To the Editor: In discussing dose-finding trials, Rogatko et al. mention “modified Fibonacci escalation design” but do not elaborate on exactly what they mean, and the references they cite do not clarify the matter, other than implying that a popular but not entirely satisfactory scheme involves decreasing increments of dose (in groups of three patients at each dose level, adding three more when dose-limiting toxicity is encountered).
Fibonacci, modified or not, does not seem to be relevant to this subject although the name of this 13th century mathematician has been invoked repeatedly, with varying meaning, in the phase I chemotherapy literature (1). The late Marvin Schneiderman, many years ago, proposed a decreasing step scheme, but then tried to link it to Fibonacci as follows: “Three decisions have to be made here: the initial dose d, the maximum possible dose d′, and N, the number of steps allowable in moving upward from dose d to dose d′. By taking a Fibonacci series of length N + 1, inverting the order, and spacing the doses in proportion to the N intervals in the series, one would take smaller and smaller steps in moving from d to d‴ (2). What emerged subsequently in the literature as 2n, 3.3n, 5n, 7n, 9n, 12n, 16n multiples of the initial dose, or 100%, 65%, 52%, 40%, 29%, 33%, 33% increases over the previous dose, does provide decreasing increments, but the derivation from 0, 1, 1, 2, 3, 5, 8, 13, 21… (Fibonacci numbers: each one is the sum of the two previous numbers) is not apparent. Fibonacci numbers have many uses and implications but this does not seem to be one of them. In the absence of a clear link, it might be best, in discussing this type of dose increase, to specify decreasing increments, or whatever is meant, without referring to Fibonacci.
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