Determining a maximum tolerated cumulative dose: dose reassignment within the TITE-CRM

Abstract

We present a phase I design that is a modification to the time-to-event continual reassessment method (TITE-CRM) by Cheung and Chappell that is useful when each dose actually denotes how long a drug is administered. Because of the lengthy duration required for subjects receiving the higher doses, we enroll each subject on the best estimate of the maximum tolerated cumulative dose (MTCD) as soon as each subject is eligible. Once each previously enrolled subject is fully evaluated, we update our estimate of the MTCD and modify currently enrolled subjects to receive the MTCD if they are currently receiving a nonoptimal dose. Thus, our method is adaptive both between subjects and within subjects. We show through simulation that our study design has excellent operating characteristics that are as good as the TITE-CRM while not exposing greater numbers of subjects to doses beyond the MTCD. Our simulations are based upon a study in bone marrow transplant patients that seeks to determine how many weeks of recombinant human keratinocyte growth factor can be administered while keeping toxicity rates below a desired threshold.

Introduction

In an allogeneic bone marrow transplant (BMT), a subject (host) receives the bone marrow donated by another subject. This donated marrow (graft) contains crucial T and natural killer cells that allow the host to develop an immune response against any residual leukemia [1]. This immune response is known more commonly as a graft-versus-leukemia (GVL) effect. A GVL effect, however, is closely associated with graft-versus-host disease (GVHD), which can lead to substantial damage in the skin, liver, and gastrointestinal (GI) tract. In animal studies, recombinant human keratinocyte growth factor (rHuKGF) has been found to markedly reduce chemotherapy- and radiation-induced injury to the mucosal lining of the lower GI tract [2]. From these preclinical data, it is hypothesized that rHuKGF can shield the GI tract from the effects of GVHD in humans as well [3].

In pilot trials, subjects have received two weekly schedules of rHuKGF after BMT and the observed rate of unacceptable toxicities has been low. Because the manifestation of acute GVHD (aGVHD) can take up to 100 days after BMT, we wish to determine whether lengthier administrations of rHuKGF, up to 12 weeks, can offer further protection against aGVHD during the entire period when a patient is at risk and still maintain a low rate of toxicity. Therefore, we have proposed a phase I clinical trial that examines rHuKGF administration schedules of 2, 4, 6, 8, 10, and 12 weeks, treating each cumulative number of weeks as a “dose.” Each subject will be followed for an additional 2 weeks after their last administration of rHuKGF to promote patient safety and increase our ability to observe late-onset toxicities.

The cumulative nature of each dose in our study challenges phase I designs such as the continual reassessment method (CRM) and its later modifications [4], [5]. In the CRM, the probability of toxicity, p = F(d; β), is assumed to increase monotonically with dose, d, through a single parameter β, which is assigned a vague prior distribution. A cohort of one or more subjects enters the study at a specified dose; based upon the cohort's experience and the prior placed upon β, the CRM computes a posterior distribution for β once all members of the cohort have been fully evaluated. The posterior mean of β is then used to estimate the probability of toxicity seen at each dose. The next cohort is entered into the trial at the dose whose estimated probability of toxicity is closest to the desired threshold that was set at the beginning of the trial. When the prespecified stopping criteria have been met, the maximum tolerated cumulative dose (MTCD) is selected as that dose with a toxicity rate closest to the optimal rate, based upon data from all the cohorts.

One shortcoming of the CRM is that the MTCD can only be estimated from subjects in each enrolled cohort who have been fully evaluated. Thus, enrollment of new subjects is typically delayed until the complete observation of all currently enrolled subjects. Such a delay in enrollment would be particularly detrimental to our study because the largest doses are in fact the longest doses, and postponing enrollment for the full observation of all previous subjects would make the entire trial unfeasibly long. Furthermore, it is expected that patients toward the end of this study will be awaiting enrollment while some subjects have been only partially treated. Due to the nature of their underlying disease, many of the patients will be unable to delay their transplants and thus would be denied the opportunity to participate. We also considered using other phase I designs but felt none were suitable because they also required the full observation of each cohort before enrolling additional cohorts [6], [7], [8].

The recent introduction of the time-to-event continual reassessment method (TITE-CRM) eliminated the need for full observation of each subject before estimating the MTCD [9]. In its simplest form, the TITE-CRM takes into account how long each enrolled subject has been observed as a proportion of their maximum length of observation. Enrolled subjects without toxicity are weighted by that proportion and enrolled subjects with toxicity are given full weight; these weights are then applied to the likelihood used in the CRM to determine the MTCD. As a result, subjects can be entered into a study while previous subjects are still under observation, thereby shortening the duration of the entire trial.

We have made two changes to the TITE-CRM to better fit our study. First, the TITE-CRM does not permit enrolled subjects to be reassigned to the updated value of the MTCD. In contrast, we want the ability to modify the doses of currently enrolled subjects, if necessary, because each dose in our study is a cumulative amount of rHuKGF. If a subject is assigned to a duration of rHuKGF that later is determined to be overly toxic, we can intervene and give that subject a shorter duration of rHuKGF. If a subject is assigned to a duration of rHuKGF that later is estimated to be less than the MTCD, we can intervene and give that subject the MTCD.

Second, the TITE-CRM determines an updated MTCD each time a new subject enrolls in the trial and assigns the newest subject to that updated MTCD. In contrast, we want to update the MTCD as soon as each enrolled subject is fully evaluated in order to potentially discontinue or reduce treatment of other enrolled subjects. By continually updating the MTCD before new subjects are enrolled, we have the ability to reassign the doses of currently enrolled subjects as dictated by our first modification. New subjects are simply enrolled to receive the current estimate of the MTCD.

With the two modifications just listed, our method is adaptive both between subjects as well as within subjects, and we hope to allocate subjects more efficiently to the MTCD. As a result, we expect to reduce the number of subjects given doses other than the MTCD and increase the likelihood that we correctly identify the MTCD. We denote our phase I study design as the TITEr-CRM (r for retroactive), which is applicable to any phase I study examining cumulative doses of a therapeutic agent. Below we describe the statistical and practical issues of the TITEr-CRM, then compare the performance of the TITEr-CRM to the TITE-CRM in a variety of settings.