Fibonacci escalation scheme

Some version of the modified Fibonacci escalation scheme is probably the most frequently used escalation scheme, particularly in oncologic Phase I studies. However, its pre-eminence is fading. The sequence 

FIGURE 31.1 Modified Fibonacci dose escalation procedure, expressed as a ratio of the human dose to a reference dose in mice [e.g., the 10% lethal dose (LD o)]- Human studies typically start at one-tenth the murine dose, expressed on the basis of body surface area. If tolerated, the next dose is initially doubled, then the percentage change at each escalation step decreases. (Reproduced from Collins JM, Zaharko DS, Dedrick RL, Chabner BA. Cancer Treat Rep 1986 70 73 0.) 

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Buoen et al. (9) reported that the dose-escalation schemes used in FTIH studies could be categorized as linear, logarithmic, modified Fibonacci, or miscellaneous. The latter included dose-escalation regimens in which the three standardized methods are combined. The authors reported that in 12 out of the 105 studies they reviewed a linear escalation method with fixed dose increment was used. A logarithmic dose-escalation scheme in which the relative dose increment was the same (e.g., 100%) was used in 22 studies. Four of the studies used a modified version of the Fibonacci escalation scheme, which is frequently used in cancer Phase 1 trials (6, 12-14). For most of the studies reviewed (i.e., 63.8%, or 67 studies) the dose-escalation schemes used did not seem to follow one particular scheme. In some cases two of the escalation schemes described above were combined (e.g., starting with a logarithmic escalation to convert later into a modified Fibonacci sequence), while for other studies, no escalation scheme was apparent. The doses appeared to have been chosen arbitrarily (11). 

The main differences between the diverse designs encountered in drug development are related to the dose-escalation scheme, the number of patients per level, and the stopping rule definition. The oldest and most frequently used dose-escalation method for the last 20 years is the well known standard method based on Fibonacci series. Because of the limitations of this method, more sophisticated approaches have been developed, namely ... 

The goal of dose escalation is to determine the maximum tolerated dose both efficiently and conservatively. Optimally, any scheme should not produce long and expensive Phase I studies, and at the same time should avoid the risks of overdosing and serious adverse events. One approach is to double doses with each escalation until a pharmacological response is observed, and proceed more conservatively with subsequent escalations, for example, calculating increases based upon a modified Fibonacci series (Table 4.1). 

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