As indicated earlier, in many clinical trials, a parallel group design alone or a crossover design alone may not be appropriate for evaluation of the safety and efficacy of some drug products. Instead, a combination of a parallel group design or a crossover design with the characteristics of some other designs, such as titration design and enrichment design, may be more appropriate. For example, for evaluation of the efficacy and safety of drug products for treatment of erection dysfunction in male subjects, a design that consists of a titration phase for achieving optimal dose and a crossover active treatment phase with two placebo challenges (i.e., pre- and post-treatment) is often considered. We will refer to the design of this kind as a placebo-challenging design.
For the placebo-challenging design of this kind, subjects are evaluated for eligibility at screening based on medical history, laboratory test, and physical examination. Eligible subjects then enter the dose titration phase. Each subject proceeds a stepwise dose titration until a minimal dose that produces the optimal response is identified. An optimal response is defined as an erection sufficient to achieve vaginal penetration and lasting from 30 to 80 minutes. At the start of treatment, subjects are required to undergo an in-clinic evaluation of a double-blind placebo-challenge (i.e., subjects will be randomized to receive either the placebo or the active dose at the level identified during the titration). After this first period of in-clinic study, all subjects are to receive a three-month home treatment period at the dose identified during the titration. At the end of three-month treatment, a second in-clinic double-blind placebo-challenging is conducted. Note that at the second placebo-challenging, patients are randomly assigned to receive either the placebo or the active dose. As a result, the above design is in fact the combination of a titration design and a four-sequence, two-period (4 X 2) crossover design. In other words, during the crossover phase, there are four sequences of treatments, namely, PP, PA, AP, and AA. As an example, for the sequence of AP, subjects are randomized to receive the active dose at the start of the home treatment and are randomly assigned to receive the placebo at the end of the three-month home treatment.
For the placebo-challenging design described above, standard statistical procedures may not be applicable. Chow et al. (2000) studied statistical properties of a placebo-challenging design and developed some new statistical methodology for analysis of data collected from such a design. The statistical methodology is briefly outline below.
Suppose that there are a total of 2n subjects in a placebo-challenging design, as described above, qualified subjects are randomly assigned to two treatment groups (i.e., placebo and treatment) in the first and the last periods of the study. Each group consists of n patients, and the assignments in two periods are independent. Thus, 2n patients can be classified into the following four groups according to the type of treatments received in two periods:
where n + n2 = n. Data will be collected in the first and the last periods. A three-month home treatment period will be given to each patient, and no data will be collected.
Note that the placebo-challenging design is very similar to that of a four-sequence, two-period (4 x 2) crossover design (Jones and Kenward, 1989). The major difference between the two designs is that in the placebo-challenge study, there is a three-month home treatment between the two periods of placebo/treatment. Consequently, statistical models (parameter specifications) under the two designs are different. For example, in a 4 x 2 crossover design, one can estimate the period effect, but in a placebo-challenge design, the period effect is confounded with the three-month home treatment effect. As the period effect is usually much smaller than the three-month home treatment effect, we may assume that the former is negligible so that the three-month home treatment effect is estimable.
Let yijk be the observation from the ith patient in the j period and the kth group. We propose the following statistical model:
Group Treatment Number of patients
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