On Two-Stage Seamless Adaptive Design in Clinical Trials Shein-Chung Chow,1* Yi-Hsuan Tu2

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ORIGINAL ARTICLE

On Two-stage Seamless Adaptive Design in Clinical Trials Shein-Chung Chow,1* Yi-Hsuan Tu2

In recent years, the use of adaptive design methods in clinical research and development based on accrued data has become very popular because of its efficiency and flexibility in modifying trial and/or statistical procedures of ongoing clinical trials. One of the most commonly considered adaptive designs is probably a two-stage seamless adaptive trial design that combines two separate studies into one single study. In many cases, study endpoints considered in a two-stage seamless adaptive design may be similar but different (e.g. a biomarker versus a regular clinical endpoint or the same study endpoint with different treatment durations). In this case, it is important to determine how the data collected from both stages should be combined for the final analysis. It is also of interest to know how the sample size calculation/allocation should be done for achieving the study objectives originally set for the two stages (separate studies). In this article, formulas for sample size calculation/allocation are derived for cases in which the study endpoints are continuous, discrete (e.g. binary responses), and contain time-to-event data assuming that there is a well-established relationship between the study endpoints at different stages, and that the study objectives at different stages are the same. In cases in which the study objectives at different stages are different (e.g. dose finding at the first stage and efficacy confirmation at the second stage) and when there is a shift in patient population caused by protocol amendments, the derived test statistics and formulas for sample size calculation and allocation are necessarily modified for controlling the overall type I error at the prespecified level. [J Formos Med Assoc 2008;107(12 Suppl):S52–S60]

Key Words: adaptation, adaptive dose-escalation trial, adaptive seamless phase II/III trial, moving target patient population, protocol amendments

In clinical trials, it is not uncommon to modify methods include randomization, study design, trial and/or statistical procedures during the trial, study objectives/hypotheses, sample size, data based on a review of interim data. The purpose is monitoring and interim analysis, statistical analy- not only to efficiently identify clinical benefits of sis plan, and/or methods for data analysis. In this the test treatment under investigation, but also article, we will refer to the adaptations (or modifi- to increase the probability of success of clinical cations) made to the trial and/or statistical pro- development. Trial procedures are referred to as the cedures as the adaptive design methods. Thus, an eligibility criteria, study dose, treatment duration, adaptive design is defined as one that allows adap- study endpoints, laboratory testing procedures, tations to trial and/or statistical procedures of the diagnostic procedures, criteria for evaluability, trial after its initiation, without undermining the and assessment of clinical responses. Statistical validity and integrity of the trial.1 In their recent

©2008 Elsevier & Formosan Medical Association ...... 1Department of Biostatistics and Bioinformatics, Duke University School of Medicine, Durham, North Carolina, USA, and 2Department of Statistics, National Cheng Kung University, Tainan, Taiwan.

Received: July 26, 2008 *Correspondence to: Professor Shein-Chung Chow, Department of Biostatistics Revised: September 9, 2008 and Bioinformatics, Duke University School of Medicine, 2400 Pratt Street, Room Accepted: September 25, 2008 0311 Terrace Level, Durham, NC 27705, USA. E-mail: [email protected]

S52 J Formos Med Assoc | 2008 • Vol 107 • No 12 Suppl Two-stage seamless adaptive design in clinical trials publication, which emphasized the feature of by adaptive design in clinical research and develop- design adaptations only (rather than ad hoc adap- ment. A two-stage seamless adaptive trial design is tations), the Pharmaceutical Research Manufac- a study design that combines two separate studies turer Association Working Group on Adaptive into one single study. In many cases, study objec- Design refers to an adaptive design as a clinical trial tives and/or endpoints considered in a two-stage design that uses accumulating data to decide on seamless design may be similar but different (e.g. how to modify aspects of the study as it continues, a biomarker versus a regular clinical endpoint). without undermining the validity and integrity In this case, it is important to determine how the of the trial.2 In many cases, an adaptive design is data collected from both stages should be com- also known as a flexible design. bined for the final analysis. It is also of interest to The use of adaptive design methods for mod- know how the sample size calculation/allocation ifying the trial and/or statistical procedures of should be carried out to achieve the study objec- ongoing clinical trials based on accrued data has tives originally set for the two stages (separate been practiced for several years in clinical research. studies). In this article, formulas for sample size Adaptive design methods in clinical research are calculation/allocation are derived for cases in very attractive to clinical scientists for the following which the study endpoints are continuous and reasons. First, they reflect medical practice in the discrete (e.g. binary responses), and time-to-event real world. Second, they are ethical with respect data that assume that there is a well-established to both efficacy and safety (toxicity) of the test relationship between the study endpoints at dif- treatment under investigation. Third, they are not ferent stages. only flexible, but also efficient in the early phase In the next section, the commonly employed of clinical development. However, there can be two-stage adaptive seamless design is briefly out- concern over whether the p value or confidence lined. Also included in this section is a comparison interval regarding the treatment effect obtained between the two-stage adaptive seamless design after the modification is reliable or correct. In ad- and the traditional approach in terms of type I dition, it is also of concern that the use of adap- error rate and power. The section titled Sample tive design methods in a clinical trial may lead to Size Calculation/Allocation provides procedures a totally different trial, which is unable to ad- for sample size calculation/allocation for a two- dress scientific/medical questions that the trial is stage adaptive seamless design in which the study intended to answer.3,4 endpoints at different stages are different. Some Based on the adaptations employed, commonly practical issues when implementing a two-stage considered adaptive design methods in clinical adaptive seamless design are discussed in the sec- trials include, but are not limited to: (1) an adaptive tion titled Major Obstacles and Challenges. Some randomization design; (2) a group sequential de- concluding remarks are then given. sign; (3) an N-adjustable design or a flexible sample size re-estimation design; (4) a drop-the-loser (or pick-the-winner) design; (5) an adaptive dose- Two-stage Adaptive Seamless Design finding design; (6) a biomarker-adaptive design; (7) an adaptive treatment-switching design; (8) a Definition and characteristics hypothesis-adaptive design; (9) an adaptive seam- A seamless trial design is referred to as a program less trial design; and (10) a multiple adaptive de- that addresses study objectives within a single trial sign. Detailed information regarding these adaptive that are normally achieved through separate tri- designs can be found in Chow and Chang (2006).5 als in clinical development. An adaptive seamless In this article, however, we will only focus design is a seamless trial design that uses data from on the two-stage adaptive seamless trial design, patients enrolled before and after the adaptation which is probably the most commonly considered in the final analysis.6 Thus, an adaptive seamless

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design is a two-stage design that consists of two seamless phase II/III design, the study objective phases (stages), namely a learning (or exploratory) is for treatment selection (or dose finding) in the phase and a confirmatory phase. The learning first stage, while the study objective of the second phase provides opportunities for adaptations such stage is efficacy confirmation. as stopping the trial early because of safety and/or futility/efficacy based on accrued data at the end Comparison of the learning phase. A two-stage adaptive seam- A two-stage adaptive seamless design is considered less trial design reduces the lead time between a more efficient and flexible study design than the learning (i.e. the first study for the traditional the traditional approach of having separate studies approach) and confirmatory (i.e. the second study in terms of controlling type I error rate and power. for the traditional approach) phases. Most im- For controlling the overall type I error rate, con- portantly, data collected in the learning phase are sider, as an example, a two-stage adaptive seamless

combined with those obtained in the confirmatory phase II/III design. Let aII and aIII be the type I phase for final analysis. error rate for phase II and phase III studies, re- In practice, two-stage seamless adaptive trial spectively. Overall, a for the traditional approach = designs can be classified into the following four of having two separate studies is given by a aIIaIII. categories depending on study objectives and In a two-stage adaptive seamless phase II/III de- study endpoints at different stages: Category I— sign, on the other hand, the actual a is given by = same study objectives and same study endpoints; a aIII. Thus, a for a two-stage adaptive seamless

Category II—same study objectives but different phase II/III design is actually 1/aII times larger than study endpoints; Category III—different study the traditional approach for having two separate objectives but same study endpoints; Category phase II and phase III studies.

IV—different study objectives and different study Similarly, for the evaluation of power, let PowerII

endpoints. Note that different study objectives are and PowerIII be the power for phase II and phase usually referred to dose finding (selection) at the III studies, respectively. Then, overall power for first stage and efficacy confirmation at the second the traditional approach of having two separate = × stage, while different study endpoints are directed studies is given by Power PowerII PowerIII. In the to biomarkers versus clinical endpoints or the same two-stage adaptive seamless phase II/III design, = clinical endpoint with different treatment dura- the actual power is given by Power PowerIII. Thus, tions. Category I trial design is often viewed as a the power for a two-stage adaptive seamless phase

similar design to a group sequential design with II/III design is actually 1/PowerII times larger than one interim analysis, despite there being differences the traditional approach for having two separate between a group sequential and a two-stage seam- phase II and phase III studies. less design. In this article, our emphasis is on In clinical development, it is estimated that it Category II designs. The results obtained can be will take about 6 months to 1 year before a phase similarly applied to Category III and Category IV III study can be started after the completion of a designs, with some modification for controlling phase II study. This lead time is necessary for the overall type I error rate at a prespecified level. data management, data analysis, and statistical/ In practice, typical examples of a two-stage clinical report. A two-stage adaptive seamless de- adaptive seamless design include a two-stage adap- sign could, with good planning, reduce lead time tive seamless phase I/II design and a two-stage between studies. The study protocol does not need adaptive seamless phase II/III design. For a two- to be resubmitted to individual institutional review stage adaptive seamless phase I/II design, the ob- boards for approval between studies if the two jective of the first stage is biomarker development studies have been combined into one single trial. and the study objective of the second stage is to In addition, when compared with the tradi- establish early efficacy. For a two-stage adaptive tional approach of having two separate studies,

S54 J Formos Med Assoc | 2008 • Vol 107 • No 12 Suppl Two-stage seamless adaptive design in clinical trials a two-stage adaptive seamless trial design that com- (e.g. a biomarker) from the ith subject in phase II, = bines two separate studies may require a smaller i 1, …, n, and let yj be the observation of another sample size to achieve the desired power to address study endpoint (the primary clinical endpoint) the study objectives of both individual studies. from the jth subject in phase III, j = 1, …, m. Now,

assume that xi values are independently and identi- = = 2 Practical issues cally distributed with E(xi) n and Var(xi) t ; and

As indicated earlier, a two-stage adaptive seamless assume that yj values are independently and iden- = = 2 trial design combines two separate studies that may tically distributed with E(yj) m and Var(yj) s . use different study endpoints to address different Chow et al have proposed using the established study objectives. As a result, we may have different functional relationship to obtain predicted values study endpoints and/or different study objectives of the clinical endpoint based on data collected at different stages for a two-stage adaptive seamless from the biomarker (or surrogate endpoint).7 Thus, trial design. This leads to four different kinds of these predicted values can be combined with the two-stage seamless designs: (1) same study end- data collected in the confirmatory phase to develop point and same study objective; (2) same study a valid statistical inference for the treatment effect endpoint but different study objectives (e.g. dose under study. Suppose that x and y can be related finding versus efficacy confirmation); (3) different in a straight-line relationship: study endpoints (e.g. biomarker versus clinical end- = + + y b0 b1x e (1) point) but same study objective; and (4) different study endpoints and different study objectives. where e is an error term with zero mean and vari- 2 One of the questions commonly asked when ance z . Furthermore, e is independent of x. In applying a two-stage adaptive seamless design practice, we assume that this relationship is well- in clinical trials is how to perform sample size explored and that the parameters b0 and b1 are calculation/allocation. For the first kind of two- known. Based on (1), the xi values observed in + stage seamless design, the methods based on in- the learning phase will be translated to b0 b1xi ˆ dividual p values as described in Chow and Chang (denoted by yi ), and combined with the yi can be applied.5 However, these methods are not values collected in the confirmatory phase. ˆ appropriate if different study endpoints are used Therefore, yi and yi values are combined for the at different stages. Here, formulas and/or proce- estimation of the treatment mean m. Consider dures for sample size calculation/allocation, under the following weighted-mean estimator: a two-stage seamless study design using different mwˆ =+−yyˆ (1 w ) (2) study endpoints for achieving the same study 1 n 1 m objective are derived for various data types in- ˆˆ= = where yy∑ i , y ∑ y j , and 0 ≤ w ≤1. cluding continuous, discrete (binary response) and n i=1 m j=1 time-to-event data, assuming that there is a well- It should be noted that mˆ is the minimum vari- established relationship between the two study ance unbiased estimator among all weighted- endpoints. In other words, the study endpoint mean estimators when the weight is given by: considered in the first stage is predictive of that n/(bt22 ) employed in the second stage. w = 1 (3) 22+ 2 nm/(bt1 ) / s

2 2 2 if b1, t and s are known. In practice, t and Sample Size Calculation/Allocation s2 are usually unknown, and w is commonly estimated by: Continuous study endpoints 2 Consider a two-stage seamless phase II/III study. ns/ 1 wˆ = (4) ns//22+ ms Let xi be the observation of one study endpoint 12

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2 2 where s1 and s2 are the sample variances of yˆi second stages, respectively. Based on these observed θ and yj values, respectively. The corresponding es- data, the likelihood functions L( i) for the test timator of m, which is denoted by: treatment and the control treatment are:

nr− =+− qq=−ri [] qii mwˆ GD ˆˆyy(1 w ˆ ) (5) LGcLGcL()ii (,)iii1 (,) m −s GLsi (,qq )[]1 − GL (, ) iii is called the Graybill–Deal estimator of m. Based i iii on (5), we can test for differences between two for i = 1, 2; where i = 1 represents the test treatment treatments, i.e. a test treatment versus a control and i = 2 represents the control treatment. Assume treatment. For illustration purposes, consider that the lifetimes under test and control treatments testing the following hypotheses of equality: are exponentially distributed with parameters θ = l1 and l2, respectively. Thus, G1(t; 1) G(t, l1) and H : m = m0 vs. H : m ≠ m0 01 11 θ = G2(t; 2) G(t, l2). Then, the likelihood functions = r = + r Let m n. Then N (1 )n. It can be verified that become: the following formula provides an approximation −−−ll =− iicL r() n iii r cL to the required sample size n for achieving the Lee()(li 1 )

−−−ll desired power at the 5% level of significance, and ()1 − eeiiLs() m iii s L (7) is given as: ˆ Let li be the maximum likelihood estimate (MLE) ⎛ + ⎟⎞ Mfixed ⎜ 81()r ⎟ of l . Then, for i = 1, 2, lˆ can be found by solving n = ⎜11++ ⎟ (6) i i + −1 ⎜ + ⎟ 2()r rr⎝ ()1 r Mfixed ⎠ the following likelihood equation:

rci + si −−−−= 22 llcL L ()(),nrcmsii i i0 (8) ()zz+ s eeii− 11− where M = ab/2 is called the fixed fixed − 2 ()mm0 = 2 2 2 which is obtained by setting the first order partial sample size, and r b1 t /s . Note that in practice, derivative L(l ) with respect to l to zero. Note an initial estimate of r is often obtained by tak- i i that the MLE of l exists if and only if r /n and ing the ratio of the sample sizes obtained from i i i s /m do not equal 0 or 1 at the same time. Based on individual studies. i i the asymptotic normality of MLE (under suitable regularity conditions), lˆ asymptotically follows Binary responses i a normal distribution.9 In particular, as n and m Lu et al considered cases in which the study i i tend to infinity, the distribution of ( lˆ −l )/s (l ) endpoint is a discrete variable such as a binary i i i i converges to the standard normal distribution response.8 Suppose that the study duration of the where: first stage is cL and the study duration of the sec- − < < −−l λ − 12/ ond stage is L with 0 c 1. Assume that the re- =−+−12iicL 1L 1 slii()Lnce() i (11 ) mei ( ) sponse is determined by an underlying lifetime t, ˆ and the corresponding lifetime distribution of t Let si(li ) be the MLE of sili. Based on the θ 10 for the test treatment is G1(t, 1), while for the consistency of MLE, by Slutsky’s theorem, θ lˆ −l s ˆ control, it is G2(t, 2). If there are n1 and m1 ran- ( i i)/ i(li ) follows a standard normal distri- domly selected individuals in the first and second bution asymptotically. Consequently, an approx- − stages for the test treatment, respectively, let r1 and imate (1 a) confidence interval of li is given as ˆˆˆˆ−+ s1 be the numbers of respondents observed in the ()lsllsliiiiiizzaa/2 (), /2 (), where za/2 is the first and second stages for the test treatment, re- (1 − a/2)-quartile of a standard normal distribu- spectively. Similarly, for the control treatment, tion. Under an exponential model, comparison

there are n2 and m2 randomly selected individuals of two treatments usually focuses on the hazard

for the control treatment. Let r2 and s2 be the rate li. For the comparison of two treatments numbers of respondents observed in the first and in pharmaceutical applications, namely, control

S56 J Formos Med Assoc | 2008 • Vol 107 • No 12 Suppl Two-stage seamless adaptive design in clinical trials versus treatment, it is often interesting to study the likelihood function for the test treatment and the hypotheses testing of equality, superiority, the control treatment can be obtained as follows: noninferiority and equivalence of two treatments. n 2 ij − d 1 d ijk qqq=−ijk ⎡ ⎤ Furthermore, to facilitate the planning of a clinical LgxGx()ii∏∏ (jk ,)i⎣⎢1 (ijk ,) i ⎦⎥ (11) j k == 11 study, researchers are also interested in determining the required sample size that would allow the for i = T, R. In particular, suppose that the observed corresponding tests to achieve a given level of time-to-event data are assumed to follow a Weibull power.11 For illustration purposes, consider testing distribution. Denote the cumulative distribution the following hypotheses for equality: function (cdf) of a Weibull distribution with b l, b > 0 by G(t; l, b) where Gt(;,)lb =−1 e−(/t l ). H : l = l vs. H : l ≠ l (9) 0 1 2 0 1 2 q = q = Suppose that G(t; T) G(t; lT, bT) and G(t; R) = r = g = Let mi ni and n2 n1, i 1, 2. Then the total sam- G(t; l , b ), i.e. t follows the Weibull distribution + + R R ijk ple size NT for two treatments is (1 r)(1 g)n1, with cdf G(t; li, bi). Then the likelihood function where: in (11) becomes: 2 2 2 ++ 2 nij ()(()())zzabsl sl /2 1 122 d n = ∑∑ ijk 1 2 (10) −b == − = i j k 11 ()l12l L(,)(lbii bl ii ) − n − ll−−1 2 ij 2 22 11cL 1 L 1 − sl=−+−() r ∑∑ xijk 2 nij 1 ()1 Lce (11 ) ( e ) − j k == 11 (bbdiijk1) ex∏∏ ijk (12) and j k== 11 b = i = − where xx()l . Let l(li, bi) log(L(li, bi)) −− ll− −1 ijk ijk i sl 2()=−+−Lce212 g() (22cL 11 )1 r ( eL )1 2 2 be the log-likelihood function. Based on the log-

likelihood function, the MLEs of bi and li (denoted Time-to-event data ˆ ˆ by b i and li ) can be obtained. Under the as- Similar ideas can be applied to derive formulas for sumption of asymptotic normality of MLE, it can sample size calculation/allocation for time-to-event ˆ ˆ be shown that li and b i are asymptotically nor- 12 9 data. Let tijk denote the length of time from a mally distributed. Thus, formulas for sample size patient entering the trial to the occurrence of some calculation/allocation can be similarly obtained. th th events of interest for the k subject in the j stage For illustration purposes, consider testing the fol- th = = = of i treatment, where k 1, 2, …, nij, j 1, 2, i T lowing hypothesis of equality between medians: and R. Assume that the study durations for the H : M = M vs. H : M ≠ M (13) first and second stage are different, which are given 0 T R 1 T R = by cL and L respectively, where c < 1. Furthermore, where Mi is the median of G(t; li, bi), i T, R. Let ˆ q Mi be the MLE of Mi and ui be the variance of Mi. assume that tijk follows a distribution with G(t, i) q We first consider the one treatment case, i.e. the and g(t, i) as the cumulative distribution function and probability density function with parameter following hypothesis is considered: q = ≠ vector i, respectively. The data collected from the H0 : MT M0 vs. H1 : MT M0 (14) study can then be represented by (xijk, dijk), where ˆ Based on the asymptotic normality of MLE MT , d = 1 indicates that the event of interest is ob- ijk we can then reject the null hypothesis at an ap- = = served and that xijk tijk, while dijk 0 means that ˆ − proximate a level of significance if ||MMT 0 the event is not observed during the study, i.e. xijk < −1 υ> ˆ −υ−1 is censored and that xijk tijk. In clinical trials, it is nzTT1/ˆ α 2. Since ()/MMTT n TT1 ˆ approxi- not uncommon to observe censored data due to mately follows the standard normal distribution, drop-out, loss to follow-up, or survival at the end of the power of the above test under H1 can be Φ−−1 − the trials. In this article, for simplicity, we will only approximated by ()||MMTT01 nuT za /2 , consider the case where censoring is due to survival where F is the distribution function of the standard at the end of the trials. Given the observed data, normal distribution. Hence, in order to achieve

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a power of 1 – b, the required sample size satisfies Major Obstacles and Challenges −−=−1 = ||MMTT01 nuT zab/2 z. If nT2 rnT1, the required total sample size N for the two phases is Instability of sample size = + given as N (1 r)nT1, where nT1 is given by: Under certain assumptions, sample size for testing hypotheses of equality can be obtained as follows: + 2 ()zzab/2 uT = 22 nT1 (15) + − 2 ()zzab/2 s ()MM10 N = , 0 d 2 Following the above hypothesis, the corresponding where s2/d2 is often estimated by sample mean sample size to achieve a prespecified power of 1 – b and sample variance from some pilot studies. Let with a significance level of a can be determined. q = s2/d2. Then, it can be verified that bias of Hence, the corresponding required sample size for qdˆˆ= s22/ is given by: testing the hypothesis in (13) satisfies the following equation: ˆ −=−12{} + ENo()qq 30 q 1 (1). (17)

−+−=−−1 1 As a result, sample size obtained based on ||MMTR n TTRR1uu n1 zab/2 z. qdˆˆ= s22/ can be substantial, and consequently = = Let ni2 rini1 and nR1 gnT1. It can be easily derived lead to instability of the sample size calculation.

that the total sample size NT for the two treatment To reduce bias, one may consider using the me- + + + 22 groups in two stages is nT1[1 rT (1 rR)g], with dian of s /dˆ such that:

nT1 given as: 2 ˆ ≤=η Ps{/d 0.5 }0.5 ()()zz++21ugu− n = ab/2 TR(16) It can be verified that the bias of median estimate T1 ()MM− 2 TR is much less as compared with that of (17), i.e.

−=−−1 {} = Remarks hq05. 15.().No0 q 1 1 (18) For illustration purposes, formulas for sample size Equation (18) suggests that a bootstrap-median calculation/allocation were derived for continuous, approach be considered for a stable sample size discrete, and time-to-event data for testing hypoth- calculation in clinical trials. eses of equality, assuming that: (1) there is a well- established relationship between different study Moving patient population endpoints at different stages; and (2) the study In practice, it is not uncommon to have protocol objectives for both stages are the same. Formulas amendments during the conduct of clinical tri- for sample size calculation/allocation for testing als. As a result, it is likely that a shift in patient superiority and noninferiority/equivalence can be population may have occurred before and after similarly derived. protocol amendments. Chow et al13 suggested In practice, it should be noted that such a assessing the shift in patient population using relationship (i.e. one study endpoint is predictive the following sensitivity index: of the other study endpoint) may not exist. Thus, the relationship should be validated based on m me+ Δm E ==0 = 0 historical or observed data. When the study objec- s Cs 0 s 0 tives are different at different stages (e.g. dose m ==ΔΔ0 (19) finding at the first stage and efficacy confirmation E0 , s 0 at the second stage), the above derived formulas

are necessary for controlling the overall type I where E0 and E are the effect sizes before and ⌬ = + error rate at a and for achieving the desired powers after protocol amendment, and (1 e/m0)/C at both stages. is the sensitivity index before and after protocol

S58 J Formos Med Assoc | 2008 • Vol 107 • No 12 Suppl Two-stage seamless adaptive design in clinical trials amendment. When a shift in patient population adaptive randomization may be applied at the has occurred, we recommend the following sam- end of the first stage. Although this approach ple size adjustment: sounds reasonable, it is not clear how the overall

⎪⎧ ⎛ a ⎞⎪⎫ type I error rate can be controlled. More research ⎪ ⎜ E ⎟⎪⎪⎪ = ⎨ ⎜ 0 ⎟⎬ NNminmax ,max⎜ NsignEEmin , (0 ) N0 ⎟ , is needed. ⎪ ⎝⎜ E ⎠⎟⎪ ⎩⎪ ⎭⎪ From a clinical point of view, adaptive design (20) methods reflect real clinical practice in clinical where Nmin and Nmax are the minimum and maxi- development. Adaptive design methods are very mum sample sizes, a is a constant, and sign(x) = 1 attractive because of their flexibility, and are es- for x >0; otherwise, sign(x) =−1. Note that a should pecially useful in early clinical development. How- be chosen so that the sensitivity ⌬ is within an ever, many researchers are not convinced and still acceptable range. challenge its validity and integrity.15 From the statistical point of view, the use of adaptive methods in clinical trials makes good statistical practice Concluding Remarks even more complicated. The validity of the use of adaptive design methods is not well established. In this article, formulas for sample size calcula- The impact of statistical inference on treatment tion/allocation under a two-stage seamless adaptive effect should be carefully evaluated within the trial design that combines two separate studies with framework of moving target patient population different study endpoints but the same study ob- as the result of protocol amendments (i.e. modi- jective are derived assuming that there is a well- fications made to the study protocols during the established relationship between the two different conduct of the trials). In practice, regulatory agen- study endpoints. In practice, a two-stage seamless cies may not realize that the adaptive design adaptive trial design that combines a phase II methods for review and approval of regulatory study for dose finding and a phase III study for submissions have been employed for several years efficacy confirmation is commonly considered.14 without any scientific basis. Guidelines regarding In this case, the study objectives at different stages the use of adaptive design methods must be de- are similar but different (i.e. dose finding versus veloped so that appropriate statistical methods efficacy confirmation). A two-stage seamless adap- and statistical software packages can be developed tive trial means one that is able to address both accordingly. study objectives with the desired power, and com- bine data collected from both stages for a final analysis. In this case, it is important to establish References how to control the overall type I error rate and achieve the desired powers at both stages. A typical 1. Chow SC, Chang M, Pong A. Statistical consideration of approach is to consider precision analysis at the adaptive methods in clinical development. J Biopharm Stat first stage for dose selection and power the study 2005;15:575–91. 2. Gallo P, Chuang-Stein C, Dragalin V, et al. Adaptive design in for detecting a clinically meaningful difference at clinical drug development—an executive summary of the the second stage (by including the data collected at PhRMA Working Group (with discussions). J Biopharm Stat the first stage for the final analysis). For precision 2006;16:275–83. analysis, the dose with highest confidence level for 3. Committee for Proprietary Medicinal Products. Points to achieving statistical significance will be selected Consider on Methodological Issues in Confirmatory Clinical Trials with Flexible Design and Analysis Plan. London: The under some prespecified selection criteria. Some European Agency for the Evaluation of Medicinal Products, adaptations such as dropping the inferior arms 2002 (CPMP/EWP/2459/02). or picking up the best dose, stopping the trial 4. Committee for Medicinal Products for Human Use. early because of safety and/or futility/efficacy, or Reflection Paper on Methodological Issues in Confirmatory

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