authors also wish to thank John McHutchison, M.D., Ralph Corey, M.D.,
and colleagues from Duke University School of Medicine and Nancy Simonian,
M.D. and colleagues from Millennium Pharmaceuticals, Inc. for their
encouragement, support, constructive discussions and valuable comments
during the preparation of this article.

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\section{Figure legends}

Figure 1: Response-adaptive randomization

Figure 2: Sample size re-estimation

Figure 3: Phase II/III seamless trial design

Figure 4: Non-Hodgkin's lymphoma trial

\section{Tables}

Table 1: Summary of simulation results for the designs

\begin{center}
\begin{tabular}{ccccc}
\hline
Method & Assumed & Mean & Mean Number & Mean Number \\ \hline
& True MTD & Predicted MTD & of Ppatient & of DLTs \\ 
3+3 TER & 100 & 86.7 & 14.9 & 2.8 \\ 
CRM & 100 & 99.2 & 13.4 & 2.8 \\ 
3+3 TER & 150 & 125 & 19.4 & 2.9 \\ 
CRM & 150 & 141 & 15.5 & 2.5 \\ 
3+3 TER & 200 & 169 & 22.4 & 2.8 \\ 
CRM & 200 & 186 & 16.8 & 2.2 \\ \hline
\end{tabular}
\end{center}

\bigskip 

Table 2: Simulation results of phase IV drop-the-loser design

\begin{tabular}{lll}
\hline
Interim sample size & Final sample size & Probability of identifying \\ 
\hline
per group & per group & the optimal arm \\ 
25 & 50 & 80.3\% \\ 
50 & 100 & 91.3\% \\ \hline
\end{tabular}%
\qquad \qquad

Note: response rate for the five arms: 0.4, 0.45, 0.45, 0.5, and 0.6.

\section{Additional files}

\paragraph{Additional file 1}

File name: Figure1

File format: JPEG

Title: Response-adaptive randomization

\end{document}
