Calibration, bioassay, and dose-response curves.

Abstract

Here are some definitions commonly encountered in this branch of data analysis, but note that there are many other equivalent definitions which the context should clarify.

Calibration details

Calibration involves one or more typical procedures.

Sometimes s is known independently, but is often supposed constant and unweighted regression is unjustifiably used. Sometimes a deterministic model is used for f(x), e.g. a sum of Logistics or Michaelis-Menten functions, but this is unwise. Calibration curves arise from the operation of numerous effects and cannot usually be described by one simple equation. Use of such equations can lead to biased predictions and is not recommended. Polynomials are useful for gentle curves as long as the degree is reasonably low (say, less than 3 ?) but, for many purposes, a weighted least squares data smoothing cubic spline is the best choice.

Unfortunately polynomials and splines are too flexible and follow outliers, leading to oscillating curves rather than data smoothing which is really required. Also they cannot fit horizontal asymptotes. You can help in several ways:-

Dose-response curve details

It should be pointed out first of all that Simfit is set up to use x not log(x) as the independent variable, e.g., concentration and not log(concentration). If a hyperbolic saturation curve is fitted to y(x) data, then Simfit can automatically plot y as a function of log(x) after fitting if sigmoidal hardcopy is required in semilogarithmic format.

Dose-response curves are special types of calibration curves that are usually constructed in order to estimate such parameters as maximal response, maximum growth rates, maximum inhibition rates, half saturation points, times to half maximal response, LD50, etc. It is also usual to require 95% confidence limits when fitting such curves, and this can lead to complications. Probably GCFIT is the most versatile Simfit program for this sort of analysis, but the subject is complicated and controversial so a number of issues should be considered.

First of all, polynomials or splines can fitted, and this is sometimes the best thing to do if the data are very noisy or you have no idea what would be a satisfactory model. Unfortunately, such curves can have turning points and do not fit asymptotes well. However, the sort of models that are often fitted to dose response curves to accomodate asymptotes have restricted shapes, which can lead to biased parameter estimates. For instance, hyperbolic kinetic or binding curves cannot fit sigmoid curves, and the usual models fitted to sigmoid curves (arctan, tanh, logit, logistic, probit, etc.) often fail to fit because they are too symmetrical. Since every case has to be treated on its own merits, the only way to achieve success is to experiment by fitting alternative models until the best option is discovered. Never accept a computer calculated value unless you have inspected a plot and confirmed that the best-fit curve is a sensible choice. A list of suggestions follows.

Some advice


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