Bioanalytical Community

Four parameter logistic (4PL) curve is a regression model often used to analyze bioassays such as ELISA. They follow a sigmoidal, or "S", shaped curve. We've seen 4PL being modelled on Y~log(X) and log(Y) ~log(X). Most time the curve only shows "S" shape when the data is plotted on a certain scale, the decision on which scale to model is based on the plot showing the curve reaches the plateau on both ends. I recently noticed a set of data shows "S" shape on log-log scale and half "S" shape on linear-log scale. Naturally I modeled 4PL on log-log scale. One of my colleagues pointed out that 4PL is symmetric. The model will converge even if the data only reach one plateau. And he is right, the model did converge. With the models converge for both log-log and linear-log, what scale would you choose to model? In my example, we examined assay accuracy and it was very similar for both models. I'd love to hear your experiences on how to select which scale to model for your 4PL. 

Four parameter logistic (4PL) curve is a regression model often used to analyze bioassays such as ELISA. They follow a sigmoidal, or "S", shaped curve. We've seen 4PL being modelled on Y~log(X) and log(Y) ~log(X). Most time the curve only shows "S" shape when the data is plotted on a certain scale, the decision on which scale to model is based on the plot showing the curve reaches the plateau on both ends. I recently noticed a set of data shows "S" shape on log-log scale and half "S" shape on linear-log scale. Naturally I modeled 4PL on log-log scale. One of my colleagues pointed out that 4PL is symmetric. The model will converge even if the data only reach one plateau. And he is right, the model did converge. With the models converge for both log-log and linear-log, what scale would you choose to model? In my example, we examined assay accuracy and it was very similar for both models. I'd love to hear your experiences on how to select which scale to model for your 4PL. 

Hi Jianfang,

have you tried 5-PL instead since this one is not symetrical?

Kind regards,

Jean-Michel.

Four parameter logistic (4PL) curve is a regression model often used to analyze bioassays such as ELISA. They follow a sigmoidal, or "S", shaped curve. We've seen 4PL being modelled on Y~log(X) and log(Y) ~log(X). Most time the curve only shows "S" shape when the data is plotted on a certain scale, the decision on which scale to model is based on the plot showing the curve reaches the plateau on both ends. I recently noticed a set of data shows "S" shape on log-log scale and half "S" shape on linear-log scale. Naturally I modeled 4PL on log-log scale. One of my colleagues pointed out that 4PL is symmetric. The model will converge even if the data only reach one plateau. And he is right, the model did converge. With the models converge for both log-log and linear-log, what scale would you choose to model? In my example, we examined assay accuracy and it was very similar for both models. I'd love to hear your experiences on how to select which scale to model for your 4PL. 

Jianfang,

You may want to take a look at this white paper from Brendan Bioanalytics (STAT-LIA).

Gottschalk, P.G.; Dunn, J.R. The Five Parameter Logistic: A Characterization And Comparison With The Four Parameter Logistic.  Analytical Biochemistry 2005, 343, 54 – 65.

Bill

Hi Jianfang,

have you tried 5-PL instead since this one is not symetrical?

Kind regards,

Jean-Michel.

Four parameter logistic (4PL) curve is a regression model often used to analyze bioassays such as ELISA. They follow a sigmoidal, or "S", shaped curve. We've seen 4PL being modelled on Y~log(X) and log(Y) ~log(X). Most time the curve only shows "S" shape when the data is plotted on a certain scale, the decision on which scale to model is based on the plot showing the curve reaches the plateau on both ends. I recently noticed a set of data shows "S" shape on log-log scale and half "S" shape on linear-log scale. Naturally I modeled 4PL on log-log scale. One of my colleagues pointed out that 4PL is symmetric. The model will converge even if the data only reach one plateau. And he is right, the model did converge. With the models converge for both log-log and linear-log, what scale would you choose to model? In my example, we examined assay accuracy and it was very similar for both models. I'd love to hear your experiences on how to select which scale to model for your 4PL. 

Hi Jianfang,

have you tried 5-PL instead since this one is not symetrical?

Kind regards,

Jean-Michel.

Four parameter logistic (4PL) curve is a regression model often used to analyze bioassays such as ELISA. They follow a sigmoidal, or "S", shaped curve. We've seen 4PL being modelled on Y~log(X) and log(Y) ~log(X). Most time the curve only shows "S" shape when the data is plotted on a certain scale, the decision on which scale to model is based on the plot showing the curve reaches the plateau on both ends. I recently noticed a set of data shows "S" shape on log-log scale and half "S" shape on linear-log scale. Naturally I modeled 4PL on log-log scale. One of my colleagues pointed out that 4PL is symmetric. The model will converge even if the data only reach one plateau. And he is right, the model did converge. With the models converge for both log-log and linear-log, what scale would you choose to model? In my example, we examined assay accuracy and it was very similar for both models. I'd love to hear your experiences on how to select which scale to model for your 4PL. 

Four parameter logistic (4PL) curve is a regression model often used to analyze bioassays such as ELISA. They follow a sigmoidal, or "S", shaped curve. We've seen 4PL being modelled on Y~log(X) and log(Y) ~log(X). Most time the curve only shows "S" shape when the data is plotted on a certain scale, the decision on which scale to model is based on the plot showing the curve reaches the plateau on both ends. I recently noticed a set of data shows "S" shape on log-log scale and half "S" shape on linear-log scale. Naturally I modeled 4PL on log-log scale. One of my colleagues pointed out that 4PL is symmetric. The model will converge even if the data only reach one plateau. And he is right, the model did converge. With the models converge for both log-log and linear-log, what scale would you choose to model? In my example, we examined assay accuracy and it was very similar for both models. I'd love to hear your experiences on how to select which scale to model for your 4PL. 

Jianfang ,

Should try the  five parameter logistic (5PL) function  and compare for both  parameter logistic (4PL)  and  (5pl) , see the best fit 

Thanks-Divya

Four parameter logistic (4PL) curve is a regression model often used to analyze bioassays such as ELISA. They follow a sigmoidal, or "S", shaped curve. We've seen 4PL being modelled on Y~log(X) and log(Y) ~log(X). Most time the curve only shows "S" shape when the data is plotted on a certain scale, the decision on which scale to model is based on the plot showing the curve reaches the plateau on both ends. I recently noticed a set of data shows "S" shape on log-log scale and half "S" shape on linear-log scale. Naturally I modeled 4PL on log-log scale. One of my colleagues pointed out that 4PL is symmetric. The model will converge even if the data only reach one plateau. And he is right, the model did converge. With the models converge for both log-log and linear-log, what scale would you choose to model? In my example, we examined assay accuracy and it was very similar for both models. I'd love to hear your experiences on how to select which scale to model for your 4PL. 

Four parameter logistic (4PL) curve is a regression model often used to analyze bioassays such as ELISA. They follow a sigmoidal, or "S", shaped curve. We've seen 4PL being modelled on Y~log(X) and log(Y) ~log(X). Most time the curve only shows "S" shape when the data is plotted on a certain scale, the decision on which scale to model is based on the plot showing the curve reaches the plateau on both ends. I recently noticed a set of data shows "S" shape on log-log scale and half "S" shape on linear-log scale. Naturally I modeled 4PL on log-log scale. One of my colleagues pointed out that 4PL is symmetric. The model will converge even if the data only reach one plateau. And he is right, the model did converge. With the models converge for both log-log and linear-log, what scale would you choose to model? In my example, we examined assay accuracy and it was very similar for both models. I'd love to hear your experiences on how to select which scale to model for your 4PL. 

@Jianfang Hu , APologies if I am late to the harbor and the ship has already sailed.

I would have thought the choice of a fitting model is dependent on the fact that the standard deviation should be the same at all sample concentrations (homoscedastic data); for heteroscedastic data), the data can be normalized using a Sum of Square Errors (SSE) using the F statistic and the Akaike's Information Criterion (AIC) methods.

My opinion would be that the choice of a log-log, semi-log, 4 or 5-PL should be statistically determined rather than empirically.

Four parameter logistic (4PL) curve is a regression model often used to analyze bioassays such as ELISA. They follow a sigmoidal, or "S", shaped curve. We've seen 4PL being modelled on Y~log(X) and log(Y) ~log(X). Most time the curve only shows "S" shape when the data is plotted on a certain scale, the decision on which scale to model is based on the plot showing the curve reaches the plateau on both ends. I recently noticed a set of data shows "S" shape on log-log scale and half "S" shape on linear-log scale. Naturally I modeled 4PL on log-log scale. One of my colleagues pointed out that 4PL is symmetric. The model will converge even if the data only reach one plateau. And he is right, the model did converge. With the models converge for both log-log and linear-log, what scale would you choose to model? In my example, we examined assay accuracy and it was very similar for both models. I'd love to hear your experiences on how to select which scale to model for your 4PL. 

@Jianfang Hu , APologies if I am late to the harbor and the ship has already sailed.

I would have thought the choice of a fitting model is dependent on the fact that the standard deviation should be the same at all sample concentrations (homoscedastic data); for heteroscedastic data), the data can be normalized using a Sum of Square Errors (SSE) using the F statistic and the Akaike's Information Criterion (AIC) methods.

My opinion would be that the choice of a log-log, semi-log, 4 or 5-PL should be statistically determined rather than empirically.

Four parameter logistic (4PL) curve is a regression model often used to analyze bioassays such as ELISA. They follow a sigmoidal, or "S", shaped curve. We've seen 4PL being modelled on Y~log(X) and log(Y) ~log(X). Most time the curve only shows "S" shape when the data is plotted on a certain scale, the decision on which scale to model is based on the plot showing the curve reaches the plateau on both ends. I recently noticed a set of data shows "S" shape on log-log scale and half "S" shape on linear-log scale. Naturally I modeled 4PL on log-log scale. One of my colleagues pointed out that 4PL is symmetric. The model will converge even if the data only reach one plateau. And he is right, the model did converge. With the models converge for both log-log and linear-log, what scale would you choose to model? In my example, we examined assay accuracy and it was very similar for both models. I'd love to hear your experiences on how to select which scale to model for your 4PL. 

Ritankar 

Can you povide some additional details or references on your suggestion "... the data can be normalized using a Sum of Square Errors (SSE) using the F statistic and the Akaike's Information Criterion (AIC) methods". I don't see how this works so would appreciate any additional information. 

Stan Altan

@Jianfang Hu , APologies if I am late to the harbor and the ship has already sailed.

I would have thought the choice of a fitting model is dependent on the fact that the standard deviation should be the same at all sample concentrations (homoscedastic data); for heteroscedastic data), the data can be normalized using a Sum of Square Errors (SSE) using the F statistic and the Akaike's Information Criterion (AIC) methods.

My opinion would be that the choice of a log-log, semi-log, 4 or 5-PL should be statistically determined rather than empirically.

Four parameter logistic (4PL) curve is a regression model often used to analyze bioassays such as ELISA. They follow a sigmoidal, or "S", shaped curve. We've seen 4PL being modelled on Y~log(X) and log(Y) ~log(X). Most time the curve only shows "S" shape when the data is plotted on a certain scale, the decision on which scale to model is based on the plot showing the curve reaches the plateau on both ends. I recently noticed a set of data shows "S" shape on log-log scale and half "S" shape on linear-log scale. Naturally I modeled 4PL on log-log scale. One of my colleagues pointed out that 4PL is symmetric. The model will converge even if the data only reach one plateau. And he is right, the model did converge. With the models converge for both log-log and linear-log, what scale would you choose to model? In my example, we examined assay accuracy and it was very similar for both models. I'd love to hear your experiences on how to select which scale to model for your 4PL. 

Hi Stan,

I have emailed you the application notes for statistical measures for curve fitting at your email ID.

I could not directly upload it here, but if you find the notes worthwhile and beneficial to the community, please feel free to distribute them.

Ritankar 

Can you povide some additional details or references on your suggestion "... the data can be normalized using a Sum of Square Errors (SSE) using the F statistic and the Akaike's Information Criterion (AIC) methods". I don't see how this works so would appreciate any additional information. 

Stan Altan

@Jianfang Hu , APologies if I am late to the harbor and the ship has already sailed.

I would have thought the choice of a fitting model is dependent on the fact that the standard deviation should be the same at all sample concentrations (homoscedastic data); for heteroscedastic data), the data can be normalized using a Sum of Square Errors (SSE) using the F statistic and the Akaike's Information Criterion (AIC) methods.

My opinion would be that the choice of a log-log, semi-log, 4 or 5-PL should be statistically determined rather than empirically.

Four parameter logistic (4PL) curve is a regression model often used to analyze bioassays such as ELISA. They follow a sigmoidal, or "S", shaped curve. We've seen 4PL being modelled on Y~log(X) and log(Y) ~log(X). Most time the curve only shows "S" shape when the data is plotted on a certain scale, the decision on which scale to model is based on the plot showing the curve reaches the plateau on both ends. I recently noticed a set of data shows "S" shape on log-log scale and half "S" shape on linear-log scale. Naturally I modeled 4PL on log-log scale. One of my colleagues pointed out that 4PL is symmetric. The model will converge even if the data only reach one plateau. And he is right, the model did converge. With the models converge for both log-log and linear-log, what scale would you choose to model? In my example, we examined assay accuracy and it was very similar for both models. I'd love to hear your experiences on how to select which scale to model for your 4PL.