WITHDRAWN: Modeling Synergy and Independence in the Combined Effects of Lethal Factors

• Author(s): Robert H. Baran
• Keywords: Generalized linear model ; Gibbs distribution ; Markov chain ; Independent effects ; Response surface ; Synergy

Abstract

Generalized linear models (GLMs) have been used and abused to show that synergy occurs when the lethality of a mixture exceeds the "sum of the effects" of N>1 individual factors. Estimating the GLM via the logit link and comparing the fitted response surface to prediction based on the hypothesis independent effects, positive interactions implied by the hypothesis have been construed as synergy. This and other paradoxes in past treatments are de-conflicted by a thermodynamic lattice model (TLM) that features one binary-valued site for each factor. The TLM admits only pair-wise interactions, giving rise to a Markov chain of N-valued states with a stationary Gibbs distribution, and the all-zero state can be defined as the survival indicator. It supports a systematic approach to testing synergy (or antagonism) as illustrated by examples from microbial toxicology and radiation effects.