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Continual reassessment method for dose escalation clinical trials in oncology: a comparison of prior skeleton approaches using AZD3514 data
© The Author(s). 2016
Received: 2 September 2015
Accepted: 10 August 2016
Published: 31 August 2016
The continual reassessment method (CRM) requires an underlying model of the dose-toxicity relationship (“prior skeleton”) and there is limited guidance of what this should be when little is known about this association. In this manuscript the impact of applying the CRM with different prior skeleton approaches and the 3 + 3 method are compared in terms of ability to determine the true maximum tolerated dose (MTD) and number of patients allocated to sub-optimal and toxic doses.
Post-hoc dose-escalation analyses on real-life clinical trial data on an early oncology compound (AZD3514), using the 3 + 3 method and CRM using six different prior skeleton approaches.
All methods correctly identified the true MTD. The 3 + 3 method allocated six patients to both sub-optimal and toxic doses. All CRM approaches allocated four patients to sub-optimal doses. No patients were allocated to toxic doses from sigmoidal, two from conservative and five from other approaches.
Prior skeletons for the CRM for phase 1 clinical trials are proposed in this manuscript and applied to a real clinical trial dataset. Highly accurate initial skeleton estimates may not be essential to determine the true MTD, and, as expected, all CRM methods out-performed the 3 + 3 method. There were differences in performance between skeletons. The choice of skeleton should depend on whether minimizing the number of patients allocated to suboptimal or toxic doses is more important.
NCT01162395, Trial date of first registration: July 13, 2010.
The purpose of phase 1 clinical trials is to determine the recommended dose for further clinical testing , whilst being efficient by minimizing the number of patients and preserving safety . Trials in cancer are different to those for other indications as patients have a metastatic disease and have exhausted other treatment options . Because of this, potential efficacy is also of major importance to patients, [4–6] investigators  and regulatory authorities , thus minimising the number of patients allocated to suboptimal doses is also important. Despite this, literature reviews found less than 5 % of patients in oncology trials experience a response [3, 8] and this number is decreasing . The 3 + 3 method is rule based and the most common design for dose escalation studies, with over 96 % of studies using this method , but is not statistically efficient as it does not use all available data to recommend the next dose level to allocate . This leads to more patients than necessary receiving suboptimal doses [10, 11] and limited ability to detect the MTD.
Model-based designs such as the continual reassessment method (CRM)  offer an alternative to rule-based designs and use Bayesian models or maximum likelihood estimation (MLE). Both rule and model-based designs aim to determine the maximum tolerated dose (MTD), the highest dose at which a pre-specified proportion of patients experience a dose-limiting toxicity (DLT). A DLT is a side effect of a treatment that is serious enough to raise concern about that dose and its definition is decided prior to dosing. Unlike rule-based designs, model-based designs use toxicity data from all dose levels, so are more statistically efficient . There are around 100 publications which demonstrate the advantage of using model based methods over rule based methods in terms of efficiency and ethical considerations . In particular, studies have found that, compared to the 3 + 3 method, the CRM allocates fewer patients to suboptimal  and harmful doses [11, 14] and identifies the true MTD a higher proportion of the time [15, 16], reducing the likelihood of making a costly and potentially unsafe decision.
Despite the benefits of model-based methods over rule-based methods, literature reviews have identified that these methods were only used in 3.3 % of phase 1 trials between 2007 and 2008  and 1.6 % of trials between 1991 and 2006 . Reasons for the low uptake of these models could include hesitancy to apply a complicated”black box” algorithm , or a lack of practical guidance for implementing these methods . Model-based methods require pre-specification of the dose-toxicity model, which consists of estimates of the prior probability of experiencing a DLT for each dose (skeleton) and the prior distribution which is the underlying confidence in the prior probabilities . The prior distribution has been investigated previously . When there is substantial knowledge of the dose-toxicity relationship from pre-clinical or clinical studies, it can be translated into an estimate of the prior probabilities . However substantial knowledge may not always be available or the translatability of the preclinical data can be in doubt. In this situation, choice of prior probabilities is a particular challenge [19, 20] and prior probabilities may not be accurate . We found limited guidance on which standard prior probabilities should be used when there is limited knowledge on dose-toxicity, which is a clear area of need. It should be noted however, that Lee Cheung 2009 proposed using indifference intervals to determine prior probabilities, rather than specifying prior probabilities, an approach which deserves some consideration .
We sought to compare the defined MTD and number of patients allocated to sub-optimal and toxic doses obtained using the Bayesian model CRM, with different prior skeleton approaches, and the 3 + 3 method. We did so by doing a post-hoc dose-escalation analysis using real life data from the AZD3514 study, a phase 1 clinical trial in patients with metastatic castration resistant prostate cancer (CRPC) . We provide a practical example of this method using our data (Appendix) and provide recommendations in the discussion to improve the uptake of these methods.
The source dataset was a study of patients with metastatic CRPC being given AZD3514, a selective androgen receptor downregulator . Patients received doses of AZD3514 monotherapy of 100 mg once daily (QD), 250 mg QD, 500 mg QD, 1000 mg QD, 1000 mg twice daily (BID) or 2000 mg BID. At the end of that study, no patients below 2000 mg BID had met the pre-determined DLT criteria. However moderate or greater nausea and vomiting were significant tolerability concerns and caused higher doses to be considered non-tolerable . Therefore, moderate or greater (CTCAE grade 2+) nausea and vomiting was retrospectively defined as a DLT. The result is a relatively unique real-world dataset of dose escalations unaffected by the subsequently-lowered DLT criteria, allowing complete capture of DLTs at each dose level up to and past MTD, with dose-doubling maintained throughout.
We created an exploratory dataset with the first six patients who completed DLT assessment from each dose level between 250 mg QD and 1000 mg BID and all four patients on 2000 mg BID. The lowest dose was omitted for simplicity, especially because it was not following a dose-doubling regime. All four patients on 2000 mg BID experienced a DLT, so it was expected that data from these four patients would be sufficient for this dose level. Because nausea and vomiting were associated with increasing dose and no patients experienced a protocol defined DLT, we defined DLT as moderate/severe/very severe (CTCAE grade 2 to 4) nausea or vomiting occurring at any time during treatment. Using this dataset we will deduce the MTD, as the highest dose where the proportion of patients experiencing a DLT is below the target toxicity dose. Doses below the MTD will be considered suboptimal, and, doses above the MTD will be considered as intolerable. This method reflects how the MTD is chosen in clinical practice.
The 3 + 3 design involves allocating three patients to the initial dose level. If no patients experience a DLT, the dose level is considered safe and the next higher dose is explored. If two or more patients experience a DLT, the dose level is considered toxic and the trial can proceed to a lower dose. If one patient experiences a DLT, then three more patients are allocated to the same dose. If no further patients experience a DLT, the dose level is considered safe but if one or more further patients experience a DLT, the dose level is considered non-tolerated. The MTD is the highest dose tolerated by >4/6 of patients that received it (i.e. at least 5 of the 6 tested). For more information refer to Jaki et al.  who provide a schematic display of this method.
The CRM uses a Bayesian model which assumes the probability of experiencing a DLT increases with dose . We need to choose the dose toxicity model, skeleton, prior distribution and target toxicity level. A dose-toxicity model should be chosen which is consistent with our a priori belief of the relationship between dose and toxicity. Examples of common dose-toxicity models include empiric  and logistic . The prior distribution represents the initial confidence we have of the dose-toxicity relationship and many examples of these distributions are provided by Chevret . The target toxicity level is the maximum proportion of patients experiencing a DLT that is acceptable given the risk benefit profile. Initial estimates of prior probabilities of DLT for each dose form the initial dose toxicity curve (skeleton). The curve is continually updated as new patient dose-toxicity information is included. If one extra patient who experienced a DLT is included in the model, the dose toxicity curve shifts upwards indicating an increase in the probability of experiencing a DLT at all doses. If one extra patient who did not experience a DLT is included in the model, the dose toxicity curve shifts downwards, indicating a decrease in the probability of experiencing a DLT at all doses. After the model is updated, the CRM will recommend that the next patient(s) are allocated the dose which is closest to the target toxicity level. If one extra patient is added, because the curve shifts are dependent on DLTs, the next recommended dose cannot increase if a DLT is experienced, and cannot decrease if a DLT is not experienced. This is demonstrated clearly in Appendix. There are various stopping rules to determine the MTD, the simplest of which is stopping after six patients have received the same dose. Goodman’s modification involved enrolling one to three patients to each cohort, starting with the lowest dose and escalating one dose each time until the first DLT is experienced . After this, the CRM method is used to determine the next dose and all further doses. The CRM method with this modification is commonly known as the extended CRM . This ensures some patients receive the lowest dose which preserves safety, making the initial dose independent of the prior probabilities. If the CRM is used to identify the first dose it will recommend the one with the initial prior probability closest to the target toxicity level.
Model calibration for the continual reassessment method
Empiric, logistic, power
Target toxicity level
0 to 100 %
A maximum of 6 patients at a single dose.
Conservative, aggressive, step-up, dose-linear, sigmoidal, O’Quigley
Adaption - Extended CRM
Allocate 1 to 3 patients to each cohort prior to the CRM
Allocate 2 patients to each cohort prior to the CRM
Two further exploratory analyses were conducted. Firstly, we examined the effect of changing the prior P(DLT) values by adding 10 percentage points to each prior P(DLT) in each prior skeleton approach and reran the approaches. For instance, the conservative approach has P(DLT) of 10 % and 30 % for the first two doses, whereas the conservative + 10 percentage points approach has 20 % and 40 % for these doses. Increased P(DLT) should lead to slower dose-escalation as the higher doses are further away from the target toxicity level line at the start. Note for prior probabilities exceeding 100 %, the prior probability was considered to be 99 %. For instance the 2000 mg BID prior probability was 96 % for the O’Quigley approach and 99 % for the O’Quigley + 10 percentage points approach. Secondly we reproduced the extended CRM with the conservative approach but instead enrolled three patients to each dose prior to the first DLT for further comparison with the 3 + 3 method. This version of the extended CRM cannot recruit less than three patients in each cohort prior to the first DLT, so may also be appropriate in circumstances where it is desirable to have more data at lower dose levels for other dose-dependent effects, such as measure of biological activity to determine a maximum biological effective dose that may be below MTD.
We performed extended CRM analysis with the empiric discrete dose-toxicity model, with a Gaussian prior distribution of mean 0 and variance 1.34 for each prior skeleton approach on the exploratory dataset, using the escalator package in R (https://www.r-project.org/). Target toxicity level was set to <33 % to aid comparison with the 3 + 3 method. A dose was identified as the MTD when six patients have already received this dose and the CRM recommended a 7th patient receive the same dose. This aids comparison with the 3 + 3 method, because another dose may be explored after six patients, but no more than 6 patients would be in a single cohort. The CRM model choices are specified in Table 1. The 3 + 3 method was also applied to the exploratory dataset, we assumed each patient in a cohort begun their treatment simultaneously.
Occurrence of DLTs
Number of DLTs
Proportion that experienced a DLT
Eligible patients experiencing DLT (DLT = D, No DLT = blank)
250 mg QD
500 mg QD
1000 mg QD
1000 mg BID
2000 mg BID
The dose escalation approaches were compared in terms of identifying the true MTD, and the number or patients who would receive suboptimal or toxic doses.
In total, 28 patients were eligible and included in the exploratory dataset, six in each AZD3514 cohort from 250 mg QD to 1000 mg BID and four in the 2000 mg BID cohort. Of the patients receiving between 250 mg QD to 1000 mg BD AZD3514, one patient was not included because they received less than 28 days of treatment at one dose, and thirteen were not included because we had already reached the maximum quota of six patients per dose level. Eligible patients had a mean age of 69 years (range 45–79).
Comparison of dose escalation methods
Number of patients (Order of receiving dose – DLTs are bold)
Number of patients
Prior skeleton approach
250 Mg QD
500 Mg QD
1000 Mg QD
1000 Mg BID
2000 Mg BID
Suboptimal (<1000 mg QD)
Intolerable (>1000 mg QD)
3 + 3
1000 Mg QD
3 (1, 2, 3)
3 (4, 5, 6)
6 (7, 8, 9, 10, 11, 12)
6 (13, 14, 15, 16, 17, 18)
Extended CRM −2a
1000 Mg QD
2 (1, 2)
2 (3, 4)
6 (5, 6, 7, 8, 9, 10)
2 (11, 12)
1000 Mg QD
2 (1, 2)
2 (3, 4)
6 (5, 6, 7, 10, 13, 15)
5 (8, 9, 11, 12, 14)
1000 Mg QD
2 (1, 2)
2 (3, 4)
6 (5, 6, 7, 8, 9, 14)
5 (10, 11, 12, 13, 15)
1000 Mg QD
2 (1, 2)
2 (3, 4)
6 (5, 6, 7, 8, 11, 15)
5 (9, 10, 12, 13, 14)
1000 Mg QD
2 (1, 2)
2 (3, 4)
6 (5, 6, 7, 8, 9, 10)
1000 Mg QD
2 (1, 2)
2 (3, 4)
6 (5, 6, 7, 8, 9, 10)
5 (11, 12, 13, 14, 15)
Extended CRM −3b
1000 Mg QD
3 (1, 2, 3)
3 (4, 5, 6)
6 (7, 8, 9, 10, 11, 14)
5 (12, 13, 15, 16, 17
Adding 10 percentage points to all priors in the sigmoidal, step-up and aggressive approaches made no difference to their dose allocation and all approaches still correctly identified the correct MTD, interestingly with the same number of patients or less (Additional file 2). The dose-linear approach required one less patient to achieve the MTD, which decreased the frequency of patients allocated to toxic dose by one and in doing so reduced the number of DLTs experienced from four to three. The conservative approach also required one less patient to achieve the MTD, one additional patient was allocated to a suboptimal dose, and two less patients were allocated to toxic doses which reduced the number of DLTs experienced from two to one. The O’Quigley approach required five less patients to identify the MTD, and the number of patients allocated to 1000 mg BID (toxic dose) reduced from five to zero, which reduced the number of DLTs experienced from four to one. Adding 10 percentage points to each prior made little difference to the final P(DLT) for the lowest three doses and dose-toxicity distribution of any prior skeleton approach (Additional file 1).
When the conservative approach was rerun with three patients allocated to each dose prior to the first DLT occurring, the approach required five additional patients to determine the DLT (Table 3). Two additional patients received suboptimal doses and three additional patients received toxic doses of 1000 mg QD which would result in two more DLTs. This approach allowed no reductions in suboptimal doses compared to the 3 + 3 method but did allocate one less patient to a toxic dose, which also resulted in one less patient overall. The final dose toxicity curve (Fig. 3g) was similar to that of the conservative approach with two patients at each dose (Fig. 3a).
This post-hoc analysis on clinical dose-escalation data compared the CRM method with various prior skeleton approaches and the 3 + 3 method. The results provide further evidence the CRM method is more efficient and may preserve safety compared to the 3 + 3 method as every prior skeleton approach required less patients to identify the MTD, and allocated less patients to suboptimal and toxic doses. It is notable that the CRM outperformed the 3 + 3 even though the true dose-toxicity curve was steeper than any of our chosen prior skeleton approaches. We found the underlying model of the dose-toxicity relationship influences the number of patients allocated to toxic doses, but in all cases the correct optimal dose was chosen.
To our knowledge this is the first study to compare prior skeleton approaches in the CRM method. O’Quigley & Chevret also found that even if prior probabilities are underestimated or overestimated the performance of the CRM will be at least as good as standard methods . Lee & Cheung observed that most studies use the O’Quigley et al.  prior skeleton approach without providing justification . Many dose escalation studies that we identified did not display the prior probabilities they used or justify how they obtained them.
For our data, the conservative prior skeleton approach was more successful then the step-up and dose-linear approaches as it allocated less patients to toxic doses despite the original dose-toxicity curves of these approaches being closer to the true relationship. This may suggest the overall spacing between prior probabilities is a key factor of the dose-toxicity relationship in the original prior combination, and the spacing may be more important than the overall shape of the curve. Another plausible dose-toxicity relationship is the one used in the sigmoidal approach, but no patients were allocated to 1000 mg BID despite only one out of six patients at the dose below experiencing a DLT. If the spacing between 1000 mg QD and 1000 mg BID was closer, then some patients may have been allocated to the next highest dose which highlights the strong barrier to dose escalation that the steep part of the curve presents. One concern was that the O’Quigley, aggressive, step-up and dose-linear approaches allocated a further patient to 1000 mg BID despite two out of four patients on this dose experiencing a DLT. This could be caused by insufficient spacing between the P(DLT) for 1000 mg QD and 1000 mg BID (10 % aggressive, 20 % step-up, 25 % dose-linear and 29 % O’Quigley approaches) or prior probabilities of the toxicity of the 1000 mg BID dose not high enough (50 % dose-linear, 60 % aggressive, 64 % O’Quigley and 65 % step-up approaches). Notably in the conservative and O’Quigley approaches when the prior probability of 1000 mg BID was 64 % and 70 % respectively, some patients received this dose, when it was 74 % and 80 % respectively (conservative + 10 percentage points and O’Quigley + 10 percentage points approach) no patients received this dose. The highest prior probability to receive any dose was 75 % and was the 1000 mg BID dose from the step-up + 10 percentage points approach.
To escalate faster and reduce the number of patients on suboptimal doses, we could lower the P(DLT) prior probabilities but this would put more patients at risk of a DLT, which causes a suboptimal/toxic dose ethical dilemma. Therefore choice of prior skeleton approach for studies should partially depend on which of minimising suboptimal or minimising toxic doses is more important. Daugherty et al. reported a cancer trial where patients got to select their own dose and found patients would chose the highest dose even with knowledge of the increased toxicity risk and patients thought more about possible benefits than side effects when choosing their dose .
Clinical opinion should also be used in decisions to recommend the next dose to improve the flexibility of choice. We identified two situations where investigators may have wished to override the CRM decision. Firstly, where one dose is considered safe (i.e. target toxicity not exceeded), but at the dose level above, either no patients (sigmoidal approach) or a small number of patients (conservative approach) have been tested, the investigators may wish to test more patients at the higher dose, thus overriding the CRM decision. Secondly, other CRM prior skeleton approaches allocated a patient to 1000 mg BID despite two of four patients who had already received this dose experiencing a DLT, investigators may wish to stop this extra patient receiving this dose. Including an additional modification to the CRM method such as escalation with overdose control (EWOC) may also prevent too many patients receiving a toxic dose .
We chose a stopping rule to be a maximum of 6 patients treated at a single dose and identified a dose as the MTD when the CRM recommended a 7th patient to receive the same dose. This enabled a direct comparison of CRM with the 3 + 3 design. To increase confidence in dose-toxicity relationship and the prediction of MTD, it is possible to allocate additional patients to dose levels. Clinical opinion is also important in the 3 + 3 method. For the 1000 mg BID dose, one out of the first three patients experienced a DLT. For the 4th, 5th and 6th patients allocated to this dose, a clinician may have suggested allowing time between these patients receiving their first doses, which may prevent more than one DLT occurring in these patients.
Since this study was designed to compare effects of different models on MTD assessment, the scenario chosen was one where toxicity is assumed to be the primary determinant of the recommended phase II dose. Pharmacodynamic response could be modelled in a similar way and determination of a maximum biological effective dose would be expected to raise similar issues of rule-based systems versus statistically efficient model-based systems or Bayesian approaches.
Strengths + limitations
This study has several strengths. It is a post-hoc analysis on a real phase 1 clinical trial, there were at least six eligible patients at four doses, the probability of DLT increased markedly with increased dose and information on patient characteristics was available, and we considered several skeleton scenarios that covered a range of prior beliefs of toxicity. A limitation of this study is that we did not consider time between each patient being allocated a dose. In practice, this process could be sped up by allocating doses to two patients at a time.
This research has implications for future phase I trials. Further support is provided for using the CRM instead of standard methods. The importance of selecting an appropriate prior dose-toxicity model has been shown. Specifying a wide prediction interval for each prior probability allows the model to be influenced by the data so highly accurate estimates of each prior probability may not be essential to determine the true MTD. Several prior dose-toxicity models have been proposed, and compared, and recommendation made for their use in future trials.
The CRM model is more efficient and may expose less patients to toxic doses compared to the 3 + 3 method, even when the optimal dose-toxicity curve is unknown. Choice of the prior skeleton approach and initial estimates should depend on whether minimizing the number of patients allocated to suboptimal or toxic doses is more important. Highly accurate initial estimates may not be essential to determine the true MTD. This manuscript describes prior dose-toxicity models that could be used when limited dose-toxicity relationship data is available and raises the importance of further exploration into this. It also reiterates the importance of combining the CRM recommendations with clinical opinion for decisions to escalate/de-escalate dose. We advise authors who are using CRM methods to make available their initial priors and final dose-toxicity graphs so optimal generic graphs can be derived and to support the uptake of these methods.
AZD3514 study 1 clinical investigators and patients. Paul Metcalfe for creating the escalator package for use in R which allowed us to conduct the continuous reassessment method. Only named authors contributed to the design, analysis, and interpretation of this research.
This research was funded by AstraZeneca.
Availability of data and materials
The data is already in the public domain at https://clinicaltrials.gov/6.. Trial registration number is written above. In addition the following manuscript details further information about the results of this study .
GDJ designed the analysis in collaboration with JM. GDJ undertook data extraction, analysis and interpretation and the literature review. GDJ, SS, JM, JY and GC contributed to drafting of the paper and development of core ideas. GDJ is the guarantor. All authors read and approved the final manuscript.
The authors declare that they have no competing interest in relation to this article. GDJ is an employee of PHASTAR. JM and GC are employees of AstraZeneca. SS is an employee of the University of Edinburgh and received fellowship funding from AZ. JY is a self-employed consultant and a former AZ employee.
Consent for publication
All patients consented to take part in the study and no individual data are presented.
Ethics approval and consent to participate
Research on the AZD3514 compound was approved by the West of Scotland Research Ethics Service in 2010. All patients were required to provide signed and dated written informed consent prior to any study specific procedures.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
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