SEMIPARAMETRIC DOSE FINDING METHODS FOR PARTIALLY ORDERED DRUG COMBINATIONS

Abstract

We investigate a statistical framework for Phase I clinical trials that test the safety of two or more agents in combination. For such studies, the traditional assumption of a simple monotonic relation between dose and the probability of an adverse event no longer holds. Nonetheless, the dose toxicity (adverse event) relationship will obey an assumption of partial ordering in that there will be pairs of combinations for which the ordering of the toxicity probabilities is known. Some authors have considered how to best estimate the maximum tolerated dose (a dose providing a rate of toxicity as close as possible to some target rate) in this setting. A related, and equally interesting, problem is to partition the 2-dimensional dose space into two sub-regions: doses with probabilities of toxicity lower and greater than the target. We carry out a detailed investigation of this problem. The theoretical framework for this is the recently presented semiparametric dose finding method. This results in a number of proposals one of which can be viewed as an extension of the Product of Independent beta Priors Escalation method (PIPE). We derive useful asymptotic properties which also apply to the PIPE method when seen as a special case of the more general method given here. Simulation studies provide added confidence concerning the good behaviour of the operating characteristics.

Keywords: Bayesian method; Dose-finding design; Partial ordering; Phase I clinical trials; semiparametric method.

Figure 1:

A simulated trial under scenario T using poSPM and the final posterior Π₆₀, which means the probabilties of each dose combination for being the MTD conditionnaly to observation on 60 patients. Red cross: Dose Limiting Toxicity; black circle: no toxicity response.

Figure 2:

Two contours called (a) and (b): the green squares represent the dose combinations belonging to the minimal set. Contour (a) corresponds to the one of Scenario T (Table 1)

Figure 3:

Model of two competitive contours: The blue and green models corresponds to contours (a) and (b) (Figure 2). Figures (a) and (b) show the modes of ${\Lambda }_{(a)}^d$ and ${\Lambda }_{(b)}^d$ for each dose d in comparison to the target α = 0.20. Figures (c) and (d) represent sampling of marginal scenarios under these models when agent A1 (respectively A2) is fixed at dose level 3.

Figure 4:

A simulated Trial under scenario T using poSPMc and the final posterior ${\tilde{\Pi }}_{60}$.on the dose combinations. Red cross: Dose Limiting Toxicity; black circle: no toxicity response.