1. It is best not to assume that 5PL equations are necessarily better than 4PL equations. 5PL equations require more calibrators to generate a meaningful curve, including points describing both the top and bottom plateaus; if you have these points and the 5PL fitting is advantageous because you see a lack of symmetry when reaching the plateaus, 5PL is the way to go. However, simpler equations are generally prefered if they fit the data, so 4PL equations are still widely used.

Contradicoary note: in my experience, 5PL have also been useful in fitting curves for ECL counts where there is often no hint of a top plateau. Anchor points are however often needed.

2. Some softwares include automatic weighting and can consider many curves generated with the same assay to determine the best weighting scheme. But to keep things simple, the weighting that that has generally given me the best results for immunoassays is 1/y^2 as it normalizes the importance given to the points at the top of the curve compared to the bottom of the curve. However, if you have an assay with a very small dynamic range (ODs of 0.2 to 0.5 for example), weighting will probably not help. And remember, choosing a simpler model is always preferable when possible.

3. In conclusion, I prone testing curve fitting every time. A tool I now used to compare 4PL vs 5PL is the "F" test which balances the importance of the simpler model and minimising the sum of squares of the curve fit. There is a free tool on the web from GraphPad which can perform the F test and gives oodles of helpful information: http://www.graphpad.com/quickcalcs/aic1/. The tool is more complete if you have the software, but the free tool gives you a good idea. Choosing the best curve fit will lead to accurate back-calculations of the most data points on your curve (especially near the top and bottom plateaus), so it is not something to be taken lightly.

Cheers,

André

1. It is best not to assume that 5PL equations are necessarily better than 4PL equations. 5PL equations require more calibrators to generate a meaningful curve, including points describing both the top and bottom plateaus; if you have these points and the 5PL fitting is advantageous because you see a lack of symmetry when reaching the plateaus, 5PL is the way to go. However, simpler equations are generally prefered if they fit the data, so 4PL equations are still widely used.

Contradicoary note: in my experience, 5PL have also been useful in fitting curves for ECL counts where there is often no hint of a top plateau. Anchor points are however often needed.

2. Some softwares include automatic weighting and can consider many curves generated with the same assay to determine the best weighting scheme. But to keep things simple, the weighting that that has generally given me the best results for immunoassays is 1/y^2 as it normalizes the importance given to the points at the top of the curve compared to the bottom of the curve. However, if you have an assay with a very small dynamic range (ODs of 0.2 to 0.5 for example), weighting will probably not help. And remember, choosing a simpler model is always preferable when possible.

3. In conclusion, I prone testing curve fitting every time. A tool I now used to compare 4PL vs 5PL is the "F" test which balances the importance of the simpler model and minimising the sum of squares of the curve fit. There is a free tool on the web from GraphPad which can perform the F test and gives oodles of helpful information: http://www.graphpad.com/quickcalcs/aic1/. The tool is more complete if you have the software, but the free tool gives you a good idea. Choosing the best curve fit will lead to accurate back-calculations of the most data points on your curve (especially near the top and bottom plateaus), so it is not something to be taken lightly.

Cheers,

André

Dear sir

Now there are many software to automatic weighting

We use Dplot for fitting ELISA data. See Bioconjugate Chemistry 23:485 (2012).

Merry Sherman

Andre,

thank you very much for the answer and link to calculator which can be very useful tool...

I have two questions:

1. I’m not sure if I understand it correctly, but “Number of data points (N)” in case of curve consist of 7 duplicate standards N will be 14?

2. in this calculator I can compare 4-PL fit to 5-PL fit, but it is not possible to compare 5-PL to 5-PL with 1/Y^2, right?

And general question:

Is there an easy way to recognize which sigmoidal curve is symmetrical and which is not? or the only way is to do 4-PL and then 5-PL fitting and check which is better?

(I'm using WorkOut 2.5 software)

Hanna,

1. the number of data points to use is indeed 14 in your case

2. I don't think you can compare two weightings of the same model (same number of parameters) using these comparison tests (Akaike and F-test).

Hello Hanna,

Olivier and you are correct, the N you want to be using is 14. And Olivier is correct again is stating that the F and AIC tests can't be used to compared weighting versus no weighting...

As for recognizing a symmetrical curve versus an asymmetrical curve, you need to look at how the curve reaches the top and bottom plateaus (shape of the curve). If the shape in both cases is a mirror image, you are dealing with a symmetrical curve. But in cases where, as in the attached example, the curve leaves the bottom plateau very gradually but reaches the top plateau very abruptly, it is an asymmetrical curve. As mentioned before, this is why meaningful 5PL curve fitting often requires more points as you need to clearly define how the curve reaches both plateaus. In summary, a visual inspection of a good data set can often give you a pretty good idea if you should be using 4PL or 5PL.

Hope this helps,

André

In general, the curve fitting model should fit to the chemical background, the law of mass action. Thats necessary to exclude by statistical methods points from the calibration curve which doesn't fit. The example above is a good one. Which of the three upper points is the wrong one?

Thats why the 3 parameter Rodbard model is one of the best. The more parameter a logistic regression have, the more is the curve fitting like a prostitute. This will fit to any point cloud.

see at: Rodbard D , Frazier GR . Statistical analysis of radioligand assay data.

Methods Enzymol . 1975 ; 37 : 3 - 22 .

There are some more parameters to be taken into account. There is LAMBERT-BEERS law. The absorbance (extinction) is the reciprocal value of the transmission. Many people forget, that therefore absorbances should not be higher than 2.0. The higher the concentration of the (oxidized) chromogenic substrate gets, the lower the differences in the absorbances will be. Many instruments market the product that they are ablte to measure absorbances up to 4. That's nonsence, they forget the reciprocal relationship. Thry to keep the absorances for the negative controls below 0.1 (better 0.01) and the absorbances of the positive controls between 1 and 1.5. So you have a P/N-Ratio (at least the slope) of 15 and higher. 

The other arguments about the curve fitting are mentioned above. 

Hello, I was wondering if the dissociation constant can be calculated from the 4PL curve fitting of the ELISA? Thanks.

1. Asymmetry is a characteristic of all sigmoidal dose response curves shapes in immunoassays and bioassays. The 5PL allows the upper and lower plateaus to have separate shapes, and places the inflection point at the actual point of transition from one asymptote to the other. A 4PL shape forces each plateau to the same, less optimal shape and places the transition point at the middle instead of its actual location. An accurately weighted 5PL can extend the usable dose range of an ELISA or other immunoassay an order of magnitude over an unweighted 4PL. There is a discussion of the considerations between 5PL and 4PL curves here: https://www.brendan.com/5pl-curve-fitting/.

2. Equally important is weighting the curve with accurate estimations of each response (Y) variance. Empirical formulas like 1/Y and 1/Y^2 do not provide accurate variance estimates. The reaction kinetics and other factors of each test method result in variance profiles that vary greatly between different test methods. For 5PL and 4PL curve fitting models, the RSSE in least squares regression fitting is the sum of squared differences between the observed point and the curve divided by the estimated variance at that point. Accurate variance estimates of the responses can be obtained from a pool of historical assays to compute the weighting for each test method using the model AY^B. In more than 1000 ELISA and bioassay test methods that we have examined, the weighting variances have not approached 1Y^1 (1/Y) or 1Y^2 (1/Y^2). The nature and importance of weighing can be found here: https://www.brendan.com/curve-weighting/.

3. An effective 5PL curve fitting model with accurate weighting will provide a better fit for most ELISA or bioassay data. As long as the weighting is computed for each test method to accurately model the actual variances the method's pooled responses, then a 5PL equation with accurate weighting can be specified as a "universal" protocol. Accurately weighted RSSEs that are used in the 5PL and 4PL fitting models are chi-square distributed, with N-P (number of points – number of parameters) degrees of freedom. This makes a chi-square probability of the RSSE an ideal measure for the goodness of fit of the regression curve, since it is a familiar scale that is independent of the curve model or number of data points. This means that if the fit of a 4PL is very close to that of a 5PL, the 4PL can have a higher chi-square probability due to its larger degrees of freedom.

The chi-square property of the RSSE also means that the suitability of a test method's variance profile for weighting can be easily checked. The average RSSE from a pool of dose response curves should equal the degrees of freedom N-P if the curves are accurately weighted.

Dear John R Dunn ,

what you describe is exactly what we found in our research at the European Union Reference Lab for Dioxins and PCBs in Feed and Food, aiming at optimizing bioassays for detection and "quantification" of dioxins and dioxin-like PCBs especially in low concentration ranges which we especially focussed on given that the EU has set comparatively low maximum and action levels for those contaminants resulting in assay concentrations located way down in the lower parts of concentration-response curves.

For a number of cell lines utilized, we observed more or less asymmetric curve shapes. Based on a high level of calibrator precision the 5PL function allowed us an improved curve fit and to assess assay and eventually sample concentrations more accurately in the low concentration range. This has profound meaning for compliance assessment: exceedance of a maximum level may be of considerable consequences both for consumer health protection and economically as well.

Best regards and thanks for your comments,

Johannes