3+3 Design Example for Dose-Finding in Cancer Clinical Trials
The 3 + 3 design is a popular choice for dose-finding in phase 1 cancer clinical trials. It is easy to implement and has good statistical properties.
However, it suffers from poor targeting of true MTD and the inability to de-escalate once excessive DLTs are observed — leading to long trial durations. Alternative model-based designs exist that can improve on this limitation.
Many oncology phase 1 trials use the traditional 3+3 design. This rule-based design does not require any modeling of the dose-toxicity relationship, and proceeds by allowing cohorts of three patients to be treated at increasing dosage levels that are predefined in advance. The initial dose level is based on extrapolation from animal toxicology data, and the subsequent doses are stepped up to achieve an MTD defined in advance.
While the traditional 3+3 design is simple to implement, it has significant limitations including slow pharmacokinetic titration, poor targeting of true MTD, and lack of flexibility to target alternate DLT rates. Alternative designs have been shown to be more efficient, accurate, and safe, and to produce results that more closely match clinical and theoretical true dose-toxicity relationships.
Among the most commonly used alternatives to the traditional 3+3 design are accelerated titration and continuous reassessment methods. We will describe these methods in more detail in future blogs. In simulation, these models have been shown to outperform the traditional 3+3 design in terms of MTD identification and speed of titration.
The conventional 3+3 design uses a pre-specified value of the probability that a given dose will cause DLT to select patients for subsequent cohorts. However, this approach is known to be suboptimal.
It has been shown that a CRM, which calculates the probability of DLT for each patient cohort based on the data of all previous cohorts, performs much better than the 3+3 design. It is also a relatively simple and straightforward method to implement. We have developed a freely-available macro to facilitate the implementation of the CRM in Microsoft Excel software.
There are a number of alternative methods to the 3+3 design that use a more adaptive and Bayesian approach to dose escalation. For example, accelerated titration designs and modified continual reassessment methods are designed to expose fewer patients to subtherapeutic dose levels. However, it is yet to be established whether they result in shorter trial durations.
Until recently, the traditional 3+3 design has been the preferred approach to conducting phase I clinical trials for cytotoxic drugs and molecularly targeted agents. This rule-based method requires no modeling of the dose-toxicity curve and proceeds with cohorts of three patients. Each successive cohort is treated with a dose level that has been pre-specified and is either extrapolated from animal toxicological data or is believed to be safe based on previous clinical trial experience.
However, the 3+3 method has been shown to be inferior to model-based methods in terms of estimating MTDs and determining recommended phase II doses (RP2Ds). It is also less efficient than adaptive/Bayesian designs.
Using the traditional 3+3 design, physicians sequentially enrol three patients into cohorts treated at increasing dose levels. If no dose-limiting toxicities (DLTs) are observed, the next three patients are enrolled at the next higher dose level. This process continues until one of the six doses tested imposes an unacceptable amount of DLTs on the patient population.
In the diagram above, you can click alternately on the period dividers between periods 5 and 6, to see what the dose-survival curve looks like at each dose level. Note that the 80% confidence band for DLTs straddles a fine red line at dose level 6, suggesting that a stop rule should be activated.
Several model-based design methods have been proposed to improve on the simple up-and-down approach illustrated here. In simulations, STARPAC and the continual reassessment method have performed better than 3+3 in terms of estimating the MTD and minimizing the number of declined patients. Both of these designs use the same model-based knowledge of toxicity rate at each dose level, but also allow clinicians to take into account their ethical concern about overdosing patients.