Investigation of the robustness of two models for assessing synergy in pre-clinical drug combination studies

Response envelope analysis for quantitative evaluation of drug combinations

MOTIVATION

The concept of synergy between two agents, over a century old, is important to the fields of biology, chemistry, pharmacology and medicine. A key step in drug combination analysis is the selection of an additivity model to identify combination effects including synergy, additivity and antagonism. Existing methods for identifying and interpreting those combination effects have limitations.

RESULTS

We present here a computational framework, termed response envelope analysis (REA), that makes use of 3D response surfaces formed by generalized Loewe Additivity and Bliss Independence models of interaction to evaluate drug combination effects. Because the two models imply two extreme limits of drug interaction (mutually exclusive and mutually non-exclusive), a response envelope defined by them provides a quantitatively stringent additivity model for identifying combination effects without knowing the inhibition mechanism. As a demonstration, we apply REA to representative published data from large screens of anticancer and antibiotic combinations. We show that REA is more accurate than existing methods and provides more consistent results in the context of cross-experiment evaluation.

AVAILABILITY AND IMPLEMENTATION

The open-source software package associated with REA is available at: https://github.com/4dsoftware/rea.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Evaluation of drug combination effect using a Bliss independence dose-response surface model

To test the anticancer effect of combining two drugs targeting different biological pathways, the popular way to show synergistic effect of drug combination is a heat map or surface plot based on the percent excess the Bliss prediction using the average response measures at each combination dose. Such graphs, however, are inefficient in the drug screening process and it doesn't give a statistical inference on synergistic effect. To make a statistically rigorous and robust conclusion for drug combination effect, we present a two-stage Bliss independence response surface model to estimate an overall interaction index (τ) with 95% confidence interval (CI). By taking into all data points account, the overall τ with 95% CI can be applied to determine if the drug combination effect is synergistic overall. Using some example data, the two-stage model was compared to a couple of classic models following Bliss rule. The data analysis results obtained from our model reflect the pattern shown from other models. The application of overall τ helps investigators to make decision easier and accelerate the preclinical drug screening.

Analysis of drug combinations: current methodological landscape

Combination therapies exploit the chances for better efficacy, decreased toxicity, and reduced development of drug resistance and owing to these advantages, have become a standard for the treatment of several diseases and continue to represent a promising approach in indications of unmet medical need. In this context, studying the effects of a combination of drugs in order to provide evidence of a significant superiority compared to the single agents is of particular interest. Research in this field has resulted in a large number of papers and revealed several issues. Here, we propose an overview of the current methodological landscape concerning the study of combination effects. First, we aim to provide the minimal set of mathematical and pharmacological concepts necessary to understand the most commonly used approaches, divided into effect-based approaches and dose-effect-based approaches, and introduced in light of their respective practical advantages and limitations. Then, we discuss six main common methodological issues that scientists have to face at each step of the development of new combination therapies. In particular, in the absence of a reference methodology suitable for all biomedical situations, the analysis of drug combinations should benefit from a collective, appropriate, and rigorous application of the concepts and methods reviewed here.

Experimental designs for detecting synergy and antagonism between two drugs in a pre-clinical study

The identification of synergistic interactions between combinations of drugs is an important area within drug discovery and development. Pre-clinically, large numbers of screening studies to identify synergistic pairs of compounds can often be ran, necessitating efficient and robust experimental designs. We consider experimental designs for detecting interaction between two drugs in a pre-clinical in vitro assay in the presence of uncertainty of the monotherapy response. The monotherapies are assumed to follow the Hill equation with common lower and upper asymptotes, and a common variance. The optimality criterion used is the variance of the interaction parameter. We focus on ray designs and investigate two algorithms for selecting the optimum set of dose combinations. The first is a forward algorithm in which design points are added sequentially. This is found to give useful solutions in simple cases but can lack robustness when knowledge about the monotherapy parameters is insufficient. The second algorithm is a more pragmatic approach where the design points are constrained to be distributed log-normally along the rays and monotherapy doses. We find that the pragmatic algorithm is more stable than the forward algorithm, and even when the forward algorithm has converged, the pragmatic algorithm can still out-perform it. Practically, we find that good designs for detecting an interaction have equal numbers of points on monotherapies and combination therapies, with those points typically placed in positions where a 50% response is expected. More uncertainty in monotherapy parameters leads to an optimal design with design points that are more spread out.

DCDB 2.0: a major update of the drug combination database

Experience in clinical practice and research in systems pharmacology suggested the limitations of the current one-drug-one-target paradigm in new drug discovery. Single-target drugs may not always produce desired physiological effects on the entire biological system, even if they have successfully regulated the activities of their designated targets. On the other hand, multicomponent therapy, in which two or more agents simultaneously interact with multiple targets, has attracted growing attention. Many drug combinations consisting of multiple agents have already entered clinical practice, especially in treating complex and refractory diseases. Drug combination database (DCDB), launched in 2010, is the first available database that collects and organizes information on drug combinations, with an aim to facilitate systems-oriented new drug discovery. Here, we report the second major release of DCDB (Version 2.0), which includes 866 new drug combinations (1363 in total), consisting of 904 distinctive components. These drug combinations are curated from ∼140,000 clinical studies and the food and drug administration (FDA) electronic orange book. In this update, DCDB collects 237 unsuccessful drug combinations, which may provide a contrast for systematic discovery of the patterns in successful drug combinations. Database URL: http://www.cls.zju.edu.cn/dcdb/