Biomedical subjects

Paul G Gottschalk

Publications and source records attributed to Paul G Gottschalk.

3 recordsLinked to original sources

PubMed2005

Determining the error of dose estimates and minimum and maximum acceptable concentrations from assays with nonlinear dose-response curves.

A method is described here that uses a modified Monte-Carlo method to provide an improved estimate of the confidence bounds of concentration estimates. This method accommodates even strongly nonlinear curve models, such as the five parameter logistic model, in contrast to the common but often poor approach of linearizing the regression problem and using linear theory to obtain the confidence bounds. The method uses an interpolation technique to reduce artifacts in the precision profile due to small simulation sample sizes and proximity to horizontal asymptotes in the curve model. The paper also describes how to define and calculate the minimum and maximum acceptable concentrations of dose-response curves by locating the concentrations where the size of the error, defined in terms of the size of the concentration confidence interval, exceeds the threshold of acceptability determined for the application.

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PubMed2005

The five-parameter logistic: a characterization and comparison with the four-parameter logistic.

Improvements in assay technology have reduced the amount of random variation in measured responses to the point where even slight asymmetry of the assay data can be more significant than random variation. Use of the five-parameter logistic (5PL) function to fit dose-response data easily accommodates such asymmetry. The 5PL can dramatically improve the accuracy of asymmetric assays over the use of symmetric models such as the four-parameter logistic (4PL) function. Until recently, however, the process of fitting the 5PL function has been difficult, with the result that the 4PL function has continued to be used even for highly asymmetric data. Various ad hoc modifications of the 4PL method have been developed in an attempt to address asymmetric data. However, recent advances in numerical methods and assay analysis software have rendered easier the fitting of the 5PL routine. This paper demonstrates how use of the 5PL function can improve assay performance over the 4PL and its variants. Specifically, the improvement in the accuracy of concentration estimates that can be obtained using the 5PL over the 4PL as a function of the asymmetry present in the data is studied. The behavior of the 5PL curve and how it differs from the 4PL curve are discussed. Common experimental designs, which can lead to ill-conditioned regression problems, are also examined.

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PubMed2005

Measuring parallelism, linearity, and relative potency in bioassay and immunoassay data.

There is often a need to determine parallelism or linearity between pairs of dose-response data sets for various biological applications. This article describes a technique based on a modification of the well-known extra-sum-of-squares principle of statistical regression. The standard extra-sum-of-squares method uses an F-distributed ratio as a statistic and an F-test based on this statistic as the parallelism test. It is shown here that this metric does not directly measure the parallelism between the two curves and can often vary in opposition to actual parallelism. To overcome this problem, a metric based on a chi-square test applied directly on the chi-square-distributed extra-sum-of-squares statistic is developed, which is shown to correspond directly to parallelism. This parallelism metric does not suffer from the shortcomings of the conventional F-test-based metric, and is a more reliable and appropriate measure of parallelism. The article also shows that the choice of curve model has a large effect on the sensitivity of either metric, and that using an asymmetric model, such as the asymmetric five-parameter logistic function, a generalization of the commonly used symmetric four-parameter logistic function, is necessary when working with asymmetric dose-response data. The effect of noise, as well as the importance of correct weighting on the parallelism metrics and the relative potency, is also studied.

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