Cubic Spline

The cubic spline fit is often recommended as the method to use for interpolating concentrations in an immunoassay.

Cubic spline should not be confused with cubic regression.

The cubic spline will produce a cosmetic plot through data points which are considered to be a true fit already, rather than to smooth the data according to any analytic model.

A pure cubic spline is capable of producing a curve which passes exactly through all data points. However, if the data is erratic this may produce apparently excessive curvature between some points, e.g.

To mitigate excessive curvature a smoothness factor can be applied to the cubic spline:

The cubic spline is a piecewise function (built from cubic segments). This means the curve is built from the average of any replicated standards. A consequence of this is that the %CV of the calculated concentrations cannot be determined (the %CV is calculated from raw data).

Spline based methods were popular in the 1980s when computers were first being used to compute results for immunoassay; this is because it is relatively simple computationally. More sophisticated methods such as 4PL/5PL were not available due to limitations in computer hardware available at the time. Kit manufacturers continue to recommend spline today primarily for historical reasons only (to follow existing protocols). These days 4PL/5PL methods are widely available (at myassays.com); these methods better model the dose/response relationship. We recommend migrating your assays to 4PL/5PL for a more resilient fit method and to avoid the limitations of spline described here.

Compare the fits yourself with your own data using the curve fitting resources available at:

• Cubic Spline

• Cubic Regression

• Four Parameter Logistic Curve

• Five Parameter Logistic Curve