The Bliss independence model is widely used to analyze drug combination data when screening for candidate drug combinations. The method compares the observed combination response (Y(O)) with the predicted combination response (Y(P)), which was obtained based on the assumption that there is no effect from drug-drug interactions. Typically, the combination effect is declared synergistic if Y(O) is greater than Y(P). However, this method lacks statistical rigor because it does not take into account the variability of the response measures and can frequently cause false-positive claims. In this article, we introduce a two-stage response surface model to describe the drug interaction across all dose combinations tested. This new method enables robust statistical testing for synergism at any dose combination, thus reducing the risk of false positives. The use of the method is illustrated through an application describing statistically significant "synergy regions" for candidate drug combinations targeting epidermal growth factor receptor and the insulin-like growth factor 1 receptor.

https://journals.sagepub.com/doi/pdf/10.1177/1087057114521867

A New Bliss Independence Model to Analyze Drug Combination Data.

during 1943-44 a study of semi-starvation in volunteers under laboratory conditions. Thirty-two conscientious objectors offered themselves as subjects and lived in the laboratory of Physiological Hygiene for over a year. During a control period of three months they were given a diet containing approximately 3,500 calories per day. Then for 6 months the diet was reduced by 1,570 calories in the form of potatoes, cabbage, turnips, and cereals, and only very small portions of animal protein each week. The experimental diet resembled approximately that consumed under famine conditions in Europe. During this period they lost on an average 24 per cent. of body weight, and were reduced to a condition closely resembling famine victims. All at some time had famine oedema. The subjects were then studied for a further 3 months in the laboratory under various regimes of rehabilitation, and most of them were observed at intervals for a further 6 to 9 months. A year after the end of the starvation period, all had returned to normal and were apparently none the worse. During the year in the laboratory the bas c physiological and psychological state of the subjects was reviewed at regular intervals by teams of investigators. Important observations were made on the weight changes, the distribution of body fluids, the basal metabolism, the energy exchanges during exercise, the capacity for work, the size of the heart, adaptations in the circulatory system, and changes in the cellular elements in the blood. The psychological observations included studies of behaviour patterns, personality changes and intellectual abilities. The many important findings cannot be summarized in a review article. The Minnesota experiment, which will bccome a classic, was planned and executed by a co-ordinated team of first class investigators, and there is no record of any comparable experiment either in human physiology or in psychology. The general plan will be of interest and indeed an obligatory study for future investigators into the problems presented by adaptation of the physiological and psychological processes in man to prolonged adverse environmental conditions, and the details are important to those concerned with the practical problems of medicine in a famine. Unfortunately the choice of presentation of this great experiment is unsatisfactory. \"Human Starvation\" weighs 3 45 kg. and suffers, like many American books to-day, from over-nutrition. Striving for completeness, the authors have stuffed the book with observations made by persons less competent or less well-placed than themselves, and in consequence the fascinating account of the Minnesota experiment is often buried. Chapter 3, containing 29 pages, is entirely devoted to old work, long dead, which might have been allowed to rest; there are many other examples of the citation of inferior work. There must be many physiologists, psychologists, and physicians who would like a brief straightforward account of this great experiment for their personal use. Is it too much to ask Professor Keys to provide such an account, which would fall within the limits of a private purse, and slip easily into the suitcase of a physician setting out by aeroplane on famine-relief work ? R. PASSMORE

https://jech.bmj.com/content/jech/5/2/121.full.pdf

Introduction to the Theory of Statistics

To test the anticancer effect of combining two drugs targeting different biological pathways, the popular way to show synergistic effect of drug combination is a heat map or surface plot based on t...

/pdf/evaluation-of-drug-combination-effect-using-a-bliss-uvyo0qqfh6.pdf

Evaluation of Drug Combination Effect Using a Bliss Independence Dose–Response Surface Model

(1971). Statistical Tolerance Regions: Classical and Bayesian. Journal of the Operational Research Society: Vol. 22, No. 3, pp. 309-310.

Statistical Tolerance Regions: Classical and Bayesian

Today, the assessment of immunogenicity is integral in nonclinical and clinical testing of new biotherapeutics and biosimilars. A key component in the risk-based evaluation of immunogenicity involves the detection and characterization of anti-drug antibodies (ADA). Over the past couple of decades, much progress has been made in standardizing the generalized approach for ADA testing with a three-tiered testing paradigm involving screening, confirmation, and quasi-quantitative titer assessment representing the typical harmonized scheme. Depending on a biotherapeutic’s structural attributes, more characterization and testing may be appropriate. Unlike bioanalytical assays used to support the evaluation of pharmacokinetics or toxicokinetics, an important component in immunogenicity testing is the calculation of cut points for the identification (screening), confirmation (specificity), and titer assessment responses in animals and humans. Several key publications have laid an excellent foundation for statistical design and data analysis to determine immunogenicity cut points. Yet, the process for statistical determination of cut points remains a topic of active discussion by investigators who conduct immunogenicity assessments to support biotherapeutic drug development. In recent years, we have refined our statistical approach to address the challenges that have arisen due to the evolution in biotherapeutics and the analytical technologies used for quasi-quantitative detection. Based on this collective experience, we offer a simplified statistical analysis process and flow-scheme for cut point evaluations that should work in a large majority of projects to provide reliable estimates for the screening, confirmatory, and titering cut points.

Recommendations for Systematic Statistical Computation of Immunogenicity Cut Points.

Many pharmacologically active molecules are formulated as solid dosage form drug products. Following oral administration, the diffusion of an active molecule from the gastrointestinal tract into systemic distribution requires the disintegration of the dosage form followed by the dissolution of the molecule in the stomach lumen. Its dissolution properties may have a direct impact on its bioavailability and subsequent therapeutic effect. Consequently, dissolution (or in vitro release) testing has been the subject of intense scientific and regulatory interest over the past several decades. Much interest has focused on models describing in vitro release profiles over a time scale, and a number of methods have been proposed for testing similarity of profiles. In this article, we review previously published work on dissolution profile similarity testing and provide a detailed critique of current methods in order to set the stage for a Bayesian approach.

/pdf/in-vitro-dissolution-curve-comparisons-a-critique-of-current-y7t0i6wlme.pdf

In Vitro Dissolution Curve Comparisons: A Critique of Current Practice

Receiver operating characteristic (ROC) curve analysis is widely used in biomedical research to assess the performance of diagnostic tests. Much of the work has been directed at developing accurate indices to describe ROC curves and appropriate statistics to test differences between them. The analysis, however, is largely built on the assumption that the test results are dichotomous. We generalize the ROC curve analysis to allow for tests to have more than two outcomes. The generalized ROC curve constitutes a surface. We propose to use the volume under the surface to measure the accuracy of a diagnostic test.

Roc surface: a generalization of roc curve analysis

Parallelism is a prerequisite for the determination of relative potency in bioassays. It involves testing of similarity between a pair of dose–response curves of a reference standard and a test sample. Methods for parallelism assessment that are currently in use include p-value-based significance tests and interval-based equivalence tests. These methods make statistical inference about the similarity between the model parameters of the dose–response curves based on the sampling distribution of the estimates of these parameters. Although the methods have some merits for parallelism testing, there is a major drawback to these approaches, namely that the similarity between the model parameters does not necessarily translate into the similarity between the two dose–response curves. As a result, a test may conclude that the model parameters are similar, yet there is little assurance on the similarity between the two dose–response curves. In this article, we reformulate the parallelism testing problem as testin...

A Bayesian Approach to Parallelism Testing in Bioassay

Validation of linearity is a regulatory requirement. Although many methods are proposed, they suffer from several deficiencies including difficulties of setting fit-for-purpose acceptable limits, dependency on concentration levels used in linearity experiment, and challenges in implementation for statistically lay users. In this article, a statistical procedure for testing linearity is proposed. The method uses a two one-sided test (TOST) of equivalence to evaluate the bias that can result from approximating a higher-order polynomial response with a linear function. By using orthogonal polynomials and generalized pivotal quantity analysis, the method provides a closed-form solution, thus making linearity testing easy to implement.

Testing Assay Linearity Over a Pre-Specified Range

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

A Two-Stage Response Surface Approach to Modeling Drug Interaction

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