# The Parallel-Line Method

Biological assays are frequently analyzed with the help of the parallel-line method. The parallel-line model is illustrated in the figure on the right. The logarithm of the doses are indicated on the horizontal axis, whereas the corresponding responses are represented on the vertical axis. The individual responses for each treatment are symbolized by the blue triangles for the standard preparation and by the green squares for the sample preparation.

With the help of the parallel-line model the statisitcal validity of the following hypotheses is tested:

- The dose-response relationship is linear for the standard and sample preparation.
- The dose-response curve has a significant slope.
- The dose-response curves of the standard and sample preparation are parallel.

The statistical analysis of an assay will produce a potency ratio that expresses the potency of the unknown sample in terms of the standard potency. The logarithmic potency ratio m can be calculated with the following formula

where b is the common slope of both lines, a are the regression parameters for the intercept with the y-axis of the standard and sample preparation.

The parallel-line procedure has several advantages compared to traditional single-point assay. Due to the check of the hypotheses mentioned above

- a linear dose-response correlation is not only assumed but also proven
- a dose-independent relative potency is obtained.

The disadvantages of the parallel-line method are the more extensive assay setup (standard and sample preparations have to be measured at different concentrations) and the complex statistical analysis of the results.