# A Mathematical Model for the Analysis of Therapies

• D. Revenstorff

## Abstract

Checking of therapeutic efficacy may be carried out at several levels of sophistication. The most elementary check is to demonstrate significance of change. This can be done in a simple before-and-after design. Apart from the problem of spontaneous remission, even here some intricate statistical problems appear (cf. HARRIS, 1962). A more comprehensive picture of therapeutic effects is provided by repeated observations of a client’s behaviour as therapy continues. Data from this kind of extended design constitute a time series. Again significance tests for change are in order. Moreover, the time course itself can be analysed with respect to rate of change, turning points, asymptotes and other features of shape. To acquire some descriptive shorthand of the change, curve fitting may be applied. The whole time series then is summarized as an exponential decay, a logarithmic curve or a parabola. Very common is the use of polynomials, which fit virtually everything if a proper degree is taken. Besides description of the data, such curve fitting sometimes has significance for the formulation of a theory to explain the change, e.g. Hull’s exponential acquisition curve of habit strength. It is only in connection with a theory that the use of a fitted curve for prediction by extrapolation appears to be reasonable.

### Keywords

Placebo Depression Hull Smoke Lobeline

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