A direct, general approach based on isobolograms for assessing the joint action of drugs in pre‐clinical experiments

Abstract

Pharmacologists and other biologists frequently use methods based on the interpretation of isobolograms to quantify the extent of synergy or antagonism between drugs used in combination in pre-clinical studies. Most methods have been unsatisfactory from a statistical viewpoint, many because they have relied solely on visual evaluation, others because the methods have not taken into account the variability of the measurements. We describe a direct approach for quantifying the joint potency of two drugs, a central feature being the use of simple isobole models that lead directly to response surface models for the expected experimental outcomes. The approach is general in the sense that one can use it for discrete or continuous responses, different underlying probability distributions, linear or non-linear dose-response functions of the drugs used singly, and a variety of experimental designs. Our approach extends the suggestions made by Hewlett for measuring the joint potency of drugs, and is similar in spirit to the approaches proposed by Greco et al. and Weinstein et al. We describe the analysis of data from an in vitro experiment conducted to evaluate the efficacy of the antiviral drugs AZT and ddI used in combination.

Analysis of Antimalarial Synergy between Bestatin and Endoprotease Inhibitors Using Statistical Response-Surface Modelling

“…The notation and analysis methods parallel those of Machado and Robinson (19). The modeling assumptions were as follows.…”

“…ϩ V 2 ϭ 1 (see equations 1, 2, and 9 in the report by Machado and Robinson [19]). Here, the interaction parameter quantifies the extent of synergy ( less than 1) or antagonism ( greater than 1); setting equal to 1 gives the zero interaction model.…”

“…Typically, empirically drawn isobolograms or histograms are used to suggest synergy between drug combinations, without any analysis of whether the data depart significantly from mere additivity (2,3). We have therefore applied a statistical response-surface modelling method (19) for the rigorous analysis of the combinations used here and believe that it should have wide application in synergy and antagonism studies. This approach is superior to previously published ones (e.g., see ref …”

IFN-β Restricts Tumor Growth and Sensitizes Alveolar Rhabdomyosarcoma to Ionizing Radiation

“…An approach based on isobolograms was used to assess the in vitro synergy between IFN-β and radiation (26,27). A weighed nonlinear dose-response model (27) using the SAS NLIN procedure was used to fit colony survival data.…”

“…A weighed nonlinear dose-response model (27) using the SAS NLIN procedure was used to fit colony survival data. Observed three-dimensional dose-response plots, fitted dose-response plots, and isobolograms were generated.…”