Abstract: Systems and methods for determining characteristic transition values such as elbow values in sigmoid or growth-type curves, such as the cycle threshold (Ct) value in PCR amplification curves. A double sigmoid function with parameters determined by a Levenberg-Marquardt (LM) regression process is used to find an approximation to a curve that fits a PCR dataset. Once the parameters have been determined, the curve can be normalized using one or more of the determined parameters. Normalization is advantageous for determining the Ct value if one chooses the arbitrary fluorescence level (AFL) approach to calculating Ct values for amplification curves. After normalization, the normalized curve is processed by applying a root-finding algorithm to determine the root of the function representing the normalized curve, which root corresponds to the Ct value. The Ct value is then returned and may be displayed or otherwise used for further processing.

Abstract: Systems and methods for identifying and removing spikes in data sets representing PCR growth curves or other sigmoid type curves or growth curves. A double sigmoid function with parameters determined using a Levenberg-Marquardt regression algorithm is used to find an approximation to the curve, and a statistical test such as a z-test is then used to identify spikes by identifying data points in the data set that do not fit well with the approximation. The identified spike(s) are removed from the data set and/or replaced with interpolated data points determined by using data points surrounding the identified spike(s). In one aspect, a spline interpolation process such as a cubic spline interpolation process is used to find an approximation to the data set with the identified spike points removed. Interpolated values to replace the spike points are then calculated using the cubic spline interpolation approximation curve.

Abstract: Systems and methods for identifying and removing spikes in data sets representing PCR growth curves or other sigmoid type curves or growth curves. A double sigmoid function with parameters determined using a Levenberg-Marquardt regression algorithm is used to find an approximation to the curve, and a statistical test such as a z-test is then used to identify spikes by identifying data points in the data set that do not fit well with the approximation. The identified spike(s) are removed from the data set and/or replaced with interpolated data points determined by using data points surrounding the identified spike(s). In one aspect, a spline interpolation process such as a cubic spline interpolation process is used to find an approximation to the data set with the identified spike points removed. Interpolated values to replace the spike points are then calculated using the cubic spline interpolation approximation curve.

Abstract: Systems and methods for determining characteristic transition values such as elbow values in sigmoid or growth-type curves, such as the cycle threshold (Ct) value in PCR amplification curves. A double sigmoid function with parameters determined by a Levenberg-Marquardt (LM) regression process is used to find an approximation to a curve that fits a PCR dataset. Once the parameters have been determined, the curve can be normalized using one or more of the determined parameters. Normalization is advantageous for determining the Ct value if one chooses the arbitrary fluorescence level (AFL) approach to calculating Ct values for amplification curves. After normalization, the normalized curve is processed by applying a root-finding algorithm to determine the root of the function representing the normalized curve, which root corresponds to the Ct value. The Ct value is then returned and may be displayed or otherwise used for further processing.