A Two-Stage Response Surface Approach to Modeling Drug Interaction
Abstract
Studies of drug combinations have become increasingly important, especially in treating malignant cancers. Researchers are interested in identifying compounds that act synergistically when combined. Such synergy is usually measured through an interaction index. The existing statistical methods, in general, estimate the interaction index using pooled data from compounds administered individually and in combination. In this article, we propose a two-stage response surface approach. Parameters of monotherapy dose–response curves are estimated and then incorporated in estimating the interaction index through a quadratic response surface model. Using multiple simulation studies, we demonstrate that the new method gives less biased estimates for both monotherapy dose–response curves and interaction index. Also developed is a bootstrapping method that allows constructing a confidence interval for interaction index at any combination dose levels. An example is provided to illustrate the method.
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Zhao et al.'s simulations indicated that two-stage models gave results almost identical to the true values of the interaction index, whereas the one-stage model gave interaction indexes that deviated from true values.
“Their simulations indicated that two-stage models gave results almost identical to the true values of the interaction index. The one-stage model, in contrast, gave interaction indexes that deviated from true values.”
From Evaluation of Drug Combination Effect Using a Bliss Independence Dose–Response Surface Model (2018) · cites this paper as Zhao et al (2012)
Zhao et al. (2012) found that one-stage modeling sometimes could not converge to proper values or had error messages in parameter estimation, but two-stage modeling could overcome these problems.
“They also found that the one-stage modeling sometimes could not converge to proper values or had error messages in the estimating of parameters, but two-stage modeling could overcome these problems.”
From Evaluation of Drug Combination Effect Using a Bliss Independence Dose–Response Surface Model (2018) · cites this paper as Zhao et al (2012)
From Zhao et al.'s simulation data, even though the one-stage method gives less accurate results than the two-stage method, the differences are not large enough to make different conclusions based on the estimated interaction indexes.
“From their simulation data, it is worth noting that even though the one-stage method gives less accurate results than the two-stage method, the differences are not large enough to make different conclusions based on the estimated interaction indexes.”
From Evaluation of Drug Combination Effect Using a Bliss Independence Dose–Response Surface Model (2018) · cites this paper as Zhao et al (2012)
Zhao et al. (2012) pointed out that one-stage models may deviate significantly from their true values, and thus potentially lead to wrong conclusions.
“Zhao et al (2012) has pointed out that one-stage models may deviate significantly from their true values, and thus potentially lead to wrong conclusions.”
From Evaluation of Drug Combination Effect Using a Bliss Independence Dose–Response Surface Model (2018) · cites this paper as Zhao et al (2012)
By incorporating the variance from the first stage into the second stage, the two-stage modeling provides more reliable inference.
“And by incorporating the variance from the first stage into the second stage, the two-stage modeling provides more reliable inference (Zhao et al. 2012).”
From Evaluation of Drug Combination Effect Using a Bliss Independence Dose–Response Surface Model (2018) · cites this paper as Zhao et al. 2012
Cited by
Sorted by citations
A New Bliss Independence Model to Analyze Drug Combination Data
Zhao, W., Sachsenmeier, K., Zhang, L., Sult, E., Hollingsworth, R. E., & Yang, H. (2014) · SLAS Discovery · doi:10.1177/1087057114521867 · Cited by 322 · see citing works
“First, a random sample of Yab P , is simulated from a multivariate normal distribution with mean and covariance matrix parameters calculated using equations (6), (7), and (8).”
MethodSelf-citationEvaluation of Drug Combination Effect Using a Bliss Independence Dose–Response Surface Model
Liu, Q., Yin, X., Languino, L. R., & Altieri, D. C. (2018) · Statistics in Biopharmaceutical Research · doi:10.1080/19466315.2018.1437071 · Cited by 216 · see citing works
- Authors
- Zhao, W., Zhang, L., Zeng, L., & Yang, H.
- Venue
- Statistics in Biopharmaceutical Research
- Publisher
- Informa UK Limited
- Published
- 2012-10
- Volume
- 4
- Issue
- 4
- Pages
- 375-383
- ISSN
- 1946-6315 (ISSN-L)
- OpenAlex
- W2035267407
- Cited by
- 12
- References
- 0
- Citations by year
- 2023: 1 · 2021: 1 · 2020: 1 · 2019: 3 · 2018: 1 · 2017: 1 · 2016: 1 · 2014: 2 · 2013: 1
- FWCI
- 1.27
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Statistics in Biopharmaceutical Research (publishedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Optimal Experimental Design Methods
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Computational Drug Discovery Methods
- Keywords
- drug interactions, combination therapy, synergistic effect, interaction index, quadratic response surface, bootstrapping, confidence intervals, cancer chemotherapy, dose-response modeling
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