dose estimation

Pharm Med 2008; 22 (1): 35-40REVIEW ARTICLE 1178-2595/08/0001-0035/$48.00/0

© 2008 Adis Data Information BV. All rights reserved.

Dose EstimationA Key Step in Malignancies Drug Development

Sarah Zohar1,2 and Vincent Levy1,2

1 Biostatistics Department, Inserm U 717, Saint-Louis Hospital, Assistance Publique, Hopitaux de Paris, Universite Paris 7,Paris, France

2 Inserm CIC 9504, Clinical Research Center, Saint-Louis Hospital, Assistance Publique, Hopitaux de Paris, Universite Paris7, Paris, France

Contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351. Maximum Tolerated Dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362. Algorithm-Based Dose-Finding Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.1 Traditional ‘A + B’ Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.2 Accelerated Titration Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3. Statistical-Based Dose-Finding Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.1 The Continual Reassessment Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.2 The Escalation with Overdose Control Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.3 Decision Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4. Futures Trends: Phase I/II Clinical Trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385. Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.1 The Homoharringtonine Trial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

This paper presents state-of-the-art statistical methods for dose-finding experiments in first-in-man clinicalAbstractstudies of drugs for the treatment of malignancies. Most early-phase clinical trials are not hypothesis driven,which might be the reason why statistical considerations have been largely ignored in dose-finding studies. Thestandard experimental design for dose-finding clinical studies employs a rule-based, dose-escalation scheme inwhich escalation depends on the number of patients at a dose level who experience dose-limiting toxicity. Thestandard design is widely used because of its algorithm-based simplicity for clinical investigators.

In the last two decades, new approaches for dose-finding have been proposed, all aiming to (i) model thetoxicity of a new treatment as a percentile of the dose-toxicity relationship; (ii) minimize the number of patientstreated at unacceptably high toxic dose levels; and (iii) minimize the number of patients needed to complete thestudy. In this paper, we describe some of these methodologies in simple terms for nonstatisticians.

Early-phase clinical trials, during which the dose level for extensive animal studies designed to select the starting dose forfurther investigation is estimated, are a key step in drug develop- use in humans, that is, the maximum recommended starting dosement. The dose-level choice is crucial for assessing efficacy and (MRSD).[1] Phase I represents the first translation from basicsafety in future development phases and thereby influences the laboratory work to the clinical setting. Usually, phase I trials aresuccess or failure of the new treatment. performed in healthy volunteers, except when the drug is intended

In humans, clinical drug development is initiated with what is for the treatment of malignancies. In this case, phase I trials aretermed ‘phase I trials’. Phase I trials follow in vitro analysis and aimed at obtaining reliable information on the safety, tolerability,

36 Zohar & Levy

pharmacokinetics and mechanism of action of a drug. More specif- In standard phase I designs, the MTD is defined as the doseically, in a healthy volunteer study, the objective is to determine level at which 20%, 33% or 50% of patients experienced a dose-the maximum safe dose under a certain pharmacokinetic or phar- limiting toxicity. In this case, the MTD is treated as being observa-macodynamic safety limit; for a cancer study, the objective is to ble from the data. Recent dose-finding methods also define thedetermine the maximum tolerated dose (MTD), defined as the MTD as an unknown population parameter that corresponds to ahighest dose with a relatively low risk of dose-limiting toxicity, or specified probability and must be estimated.[3,4] In this setting,to recommend a dose level for phase II trials.[2] several sequential designs were recently proposed, including the

continual reassessment method,[5] decision theoretic approaches[6]In phase I trials, two main competing interests must be consid-

and escalation with overdose control method.[7]ered: (i) limiting the number of patients exposed to nontherapeuticdrug doses; and (ii) ensuring the safety of the patients enrolled in

2. Algorithm-Based Dose-Finding Designsthe trial. For cytotoxic anticancer drugs, a dose-toxicity effect isassumed, whereby the higher the dose the greater the risk of dose-limiting toxicity. The goal of dose-finding studies is to estimate 2.1 Traditional ‘A + B’ Designsthe MTD that corresponds to some given acceptable toxicity rate.

The ‘A + B’ designs with or without dose de-escalation, includ-These trials are not hypothesis driven, which might be the reasoning the ‘3 + 3’ design, are most frequently used in phase I dose-why statistical considerations have been largely ignored in dose-finding clinical trials (see figure 1).[8] The traditional ‘A + B’finding studies, despite their crucial place in drug development.design can be summarized as follows: a cohort of A patients is

In this paper, we present a short review of statistical designs onincluded at dose level di. If <C/A patients experience a dose-

studies in which the selection and estimation of drug doses forlimiting toxicity, then the next cohort of A patients receives the

further development are based on two types of designs: (i) al-dose level di+1. If >D/A (where D ≥ C) patients experience a dose-

gorithm-based designs in which the MTD is treated as beinglimiting toxicity, then the dose level di–1 is considered to be the

identifiable from the data and is, thus, a statistic rather than aMTD. If ≥C/A but ≤D/A patients experience a dose-limiting toxici-

parameter with no estimation involved; and (ii) statistical-basedty, then the next additional B patients receive dose level di. If no

designs in which the MTD is treated as a population parameter.more than E (where E ≥ D) of ‘A + B’ patients experience a dose-

These designs are driven by accumulating patient observationslimiting toxicity, then the dose is escalated. If >E of ‘A + B’

that are used to refine the model for predicting the recommendedpatients experience a dose-limiting toxicity, then the previous dose

dose.[3]

is considered to be the MTD.[8] A, B, C, D and E are integers >0.The traditional ‘3 + 3’ design is a special case of this general

1. Maximum Tolerated Dose ‘A + B’ design, in which A = B = 3 and C = D = E = 1. Other casesof ‘A + B’ can be considered:

For phase I cytotoxic anticancer drugs, it is assumed that a • ‘A + B’ design with dose de-escalation;monotone dose-toxicity relationship exists, that is, the higher the • M1 A + B: a modified ‘A + B’ design with the ability to declaredose, the greater the risk of dose-limiting toxicity. A dose-res- the current dose level as the MTD;ponse relationship effect is also assumed, which stipulates that the • M2 A + B: a modified ‘A + B’ design where the first dose levelhigher the dose, the greater the possibility of obtaining a therapeu- is not necessarily the lowest dose;tic response. In this setting, the goal of phase I dose-finding studies • M3 A + B: a modified ‘A + B’ design with fewer than threeis to find the highest tolerable dosage – the MTD – that corre- patients in each cohort.sponds to a given acceptable toxicity rate.[3]

The latter three designs can be applied with or without dose de-escalation.The concept of ‘monotonicity’ is widely assumed for cytotox-

ics; that is, if a patient experiences dose-limiting toxicity at a In the traditional ‘3 + 3’ design, the study is ended as soon asspecific level, then this same patient will also experience dose- two or more toxicities are observed at one dose and for all levelslimiting toxicity if treated at any higher dose level. Conversely, if below, and MTD is defined as the highest level at which no morethe patient tolerates treatment at a specific dose, then tolerance is than one toxicity occurred out of a total of six patients. In thisassumed for all lower dose levels. This is a reasonable assumption design, allocation of the next dose level is recommended for anin most cases, but needs to be studied further with regard to incoming group of three patients depending on what happened torecently developed therapies such as cellular therapy or in vaccine the total of three or six patients treated at the current level. Alltrials. other information concerning the preceding dose levels and the

© 2008 Adis Data Information BV. All rights reserved. Pharm Med 2008; 22 (1)

Dose Estimation in Malignancies Drug Development 37

Enter A patients

Enter 3 patients

Dose level di−1 is MTDEscalate to dose level di+1

Dose level di

<C/Apatients with DLT

<1/3patients with DLT

≥C/A and ≤D/Apatients with DLT

1/3patients with DLT

>D/Apatients with DLT

>1/3patients with DLT

Enter B patients

Add 3 patients

≤E/(A + B)patients with DLT

≤1/6patients with DLT

>E/(A + B)patients with DLT

>1/6patients with DLT

Fig. 1. Escalation scheme for A + B design. Each text box is divided in half by a dashed line; the bottom half of the text boxes represent the traditional ‘3 +3’ design, which is a special case of the A + B design where A = B = 3 and C = D = E = 1. DLT = dose-limiting toxicity; MTD = maximum tolerated dose.

distribution of toxicities is ignored. Moreover, this design does not 3. Statistical-Based Dose-Finding Designsallocate as many patients as possible at and around the targeteddose level. Therefore, these designs are termed ‘memoryless’.[9] Over the last 15 years, new dose-finding designs have beenAlthough this approach has been highly criticized,[9-12] it is widely proposed for cancer cytotoxic clinical trials.[5-7] The aims of theseused in phase I clinical trials. One of the reasons why this method- methods are to: (i) model the toxicity of a new treatment as aology is so popular among clinicians is the simplicity of its percentile of the dose-toxicity relationship; (ii) minimize the num-implementation and the fact that a statistician is not necessary. ber of patients treated at unacceptably high toxic dose levels; and

(iii) minimize the number of patients needed to complete thestudy. These designs are presented in this section, and include the2.2 Accelerated Titration Designcontinual reassessment method, escalation with overdose controlmethod and decision theory; all three are Bayesian designs.Storer[13] and Simon et al.[14] described a family of ‘accelerated

titration designs’ that are based on a rapid initial dose-escalation3.1 The Continual Reassessment Methodphase and intra-patient dose escalation. The dose allocation rule is

based on the definition of dose-limiting toxicity and moderatetoxicity. The most frequently used accelerated titration design is as The continual reassessment method was proposed byfollows: one patient per cohort is included and dose-escalation O’Quigley et al.[5] to challenge the standard designs by addressingsteps are made in 40% increments. The accelerated phase ends practical and ethical concerns within a rigorous mathematicalwhen a dose-limiting toxicity is experienced in the first instance of framework. This method aims to estimate some quantile of thefirst course of treatment or a moderate toxicity is observed in the underlying dose-toxicity curve, defining the MTD as the dose thatsecond instance of first course of treatment. Once the accelerated produces some target percentage of toxicity. The MTD is estimat-phase ends, standard ‘3 + 3’ dose escalation proceeds.[15] ed from a discrete dose range, defined by the investigators prior to

This type of design can reduce the number of patients included the trial onset. Interestingly, it is an adaptive design in the sensein phase I trials compared with the standard ‘3 + 3’ dose-escalation that it uses all of the available data prior to the trial onset and alldesign, and is one of the few methods with an intra-patient dose- the data from the trial that has accumulated at the time each doseescalation rule. However, in a survey of the literature published level is selected for new patients. Moreover, the continual reas-since 2000, only 12 cancer drug trials were identified that used this sessment method is designed to allocate as many patients asdesign. possible at and around the targeted dose level.[16]


38 Zohar & Levy

The basic idea is to directly address the first two requirements 3.3 Decision Theoryfor phase I studies – to minimize the number of under-treated

Whitehead and Brunier[6] developed a Bayesian decision-theo-patients (i.e. patients treated at unacceptably low dose levels) andretic approach to estimate the dose-response relationship withto minimize the number of patients treated at unacceptably highspecific attention to the target dose (i.e. the dose level to bedose levels. The MTD can then be viewed as the level that above itestimated as the MTD or the dose level to be recommended for thewe are over-treating and below it we are under-treating. The aim ofnext phase). As with the continual reassessment method, thisthis design is to treat as many patients as possible at the MTD.method uses a model for the dose-toxicity relationship; the dose to

The essential nature of the continual reassessment method[17] isbe estimated must be pre-specified, and uses a sequential dose

a (i) sequential dose allocation rule, with the intent of assigningallocation rule. The dose level to be administered to each new

doses ever closer to the MTD; and (ii) statistical procedure thatcohort of patients, however, is based on calculating gain func-

updates the information on the probabilities of toxicity as a func-tions.[2] 1 Several gain functions have been proposed by Whitehead

tion of the observed toxicities obtained for patients already treated;and Williamson[19] to determine the best dose for the next cohort of

hence the term ‘reassessment’.[9]

patients:The objective of the continual reassessment method is not only • a dose level associated with high enough toxicity;

to identify the MTD or dose level to recommend for further• to provide a potential therapeutic benefit;

experiments, but also to estimate the probability of toxicity asso-• a dose level low enough to avoid undesirable adverse effects.

ciated with this dose level based on all of the available informa-These three approaches involve sequential updating of the

tion. Moreover, the standard continual reassessment method as-estimated MTD as a function of the dose levels and the observed

signs one patient per dose level, but this has been modified totoxicities so far observed in the trial. For the continual reassess-

cohorts of one to three patients per dose level.[10]

ment method, this is the dose that is, in some sense, close to theestimated target (or in the terminology of Whitehead, the ‘patient

3.2 The Escalation with Overdose Control Method gain’), and for the escalation with overdose control procedure thedose is selected according to the ‘Bayesian feasible’ criterion. Themodelling used in the continual reassessment method can beThe escalation with overdose control method was first pro-formulated so that doses higher than the current estimate of theposed by Babb et al.[7] to estimate the MTD as quickly as possibleMTD are not allocated to the patients.[4]under the constraints of overdose control. The continual reassess-

ment method and escalation with overdose control designs share4. Futures Trends: Phase I/II Clinical Trialssome common features:

• a parametric framework that uses a model for the dose-toxicity The aim of phase I dose-finding studies is to find the highestrelationship; tolerable dose that corresponds to some given acceptable toxicity

• a sequential dose allocation rule; rate, which is retrospectively assumed to be associated with the• the dose level administered to each new cohort of patients is the highest efficacy rate. This is reasonable in most cases with

dose level closest to the currently estimated MTD. cytotoxic drugs, but needs to be studied further with regard tonewly developed therapies. For example, for targeted anticancerHowever, the escalation with overdose control design alsoagents that act on different cellular targets, like membrane recep-incorporates an ethical constraint to minimize the chance of treat-tors (monoclonal antibodies) or anti-angiogenic drugs for exam-ing patients at unacceptably high doses by defining the expectedple, the search for an MTD is not a reasonable goal. Indeed, theseproportion of patients treated at doses above the MTD equal to atargeted anticancer agents might first act as cytostatics rather thanspecified value. This value is selected by the clinician before thecytotoxics and, secondly, might be characterized by minimaltrial onset and reflects the level of concern about overdosing. Thisorgan toxicity as compared with conventional chemotherapy.means that escalation with overdose control approaches the MTD

as quickly as possible, while keeping the expected proportion of In the early-phase development of anticancer drugs, reliablepatients overdosed to less than the pre-established value.[18] More- information on safety and tolerability must still be collected but,over, the escalation with overdose control design minimizes the unlike cytotoxics, the relationship between dose-toxicity and effi-predicted amount by which any given patient is underdosed and cacy with increasing doses is not trivial. Recently, new approachesallows for a continuous dose range scale. were proposed for phase I/II clinical trials in which the toxicity

1 A gain function is the mathematical representation in Bayesian decision theory of an improving situation.


Dose Estimation in Malignancies Drug Development 39

Table I. Estimated probabilities of toxicity of the five tested doses of semisynthetic homoharringtonine (ssHHT), updated after each newly included cohortof three patients per dose level

Cohort Administrated dose Clinical response Toxicity probabilities (%) updated after each cohort for the five dose levels(mg/m2) of ssHHT (mg/m2)a

0.5 1 3 5 6

1 0.5 NT NT NT 0.1 0.3 0.6 3.5 10.8b

2 3 NT NT T 7.3 13.6 19.5 38.7b 55.0

3 5 NT NT T 6.9 13.1 18.9 38.0b 54.4

4 5 NT NT NT 3.2 6.9 10.9 27.0b 44.6

5 5 NT T NT 3.7 7.8 12.1 28.8b 46.0

6 5 T NT T 6.2 11.9 17.4 36.1b 52.8

a Five different dose levels of ssHHT were studied (0.5, 1, 3, 5 and 6 mg/m2), each associated with initial guesses of toxicity probabilities of 5%,10%, 15%, 33% and 50%, respectively.

b The dose level closest to the toxicity target (33%).

NT = no toxicity; T = toxicity.

and efficacy of a new treatment were jointly modelled.[20-24] The • The first cohort of three patients was treated with 0.5 mg/m2

objectives of these methods are to combine the aim of a phase I with no dose-limiting toxicity occurring. The resulting updatedtrial with those of a phase II trial (i.e. simultaneously considering toxicity probabilities for the five dose levels were all lower thaninformation concerning toxicity and efficacy). The aim of such the target of 0.33, so the fifth dose level was associated with adesigns is to estimate a ‘most desirable’ or ‘most successful’ dose toxicity probability of 0.11, which was the closest to 0.33. Thisinstead of the MTD. This dose is the dose level associated with the

dose should have been recommended to the next three patienthighest efficacy probability under toxicity restrictions. All of these

cohorts, but for ethical reasons, the investigators chose not todesign propositions are still quite theoretical with rare unpublished

skip up to the fifth highest dose level, but rather to advance toapplications, which underscores the need for the dissemination ofthe third dose level.these methods in the medical literature, notably with regard to

• The second cohort of three patients was treated with 3 mg/m2their practical considerations.[25]

with one dose-limiting toxicity out of three. The updated ana-5. Application lysis of the dose-toxicity relationship showed an increased

toxicity probability at each escalating dose level, and the doseAlthough innovative new phase I dose-finding methods werelevel associated with the toxicity probability closest to thefirst proposed 15 years ago, their application in real clinical trialstarget was the fourth dose level.has been infrequent. Many authors have described new guidelines

for dose-finding, but clinicians remain reticent to apply them.[3] • The third cohort of three patients was treated with 5 mg/m2

with one of three exhibiting a dose-limiting toxicity. The updat-5.1 The Homoharringtonine Trial ed dose-toxicity relationship did not change the recommended

dose.This phase I dose-finding trial was aimed at assessing the MTDof semisynthetic homoharringtonine (ssHHT) for the treatment of • From the fourth to the sixth cohorts of three patients each, thepatients with advanced leukaemia.[26] In this trial, a modified assigned dose level was 5 mg/m2. Throughout the sequentialcontinual reassessment method design was used in the sense that it dose allocation, this dose level was associated with a toxicityincluded a cohort of three patients per dose level. The target probability closest to the target.toxicity probability was fixed at 0.33 with a sample size of 18

At the end of the trial, the selected MTD was 5 mg/m2, with anpatients. Five different dose levels of ssHHT were studied (0.5, 1,estimated toxicity probability of 0.36 (95% CI 0.16, 0.57). The3, 5 and 6 mg/m2), each associated with initial guesses of toxicitycontinual reassessment method design allocated the recommendedprobabilities of 0.05, 0.10, 0.15, 0.33 and 0.50, respectively.dose level to 12 of the 18 patients included in the trial. As a result,ssHHT dose levels were chosen based on earlier studies using themore patients benefited from the recommended dose level than ifnatural form of the drug. The sequential dose allocation rule was as

follows (table I): the standard dose allocation rule had been used.


40 Zohar & Levy

6. Whitehead J, Brunier H. Bayesian decision procedures for dose determining6. Conclusionsexperiments. Stat Med 1995; 14 (9-10): 885-93; discussion 895-9

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16. Rosenberger WF. New directions in adaptive designs. Stat Sci 1996; 11 (2): 137-49Trials[29]), at least for regulatory purposes, their role in phase I is

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role of the statistician, is sometimes more uncomfortable at this 18. Rogatko A, Babb JS, Tighiouart M, et al. New paradigm in dose-finding trials:patient-specific dosing and beyond phase I. Clin Cancer Res 2005; 11 (15):stage of the development of a drug because the great majority of5342-6

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21. O’Quigley J, Hughes MD, Fenton T. Dose-finding designs for HIV studies.All the recently proposed dose-finding methods for phase I Biometrics 2001; 57 (4): 1018-29

trials share an underlying estimation procedure that is technically 22. Thall PF, Cook JD. Dose-finding based on efficacy-toxicity trade-offs. Biometrics2004; 60 (3): 684-93difficult. This point underscores the need for disseminating these

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Acknowledgements 25. Zohar S, Chevret S. Recent developments in adaptive designs for phase I/II dose-finding studies. J Biopharm Stat. In press

26. Levy V, Zohar S, Bardin C, et al. A phase I dose-finding and pharmacokineticNo sources of funding were used to assist in the preparation of this review.study of subcutaneous semisynthetic homoharringtonine (ssHHT) in patientsThe author has no conflicts of interest that are directly relevant to the contentwith advanced acute myeloid leukaemia. Br J Cancer 2006; 95 (3): 253-9

of this review.27. Zohar S, O’Quigley J. Optimal designs for estimating the most successful dose.

Stat Med 2006; 25 (24): 4311-20

28. Rogatko A, Babb JS, Wang H, et al. Patient characteristics compete with dose aspredictors of acute treatment toxicity in early phase clinical trials. Clin CancerReferencesRes 2004; 10 (14): 4645-511. Reigner BG, Blesch KS. Estimating the starting dose for entry into humans:

principles and practice. Eur J Clin Pharmacol 2002; 57 (12): 835-45 29. International Conference on Harmonisation. E9: statistical principles for clinicaltrials. 1998 Sep [online]. Available from URL: http://www.fda.gov/cder/gui-2. Zhou Y. Choice of designs and doses for early phase trials. Fundam Clindance/ICH_E9-fnl.PDF [Accessed 2007 Oct 30]Pharmacol 2004; 18 (3): 373-8

3. Chevret S. Statistical methods for dose-finding experiments: statistics in practice.Chichester: John Wiley & Sons Ltd, 2006

Correspondence: Dr Sarah Zohar, Biostatistics Department, Inserm U 717,4. Rosenberger WF, Haines LM. Competing designs for phase I clinical trials: aSaint-Louis Hospital, Assistance Publique, Hopitaux de Paris, Universitereview. Stat Med 2002; 21 (18): 2757-70Paris 7, Paris, France.5. O’Quigley J, Pepe M, Fisher L. Continual reassessment method: a practical design

for phase 1 clinical trials in cancer. Biometrics 1990; 46 (1): 33-48 E-mail: [email protected]


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