Experimental design and sample size determination for testing synergism in drug combination studies based on uniform measures

Abstract

In anticancer drug development, the combined use of two drugs is an important strategy to achieve greater therapeutic success. Often combination studies are performed in animal (mostly mice) models before clinical trials are conducted. These experiments on mice are costly, especially with combination studies. However, experimental designs and sample size derivations for the joint action of drugs are not currently available except for a few cases where strong model assumptions are made. For example, Abdelbasit and Plackett proposed an optimal design assuming that the dose-response relationship follows some specified linear models. Tallarida et al. derived a design by fixing the mixture ratio and used a t-test to detect the simple similar action. The issue is that in reality we usually do not have enough information on the joint action of the two compounds before experiment and to understand their joint action is exactly our study goal. In this paper, we first propose a novel non-parametric model that does not impose such strong assumptions on the joint action. We then propose an experimental design for the joint action using uniform measure in this non-parametric model. This design is optimal in the sense that it reduces the variability in modelling synergy while allocating the doses to minimize the number of experimental units and to extract maximum information on the joint action of the compounds. Based on this design, we propose a robust F-test to detect departures from the simple similar action of two compounds and a method to determine sample sizes that are economically feasible. We illustrate the method with a study of the joint action of two new anticancer agents: temozolomide and irinotecan.

Modulation of Plasma Antioxidant Activity in Weaned Piglets by Plant Polyphenols

“…As seen in Table 2, the concentration compositions of 15 uniform designed mixtures were very extensively and systemically distributed in the C-space built by the 4 PP. A uniform design is a unique method requiring a minimum number of experiment runs on account of the merits of space filling and multiple levels (Tan et al, 2003;Xie and Fang, 2000). Many previous studies have employed other optimising experimental methods to design the concentration composition of multiple mixtures to effectively model any real mixture with a definite concentration composition of mixture components, such as factorial (Groten et al, 1996) and orthogonal design (Prescott and Draper, 2004).…”

Simulation of polyhedral convex contoured distributions

“…The single dose-response curves for drugs A i , i = 1, 2, 3 are assumed to be f i (x i ) = α i + β log(x i ), i = 1, 2, 3. According to (Berenbaum 1989;Tan et al 2003;Tian et al 2009) the additive model at the combination dose (x 1 , x 2 , x 3 ) is y(x 1 , x 2 , x 3 ) = α 1 + β log(z 1 ) + log((1 − ρ 0 )z 2 + ρ 0 )+…”

“…(Cutler et al 2004;Rocchini and Cignoni 2000). The simulation of uniform distributions on convex polyhedra applies in the field of drug combination studies as described in (Fang and Yang 2000;Tan et al 2003;Tian et al 2009) which is of special interest in this paper. In (Richter and Schicker 2014) the simulation of a uniform distribution on a tetrahedron is used to detect optimal production schedules.…”

“…For further details, we refer to (Tian et al 2009). Since in (Tan et al 2003) it is proved that a uniform design on P(a 0 , b 0 ) maximizes the minimum power of the F-test to detect significant deviations from additive actions of the drugs, it is of importance to be able to effectively simulate the uniform distribution on general tetragons P(a 0 , b 0 ). In (Tian et al 2009) several algorithms for the simulation of uniformly distributed random points on convex polyhedra are presented for particular two, three, and ndimensional cases.…”

Moleküler Hedefli Anti-Kanser Ajan Kombinasyonlarını Optimize Etmek İçin Stratejiler

“…Ancak, ksenograft çalışmalarında sinerji çalışmalarının sonuçlarını etkileyebilecek değişkenler çoktur, istatistiksel olarak geçerli sonuçlar elde etmek için çok sayıda hayvan ihtiyaç varken, bu gibi değerlendirmeleri yapmak için yeterli kaynaklara sahip nispeten az laboratuvar bulunmaktadır 42 .…”