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Summary
Summary
Not since this author's bestselling Manual of Pharmacologic Calculation-long out of print-has there been a reference available for drug data analysis, and even that work did not deal with drug combinations. Although pharmacologists and most other scientists know what synergism is, mainstream textbooks tend to neglect it as a quantitative topic. Few researchers are familiar with the quantitative methodology needed to differentiate synergistic responses from the simply additive responses expected from drug combinations or a single drug's interaction with endogenous chemicals.
In Drug Synergism and Dose-Effect Data Analysis, noted pharmacologist, mathematician, and author Ronald J. Tallarida finally brings these methods to light. Drawing on statistical theory and methods but keeping the special needs of the pharmacologist in mind, he begins his treatment with dose-response relations, the statistical analysis of the data, and the models that describe them. He also offers the only modern presentation of probit and logit analysis and provides detailed calculation methods not found in typical statistics books.
Numerous examples accompany a presentation that clearly illustrates the calculations and experimental design considerations for modern drug analysis. You'll find the conceptual background, the algorithms, and new research developments. In short, Drug Synergism and Dose-Effect Data Analysis has everything you need to perform, with confidence, the quantitative analysis of dose response data.
Author Notes
Ronald J. Tallarida earned the B.S. and M.S. degrees in physics/mathematics and a Ph.D. in pharmacology. His primary appointment is as Professor of Pharmacology at Temple University School of Medicine, Philadelphia; he also serves as Adjunct Professor of Biomedical Engineering (mathematics) at Drexel University in Philadelphia
Table of Contents
Preface | p. v |
The Author | p. ix |
1 Combinations of Chemicals | p. 1 |
1.1 Introduction | p. 1 |
1.2 Independent joint action of drugs | p. 3 |
1.3 Additivity | p. 3 |
1.4 Isobologram | p. 5 |
1.5 Chloral hydrate and ethyl alcohol | p. 9 |
1.6 The need for statistics | p. 10 |
1.7 The emergence of quantitative methods for studying drug combinations | p. 12 |
References and Suggested Reading | p. 15 |
2 Dose-Response Analysis | p. 21 |
2.1 Efficacy and potency | p. 21 |
2.2 Doses and concentrations | p. 24 |
2.3 Notation | p. 25 |
2.4 Logarithmic transformation | p. 26 |
2.5 Linear regression | p. 26 |
Determination of D[subscript 50] and its variance from linear regression: example | p. 31 |
2.6 Nonlinear models | p. 33 |
Appendix 2 | p. 37 |
References | p. 39 |
3 Linear Regression: A Further Discussion | p. 41 |
3.1 ANOVA in linear regression | p. 41 |
3.2 Parallel line analysis | p. 44 |
Test for parallelism | p. 44 |
3.3 The common slope and relative potency | p. 46 |
3.4 Confidence limits of the potency ratio | p. 50 |
3.5 Weighted least square regression | p. 51 |
Appendix 3 | p. 53 |
References | p. 55 |
4 Calculations for Combination Drug Analysis | p. 57 |
4.1 Experimental designs | p. 57 |
4.2 Fixed-ratio design | p. 58 |
4.3 Test of significance | p. 60 |
4.4 Graphical display with standard errors | p. 64 |
4.5 The additive total dose: a closer look | p. 64 |
4.6 Changing the effect level | p. 67 |
4.7 Selecting the drug proportions in a combination study | p. 69 |
4.8 Interaction index | p. 69 |
Appendix 4 | p. 73 |
References | p. 75 |
5 The Composite Additive Curve | p. 77 |
5.1 Construction of the additive curve | p. 77 |
5.2 Test for distinguishing two regression lines | p. 84 |
References | p. 89 |
6 Quantal Dose-Response Data: Probit and Logit Analysis | p. 91 |
6.1 Probit analysis | p. 91 |
6.2 Precision in probit calculations | p. 97 |
6.3 The composite additive probit line | p. 99 |
6.4 Testing for synergism | p. 103 |
6.5 Comparing the composite additive line and the actual combination line | p. 103 |
6.6 A closer look at probits | p. 106 |
6.7 Testing two probit regression lines for parallelism | p. 106 |
6.8 Constant relative potency in probit analysis | p. 110 |
6.9 Parallel line analysis of combined drug action | p. 110 |
6.10 Testing for additivity: parallel constraint and probit analysis | p. 112 |
6.11 Logit analysis | p. 114 |
6.12 Calculations with logits | p. 116 |
Appendix 6 Method of Litchfield and Wilcoxon | p. 119 |
References | p. 121 |
7 Analysis of Drug Combinations Over a Range of Drug Ratios | p. 123 |
7.1 Fraction plot | p. 124 |
7.2 Testing for synergism over a range of proportions | p. 126 |
7.3 Combinations of acetaminophen and tramadol | p. 128 |
Reference | p. 131 |
8 Analysis of a Single Dose Combination | p. 133 |
8.1 Constant relative potency | p. 133 |
8.2 Variable relative potency | p. 134 |
Hyperbolas with different maxima | p. 135 |
Nonparallel regression lines | p. 137 |
References | p. 141 |
9 Different Experimental Designs | p. 143 |
9.1 Combinations of an active and an inactive drug | p. 143 |
9.2 Site-site interactions | p. 144 |
Acetaminophen in Two-Site Analysis | p. 145 |
Site-Site Analysis with Opioid Receptor Subtypes | p. 147 |
9.3 Theory of competitive antagonism | p. 147 |
Schild analysis | p. 149 |
9.4 Combined inhibitory effects | p. 151 |
References | p. 155 |
10 Response Surface Analysis of Drug Combinations | p. 157 |
10.1 Additive combinations and response surface | p. 157 |
10.2 Super-additive combinations | p. 160 |
10.3 Variable relative potency | p. 161 |
Dose-effect relations | p. 163 |
10.4 Response surface analysis of morphine and clonidine | p. 163 |
Morphine-clonidine data | p. 164 |
10.5 Isobolar analysis or surface analysis | p. 167 |
References | p. 171 |
11 Nonlinear Regression Analysis | p. 173 |
11.1 Hill equation | p. 174 |
11.2 Theory | p. 175 |
11.3 Sigmoid plot | p. 179 |
References | p. 181 |
12 Statistical Concepts and Tests of Hypotheses | p. 183 |
12.1 Hypothesis testing with the t-test: two groups | p. 183 |
12.2 t-test: paired data | p. 185 |
12.3 Confidence interval | p. 187 |
12.4 Mann-Whitney test | p. 187 |
Case 1 | p. 188 |
Case 2 | p. 189 |
12.5 Analysis of variance | p. 189 |
12.6 Newman-Keuls test | p. 192 |
12.7 Chi square | p. 194 |
Adjusted chi square | p. 195 |
Comparing two proportions | p. 195 |
12.8 Confidence limits of a proportion | p. 196 |
12.9 Confidence limits for a ratio | p. 197 |
12.10 Multiple regression (equations) | p. 198 |
12.11 Sample size calculations | p. 200 |
Single proportion | p. 201 |
Two proportions | p. 201 |
Two means | p. 202 |
Sample mean | p. 202 |
References | p. 203 |
Computer Software | p. 204 |
Appendix | p. 205 |
Index | p. 243 |