The Classic 3 + 3 Design in Dose-Finding Clinical Trials and its Alternatives

Author: Genpro Statistics Team | Date Posted: 28/July/2021


One of the most important goals of Phase 1 clinical trial is to identify the Recommended Phase 2 Dose (RP2D)/Maximum Tolerant Dose (MTD) with acceptable dose-limiting toxicity of the new drug or combination of drugs for the Phase 2 clinical trial, especially in oncology trials.  Among all those dose-finding methods which the clinical industry has come across, 3 + 3 design is the prevalent one. This method has been introduced in the 1940s and later in 1989 B.E Storer described its implementation and statistical properties. The reasons for the popularity are, it is quite easy to execute without any software, not even necessary to be aware of basic statistical concepts. The process of finding the MTD using a 3+3 design starts with the selection of a pre-specified set of doses. The first dose will be determined based on the toxicological data from animal trials or based on some previous clinical trial data.

Suppose we have a set of pre-defined doses, {…, i-1, i, i+1, i+2, …}. A dose, say ‘i’ will be assigned to a cohort of 3 subjects and the outcome of interest is whether the patient will experience a DLT or not. Whereas DLT stands for Dose Limiting Toxicity which is defined as clinically significant toxicities grade 3 or higher by the CTCAE.

If no subjects in that cohort are experiencing any toxicities, the same cohort will be administered by the drug with the next immediate higher dose level, ‘i+1’ which has been fixed in advance, by adding 3 more subjects.

If 1 subject out of 3 is experiencing dose-limiting toxicity, three more subjects will be added to the first cohort, and the drug with the same dose, ‘i’ will be administered for these 6 subjects. Out of these 6, if only 1 subject is experiencing a DLT, the dose will be escalated to the next immediate dose, ‘i+1’. If at least 2 subjects out of these 6 are experiencing a DLT in ‘i’ th dose, the dose level will be de-escalated to ‘i-1’. Then 6 subjects will be treated with ‘i-1’ and if a maximum of only 1 subject is experiencing a DLT, ‘i-1’ will be considered as the Maximum Tolerated Dose, MTD.

If more than 1 subject out of 3 in the first cohort are experiencing DLT, the dose level is de-escalated to ‘i-1’ and will be treated for a total of 6 subjects. If a maximum of 1 subject out of these 6 is getting a DLT, ‘i-1’ will be selected as MTD.


Figure depicts the 3+3 escalation scheme.

                                               The figure depicts the 3+3 escalation scheme.


Below are some facts of 3+3 method:

  • 3+3 design works on a simple algorithm offering negligible toxic death rates. It does not require any modeling of the dose-toxicity curve as well. Whereas in model-based designs, assumptions on the dose-response curve are of must.
  • The Algorithm of adding 3 subjects per dosing level gives information on pharmacokinetic inter-patient variability.
  • Lack of robust statistical background.
  • Pre-defined doses for escalation could not be estimated, it should be either extrapolated from animal’s toxicological data or those dose levels should be proved to be safe from past clinical trials.
  • Does not have the flexibility of choosing cohort sizes, it is usually 3 or 6 patients in a cohort.
  • There is no scientific justification for deciding the start dose for this design, which results in exposure to large number of patients with suboptimal dose levels.
  • Suppose the MTD has been identified using a 3+3 design, it will be one of the predefined doses. But chances are high that, it may not be the true MTD thus unreliable.
  • 3+3 design could be referred to as ‘memoryless’ or ‘short memory’ design because to find the next dose assignment, it considers only the previous cohort data, not the whole data in hand.

Many dose escalation methods are now available which can provide better results compared to the traditional 3 + 3 design. It is worth to familiarizing with the alternative methods used in the clinical industry. Below are some alternative methods which the clinical industry uses to identify MTD/RP2D. Our upcoming blogs will have all these methods detailed out.

A) i3+3 Design:

This method is a rule-based design, where ‘i’ represents ‘interval’. It is having the simplicity of a 3+3 design and possesses a superior operating characteristic similar to that of a model-based design. Unlike in 3+3 design, this method has the flexibility of selecting cohort sizes. This method makes use of a decision table through which decisions such as Dose Escalation/Dose De-escalation could be taken based on the number of patients in the cohort and the number of DLTs experienced in that cohort. Similar to that of the mTPI method, a pre-specified value of the probability of dose toxicity PT is defined initially.

B) Continual Reassessment Method (CRM):

Studies prove that Maximum Tolerated Dose (MTD) could be derived more accurately using CRM compared to a rule-based approach. Various Dose-response models could be used in CRM such as Logistic, Hyperbolic, and Tangent power. The dose-toxicity curve will be estimated and MTD is identified in each step by utilizing all available trial data. The usual CRM methods will be having 4 to 8 dosing levels. The process will be continuing until the stopping rule has been reached, which will be defined by clinicians and statisticians. CRM could be designed and simulated using popular statistical programs such as STATA and R. Dose-toxicity relationship is to be estimated before performing CRM, which is attributed to the limited facility to identify that dose. Another shortcoming of this approach is that, if the estimated model for dose-toxicity is not precise, there is a greater possibility of patients being exposed to high doses of study.

C) Bayesian Logistic Regression Method (BLRM):

BLRM could be considered as a modification of CRM. The estimate of the dose-toxicity model gets updated based on the latest data. For conducting BLRM modeling, dose levels for escalation are supposed to be defined in the protocol. Unlike in the 3+3 method, the BLRM method could accurately estimate the maximum tolerated dose while avoiding toxic doses and sub-therapeutic doses since all the prior information of the trial is handled efficiently. To incorporate this method, the research team should be well versed with statistical concepts.

D) Modified Toxicity Probability Interval Design (mTPI):

This method, which was suggested in 2010, incorporates posterior inference of Bayesian-based methods with simple up and down rules. For computing the posterior probabilities, mTPI uses a Bayesian statistical model and a hierarchical Beta-Binomial model. A pre-specified value of the probability of dose toxicity PT is defined initially, and this design derives that dose of drug having the value of the probability of dose toxicity close to the target level, PT. This is a kind of design in which the probability of dose toxicity is classified into mutually exclusive intervals and thus the name, ‘Modified Toxicity Probability Interval Design’.

E) Escalation with Overdose Control (EWOC):

EWOC is a Bayesian adaptive design used in the phase 1 trial that can generate dosing levels sequentially in a consistent way without getting patients overdosed. This method is considered as the first dose identifying procedure which also restricts the patients from getting overdosed. This method is designed in such a way that, the dose assigned to the next subject in the trial has a posterior probability of exceeding the MTD equal to a pre-specified value known as feasibility bound. Many standalone applications and software are available to execute this method.

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  • 3+3 design
  • Dose Escalation Methods in Clinical Trials
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