The Expected Toxicity Rate at the Maximum Tolerated Dose in Bridging Studies in Alzheimer’s Disease

A bridging study has been recommended to determine the maximum tolerated dose in Alzheimer’s disease patients, because the maximum tolerated dose in the Alzheimer’s disease patient population versus the normal population can vary greatly. Although budging studies in Alzheimer’s disease have often been conducted, it is surprising to note that very little is known about the statistical properties of the studies. For example, even how toxic the maximum tolerated dose is has not been examined. In addition, both the number of patients needed and the number of patients who will experience the toxicity cannot be predicted either.

In this paper, we examine the exact statistical properties of a fixed-dose panel design which is frequently used in bridging studies in Alzheimer’s disease. We introduce the formulas for the overall toxicity rate at the maximum tolerated dose, the expected number of patients who will experience the overall toxicity, and the expected number of patients in the bridging studies in Ahheimer’s disease. The exact statistical properties of budging studies depend on the unknown dose-toxicity curve. In this paper, we assume the logistic and the hyperbolic tangent functions as the true dose-toxicity curves, because the two families of functions seem to include most practical dose-toxicity curves. Based on the assumptions we investigate extensively the exact statistical properties of the budging studies in Alzheimer clinical trials. The investigation shows that the expected toxicity rate at the maximum tolerated dose ranges from 18% to 30%.

Key Words

Dose finding studies; Toxicity; Phase 1 clinical trials; Complete enumeration

INTRODUCTION

The maximum tolerated dose (MTD) is a dose which can be considered safe and which also has the potential to show maximum drug efficacy. It is very important to determine the MTD correctly in drug development. Failure to determine the MTD can result in exposing patients to unsafe levels or subtherapeutic doses of specific drugs. Traditionally, the MTD is determined from Phase 1 clinical trials conducted in healthy volunteers, avoiding the complications inherent in using patients in clinical trials. However, patients are used in Phase 1 studies if a new drug is potentially toxic (such as in cancer or AIDS) or if the pharmacokinetics or pharmacodynamics of the drug are likely to differ substantially between the target population and normal volunteers. Such differences in pharmacokinetics or pharmacodynamics between patients and healthy volunteers can either pose safety problems in Phase 2/3 trials or cause a waste of valuable development time by conducting a Phase 2 trial at a wrong dose. Determining the MTD in the patient population in Phase 1 trials may provide greater confidence that Phase 2 doses will be potentially efficacious and involve a set of known potential adverse events. The Phase 1 dose-finding study in patients has been termed a “bridging study” because it would primarily facilitate the transition from Phase 1 to Phase 2 trials (1). Only studies in patients themselves can provide the actual parameters for human dosage within which a dose-response relationship can be identified.

A bridging study has been recommended to determine the MTD in Alzheimer’s disease patients. The benefit of the bridging study is that it employs a small number of patients, and can be escalated through a range of doses very quickly to determine the MTD in a patient population. The MTD in Alzheimer’s disease patients may differ substantially from the MTD determined in normal volunteers. In many compounds, the MTD is 100% greater or more in Alzheimer’s disease patients (1,2). The studies of Sramek et al. (3) and Bodick et al. (4) serve as valid illustration that the MTD should be established in the patient cohort, not in healthy volunteers.

The MTD for xanomeline, a muscarinic agonist used to treat patient with Alzheimer’s disease, in healthy volunteers was established as 50 mg tid (150 mg/day) while a bridging study by Sramek et al. (5) demonstrated that Alzheimer’s disease patients had an MTD at 100 mg tid (300 mg/day). Tollefson et al. (6) showed that only the highest dose (75 mg tid) showed superiority over placebo in an efficacy trial of three doses of xanomeline (25, 50, and 75 mg tid) in 300 patients with Alzheimer’s disease. This dose would not have been investigated if a bridging study was not previously conducted.

Even though bridging studies are conducted on a relatively small number of patients, they predicted adverse events encountered in multi-center Phase 2 trials with great accuracy. For example, the bridging study (n = 32) of xanomeline also accurately predicted the adverse events that were seen in the multicenter Phase 2 study (n = 256) (7).

Although bridging studies in Alzheimer’s disease are important, very little thing is known about the statistical properties of the studies. For example, we do not know what proportion of patients will experience the toxicities at the MTD determined from bridging studies. We cannot predict how many patients will be needed to determine the MTD and how many patients will experience the toxicities. The aim of this paper is to examine these statistical properties of bridging studies of Alzheimer’s disease. We derive the formulas for the overall toxicity rate at the MTD, the expected number of patients to experience the overall toxicity, and the expected number of required patients in the bridging studies in Alzheimer’s disease. A main obstacle in investigating the statistical properties of bridging studies is that the properties depend on the unknown dose-toxicity curves. Therefore, in this paper, we assume the logistic and the hyperbolic tangent functions as the true dose-toxicity curves, because the two families of functions seem to include most practical dose-toxicity curves. Assuming the two families of functions as the unknown toxicity curves, we investigate extensively the exact statistical properties of the bridging studies of Alzheimer’s disease.

DESIGN

A bridging study is conducted in order to evaluate the safety and tolerability of a drug in patients with Alzheimer’s disease and to determine the MTD in the patient population. A bridging study is a safety/tolerability study conducted in the patient population prior to Phase 2/3 efficacy studies. In Alzheimer’s disease, a bridging study is conducted as a randomized, placebo-controlled, double- blinded, single-center study.

Cutler and Sramek (1) recommend a bridging study using consecutive panels of six to nine patients with two to three patients on placebo in each panel. This design allows the establishment of a placebo group as large as each panel’s drug group after completion of three or four panels. For example, one bridging study (8) was designed with seven consecutive panels of eight patients each (six drug, two placebo). Another bridging study (9) was conducted with five panels of six patients each (four drug, two placebo).

In the fixed-dose design, sequential dose panels are used, in which each panel of distinct participants receives a fixed dose of drug if the previous lower dose was tolerated. We consider m panels of Alzheimer’s disease patients (i = 1, . . ., m). Each panel consists of n^sub 1^ + n^sub 2^ patients. In the ith panel, n^sub 1^ patients receive dose d^sub i^ while n^sub 2^ patients receive placebo.

The trials start with the first panel and then proceed to the next panel until the minimal intolerated dose (MID) is reached. The MID is defined as the dose at which a majority (50% or more) of the subjects receiving active drug experience severe or multiple moderate adverse events, or the dose at which one or more serious (medically unacceptable) adverse events occurs. The highest dose tolerated before reaching the MID is then designated as the MTD.

FIGURE 1

Dose-toxicity curves.

These two functions are plotted in Figure 1. The functions are thought to represent typical dose-toxicity curves and have been widely used in the investigation of Phase 1 cancer clinical trials (11-14). In the logistic function of a = 0.8 the toxicity rate is nonnegligible even at the lowest dose (5.7%) and increases gradually as does the dose level. The logistic function of a = 2.4 represents a steep dose-toxicity curve in which the toxicity rate at the first two dose levels is 0.1% and 0.2%, and the toxicity rate at the eleventh dose level is 73.1%. The curves of the hyperbolic tangent functions have similar shapes and are shifted to the right as the value of b increases. The hyperbolic tangent function of b = 0.5 represents a case of either toxicity that is too high even at low dose levels, or a dose level that is too high as an initial dose level. The hyperbolic tangent function of b = 2.0 is similar to the logistic function of a = 2.4, but its steepness is smaller than that of the logistic function of a = 2.4. Toxicity rates in each dose level are presented in Table 1.

TABLE 1

Using the above dose-toxicity curves of p^sub 1i^ and p^sub 2i^, we compute the exact distribution of the MTD based on (1). The exact distributions of the MTD with n^sub 1^ = 6 are shown in Table 2 and Table 3. Then the overall expected toxicity rates at the MTD are computed for the logistic function (0.8 ≤ a ≤ 2.4) and the hyperbolic tangent function (0.5 ≤ b ≤ 2.0) with 0.\01 increment based on (2) and displayed in Figure 2 and Figure 3. The solid and dotted lines represent the overall expected toxicity rate and the expected serious (medically unacceptable) toxicity rate, respectively. The expected toxicity rate at the MTD ranges from 18% to 30% and its values for the logistic functions are usually larger than those for the hyperbolic tangent functions. The values of w = 2.0 are slightly larger than those of w = 1.0 for both the logistic and the hyperbolic tangent functions.

The expected number of patients who will experience the overall toxicity are calculated for the logistic function (0.8 ≤ a ≤ 2.4) and the hyperbolic tangent function (0.5 ≤ b ≤ 2.0) with 0.01 increment based on (3) and displayed in Figure 4. The solid and dotted lines correspond to w = 1.0 and w = 2.0, respectively. One to two patients are expected to experience the overall toxicity when n^sub 1^ = 4, while two to five patients are expected to do so when n^sub 1^ = 6.

When n^sub 2^ = 2, the expected number of required patients in a trial is also computed based on (4) and displayed in Figure 5. As the value of parameter (a or b) increases, the expected number of required patients also increases because the chance of toxicity decreases. The logistic functions require more patients than the hyperbolic tangent functions. As the value of w moves from 1 to 2, the serious (medically unacceptable) toxicity rate decreases and more cohorts are needed to reach the MTD (see Table 2 and Table 3). Hence, the case of w = 2 requires more patients than that of w = 1.

TABLE 2

TABLE 3

Often, clinicians can choose some members in the families of the logistic and the hyperbolic tangent functions based on their experiences which are close to the true dose-toxicity curve. Then, figures in this paper tell the expected toxicity rate at the MTD and predict both the number of required patients and the number of patients who will experience the overall toxicity. Even when clinicians have no prior knowledge of the true dose-toxicity curve, results in this paper show important operating characteristics of bridging studies in Alzheimer’s disease.

FIGURE 2

Expected toxicity rate at the MTD. Logistic. TTL1 (solid line) = overall toxicity rate at the MTD. TTL3 (dotted line) = medically unacceptable toxicity rate at the MTD.

EXAMPLE

A double-blind, placebo-controlled bridging study was conducted to determine the MTD of Lu 25-109 in patients with Alzheimer’s disease (9). The study consists of five consecutive panels of six patients each (4 Lu 25-109/2 placebo). Doses for the five panels were 100, 125, 150, 200, and 225 mg tid for seven days. The study was terminated at 200 mg tid, because one patient experienced unacceptable gastrointestinal adverse events. The MTD was defined as 150 mg tid. Since the true dose-toxicity curve is unknown, we assume that both the logistic and the hyperbolic tangent functions are the true dose-toxicity curves to evaluate the bridging study with n^sub 1^ = 4. When the logistic function is assumed, the case Of n^sub 1^ =4 in Figure 2 shows that the expected toxicity rate increases gradually from about 19% to about 25% as the value of the parameter b increases from 0.8 to 2.4. The expected toxicity rate can be obtained by selecting a value of the parameter b which is believed to describe the unknown dose-toxicity curve well. When the hyperbolic tangent function is assumed, the performance of the bridging study of Lu 25-109 can be assessed similarly. The cases of n^sub 1^ = 4 in Figure 4 shows that one to two patients are expected to have the overall toxicity. Since one patient experienced a serious adverse event in the bridging study of Lu 25-109, Figure 4 describes a feature of the study well. The bridging study of Lu 25- 109 required 24 patients, which falls into the range of the expected number of patients needed in the cases of n^sub 1^ = 4 in Figure 5. On the whole, the results in the third section describe the operating characteristics of the bridging study of Lu 25-109.

FIGURE 3

Expected toxicity rate at the MTD. Hyperbolic Tangent TTL1 (solid line) = overall toxicity rate at the MTD TTL3 (dotted line) = medically unacceptable toxicity rate at the MTD.

DISCUSSION

The MTD in the Alzheimer’s disease patient population versus the normal population can vary greatly. For efficient drug development, it is imperative to establish the MTD separately in the patient population. Increasing attention has been given to the design and statistical analysis of Phase 1 cancer clinical trials during the last decade. Numerous statistical papers have recently been published on the design and statistical analysis of Phase 1 cancer clinical trials. However, very little attention has been given to the design of Phase 1 clinical trials other than cancer. This paper investigates the statistical properties of bridging studies in Alzheimer’s disease clinical trials.

Asymptotic theory has been the primary tool in the development of statistical methodology, but statisticians cannot utilize the asymptotic theory in bridging studies for the determination of the MTD due to a small sample size in the bridging study. In this paper, we develop a valuable tool to compute the exact distribution of the MTD in the bridging study. We introduce the formulas for the overall toxicity rate at the MTD, the expected number of patients who will experience the overall toxicity and the expected number of patients in bridging studies in Alzheimer’s disease.

FIGURE 4

Expected number of patients who will experience overall toxicity.

In Phase 1 cancer clinical trials, methods have been proposed such as continual reassessment method, Bayesian approaches, and strategies for monitoring both toxicity and efficacy. We hope this paper stimulates interest in the determination of the MTD for diseases other than cancer.

Acknowledgment-This work was supported by grant No. R06-2002-012- 01000-0 from the Basic Research Program of the Korea Science & Engineering Foundation.

FIGURE 5

Expected number of required patients.

REFERENCES

1. Cutler NR, Sramek J). Scientific and ethical concerns in clinical trials in Alzheimer’s patients: the bridging study. European J Clin Pharmacol. 1995; 48:421-428.

2. Cutler NR, Sramek JJ. The target population in phase I clinical trials of the ‘bridging study.’ Ahheimer’s Disease Assoc Disorder. 1995;9: 139-145.

3. Sramek JJ, Anand R, Wardle TS, Irwin P, Hartman RD, Cutler NR. Safety/tolerability trial of SDZ ENA 713 in patients with probable Alzheimer’s disease. Life Sciences. 1996;58:1201-1207.

4. Bodick NC, Walter Wo, Levey AI, Cutler NR, et al. Effects of xanomeline, a selective muscarinic receptor agonist, on cognitive function and behavioral symptoms in Alzheimer’s disease. Arch NeuTO. 1997:54:465-473.

5. Sramek JJ, Hurley DJ, Wardle TS, Satterwhite JH, Hourani J, Dies F, Cutler NR. The safety and tolerability of xanomeline tartrate in patients with Alzheimer’s disease. ) CHn Pharmacol. 1995;35: 800-06.

6. Tollefson GD, Bodick NC, Shannon HC. Xanome-line: a potent and specific Ml agonist in the treatment of Alzheimer’s disease. Presented at the annual meeting of the American College of Neuropsychopharmacology, San Juan, Puerto Rico, December 12-16, 1994.

7. Cutler NR, Sramek JJ. Investigator perspective on MTD: Practical application of an MTD definition-Has it accelerated development? J Clin Pharmacol. 2000;40:1183-1204.

8. Sramek JJ, Hourani J, Jhee SS, Cutler NR. NXX-066 in patients with Alzheimer’s disease: A bridging study. Life Sciences. 1999;64: 1215-1221.

9. Sramek JJ, Forrest M, Mengel H, Jhee SS, Hourani J, Cutler NR. A bridging study of LU 2-109 in patients with probable Alzheimer’s disease. Life Sciences. 1998:62:195-02.

10. Lin Y, Shih W. Statistical properties of the traditional algorithm-based designs for phase I cancer clinical trials. Biostatistics. 2001;2:203-15.

11. O’Quigley J, Pepe M, Fisher M. Continual reassessment method: A practical design for phase I clinical trials in cancer. Biometrics. 1990;46:33-8.

12. Goodman S, Zahurak M, Piantadosi S. Some practical improvements in the continual reassessment method for phase I studies. Stat Med. 1995;14:1149-161.

13. Kang S, Ahn C. The expected toxicity rate at the maximum tolerated dose in the standard phase I cancer clinical trial design. Drug Inf J. 2001; 35(4):1189-200.

14. Kang S, Ahn C. An investigation of the traditional algorithm- based designs for phase I cancer clinical trials. Drug Inf). 2002;36(4):865-873.

Seung-Ho Kong

Department of Statistics,

Ewha Womans University,

Seoul, Korea

Chul Ahn

Department of Internal

Medicine, University of Texas

Medical School,

Houston, Texas

Correspondence Address

Seung-Ho Kang, PhD, Department of Statistics, Ewlia Womans University, 11-1, DaeHyun-Dong, SeoDaeMun-Gu, Seoul, Korea, 120-750 (e-mail: seungho@ewha.ac.kr).

Copyright Drug Information Association 2005