Modeling dose-response functions for combination treatments with log-logistic or Weibull functions
Tim Holland-Letz1, Alexander Leibner2,3,4, Annette Kopp-Schneider2
1German Cancer Research Center, Im Neuenheimer Feld 280, 69120, Heidelberg, Germany. t.holland-letz@dkfz.de.
Archives of Toxicology
|December 2, 2019
Summary
Log-logistic functions model substance interactions. Combination effects often deviate but can be closely approximated by a single log-logistic function, with parameters predictable from individual substance properties.
Area of Science:
- Toxicology
- Pharmacology
- Biostatistics
Background:
- Log-logistic functions are standard for modeling dose-response relationships.
- Assessing combined substance effects requires understanding their resulting dose-response functions.
Purpose of the Study:
- To determine if combined substances yield log-logistic dose-response curves.
- To predict parameters for combined substance dose-response functions.
- To approximate non-log-logistic combination curves with log-logistic functions.
Main Methods:
- Mathematical analysis of combined log-logistic functions.
- Approximation of resulting dose-response curves.
- Application to Weibull-type functions.
- Validation with cell culture data for cancer treatments.
Main Results:
- Combined substance dose-response functions are generally not log-logistic.
- These functions can be closely approximated by a single log-logistic function.
- Approximation parameters are predictable from individual substance parameters.
- Simple interaction structures can be represented by a single log-logistic function.
Conclusions:
- The study provides a method to predict and approximate dose-response curves for combined substances.
- This approach is applicable to both log-logistic and Weibull-type functions.
- The findings have practical implications for designing and analyzing combination experiments in toxicology and pharmacology.
Related Concept Videos
01:03Dose-Response Relationship: Overview
4.6K
Agonists can bind with and activate receptors, resulting in the formation of drug-receptor complexes. Once formed, these complexes catalyze many biochemical processes at the cellular level and subsequently induce a pharmacologic response. The degree of response is directly proportional to the fraction of activated receptors, which in turn, depends on the concentration of the drug at the receptor site as well as the sensitivity of the receptor. An increase in the administered dose contributes to...
4.6K
01:14Parametric Survival Analysis: Weibull and Exponential Methods
950
Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
950
01:23Dosage Regimen Designs: Nomograms and Tabulations
135
Nomograms and tabulations are vital tools used by clinicians to design accurate and individualized dosage regimens. These instruments provide a straightforward method for adjusting dosages based on individual patient characteristics, including age, weight, and physiological condition. The foundation of a drug's nomogram is population pharmacokinetic data collected and analyzed using specific models. This data simplifies complex equations, presenting them diagrammatically or tabularly for easy...
135
01:22Dose-Response Relationship: Potency and Efficacy
6.2K
The potency of a drug is the measure of its ability to produce a biological response and can be compared by looking at the half-maximum effective concentration or EC50 values of different drugs. A lower EC50 value indicates higher potency of the drug. In the dose–response curve of two antihypertensive drugs, candesartan and irbesartan, a significant difference is observed in their EC50 values. A lower EC50 value for candesartan indicates that it is more potent than irbesartan, as it...
6.2K
01:12Analysis of Population Pharmacokinetic Data
632
Analysis of population pharmacokinetic data involves studying the behavior of drugs within diverse populations to understand their pharmacokinetic parameters. Traditional pharmacokinetic methods typically involve collecting samples from a few individuals and estimating these parameters. While these methods are commonly used, they have limitations in capturing the variability in drug response among individuals or heterogeneous populations. Population pharmacokinetics is employed to address these...
632
01:25Dose-Response Relationship: Selectivity and Specificity
9.4K
Drugs exert their therapeutic effects by interacting with receptors, enzymes, or ion channels that are present throughout the human body. The strength and duration of the interaction between a drug and its target receptor are characterized by the selectivity and specificity of the drug. Selectivity refers to a drug's strong preference for its intended target over other targets. For instance, isoprenaline, a non-selective β-adrenergic agonist, interacts with both β1- and...
9.4K