## Info

Design

Description

Pros

Cons

"3 + 3"

1) Begin at lowest dose, treating 3 patients. If DLT rate is —0/3, escalate (to next pre-specified dose level)

—1/3, add 3 more: then if 1/6, escalate >2/6, go to step 2) —>2/3, go to step 2)

2) If 6 patients studied at the previous dose level (1/6 AEs), declare —that dose to be the MTD; otherwise, add 3 more: Then if

—>2/6, decrease dose and continue

Easy to implement Conservative dose levels

Many patients may be treated at subtherapeutic Targeted percentile not explicit

Accelerated titration

1) Begin at lowest dose. Treat one patient at a time and double

2) the dose until DLT observed or two patients have experienced

4) Revert to "3 + 3" design with dose increments of 40% (intrapatient)

5) Dose escalation permitted in if no worse than grade 1 AE)

Easy to implement Moves quickly to therapeutic dose levels

More high-grade toxicities will occur Targeted percentile not explicit

Storer's BD design (up and down)

1) (Stage B) Begin at lowest dose. Treat one patient at a time and

2) escalate until DLT, then deescalate until first nontoxic response;

—0/3, escalate (to next prespecified dose level) —1/3, add 3 more at same dose —>2/3, deescalate Sampling continues until fixed number, nD, patients treated at stage D

Easy to implement Moves quickly to therapeutic dose levels Targeted percentile is explicit (33rd percentile)

More high-grade toxicities will occur

treatment course. As would be expected, this design reduces the number of patients in the trial who are undertreated, at the expense of a slightly higher percentage experiencing grade 3 or higher toxicity. The authors also describe a statistical model for estimating the MTD that takes into account not just whether or not a patient has experienced a DLT but the full range of toxicity data from all treatment courses. Legedza and Ibrahim describe a related longitudinal model that incorporates the effects of current dose, cumulative dose, and clearance rate on cumulative toxicity.13 In this design, dose administration within a patient is tailored over successive treatment courses in an attempt to treat all patients at more-efficacious dose levels.

### Up and Down

To provide a more solid inferential basis for estimating the MTD, Storer9,14 proposed and evaluated the properties of a number of "up-and-down" designs, including two-stage versions to allow more rapid dose escalation, as in the accelerated titration design. His BD design, for example, explicitly targets the 33rd percentile of the tolerance distribution. Initially (stage B), a single patient is treated at each dose level, escalating sequentially from the starting dose until a DLT is observed. Deescalation then occurs until the first nontoxic response, at which point the second stage (stage D) begins and cohorts of three patients are enrolled. Then, if none of the three has a DLT, the dose is escalated; if two or more have a DLT, the dose is deescalated; and if one of three has a DLT, the next cohort is treated at the same dose level. Sampling continues in this manner until a fixed number of second stage patients (for example, nD = 24) are treated. The total number of patients, n = nB + nD, is therefore variable, depending upon when the second stage is reached. After the trial is completed, a logistic regression model p(x ) = Pr(Y = 1|x ) =

is fit to the n pairs of points (x1, y1), (x2, y2), . . . (xn, yn) where Xi is the dose and yi the response (0 or 1) of the ithpatient. The method provides not only a point estimate of the MTD, but a means to derive confidence intervals as well. However, for the small sample sizes typically used in Phase I trials, computationally demanding "exact" methods may be required to obtain these confidence intervals. The method is easily modified to estimate other percentiles of the tolerance distribution (i.e., the 25th percentile). Korn et al.15 found stage B too aggressive and recommended treating two patients at a time, increasing dose levels until the first DLT is observed. Other useful variations of up-and-down designs are discussed by Ivanova et al.16

Continual Reassessment Method (CRM)

An alternative to the classic designs is the Bayesian approach developed by O'Quigley et al.,17 who called it the "continual reassessment method" or CRM (Table 8.2). This method is based on a one-parameter model for the dose— toxicity curve, for example, the logistic model (Eq. 1) with the a parameter fixed at a suitably chosen constant a0. Within the Bayesian framework, a prior probability distribution is assigned to the parameter p, data are collected, and knowledge about this parameter is updated by constructing the posterior probability distribution for p. Thus, in the CRM, a prior distribution for p is specified and the first patient is assigned to the dose level whose probability of toxicity as given by Eq. 1 is closest to the 33rd (or other desired) percentile. After observing the outcome in this patient, the posterior distribution for p is formed, toxicity probabilities updated, and the next patient assigned the dose closest to the desired percentile. This process is repeated until a fixed number of patients have been studied. The method tends to converge to the correct target level, even if the original model is incorrectly specified.18

### Modified CRM

Although it is clearly an attractive approach, some problems with the CRM were immediately recognized. First, there was discomfort about starting the first patient at too high a dose. Second, escalating more than one dose level at a time was thought to be too risky. Finally, there were concerns that trial durations would be extended unduly because of the need to await the outcome in each individual patient before enrolling the next patient. This concern led to the so-called modified CRM10,19 whereby the trial starts at the lowest dose level, the dose is increased no more than one level at a time, and the cohort size is increased to three patients. Results of a simulation study comparing the modified CRM to the original CRM and the traditional "3 + 3" design showed that the "3 + 3" design generally placed more patients at dose levels below the MTD; consequently, the CRM designs were more likely to assign patients to therapeutic dose levels and to arrive at the correct estimate of the MTD, although there were exceptions.10

A method that maintains the simplicity of the classic design, but, as in the CRM, makes better use of the cumulative data, has recently been proposed.20 The method capitalizes on the assumption that toxicity is nondecreasing with dose, using a technique known as isotonic regression to estimate the dose-toxicity curve at each step, essentially pooling and averaging outcomes from adjacent dose levels to maintain a nondecreasing curve. For example, if the current data were 1 toxicity in 6 patients treated at dose level x1, 1 in 6 at dose level x2, and 0 of 3 at dose level x3 (x1 < x2 < x3), the algorithm would first pool the data at x2 and x3 to maintain monotonicity, replacing each estimate with 1/9 = (1 + 0)/ (6 + 3). As 1/9 also is less than 1/6 from the first dose, the data would be pooled again, and all three estimates would be changed to 2/15 = (1 + 1)/(6 + 9). Additional patients are added at the current, higher, or lower dose level depending on the current DLT rate in relation to a specified target. The trial is terminated when the same dose level is indicated in three consecutive cohorts, or when some prespecified number of patients have been evaluated. A simulation study comparing the method with the traditional "3 + 3," modified CRM, and up-and-down designs found similar performance to the modified CRM and fewer patients underdosed compared to the "3 + 3" design, but on average more patients were required and were treated above the true MTD.20

TABLE 8.2. Design features for three Bayesian statistical designs for Phase I trials.

Design

Description

Pros

Cons

Continual reassessment method (CRM)

Modified CRM

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