and now something about the cut off: 

The cout off value should be the optimal value for a differentiation between positive and negative samples. Also here only a singel dilution of the sample is required.  

You know how to determine specificity and sensitivity. Normally you can change display the change of the sensitivity or specificity in a graph (Y= Sp, Se, X = cut off value). You can see here, that the specificity will decrease when you are using a lower cut off. In contrast to this, the sensitivity is getting higher the lower the cut off value will be.

Simplified: Let‘s say the cut off is „0“, you will have only positive results, so you could oversee any real positive patient (Se = 100% or 1). But, at this point the specificity is 0% (or 0). At the end, you are searching for an optimum, where you have most of the real positives found as positive (above the cut off) and most of the real negatives as negative (below the cut off). By using your training populations, you can see what will happen, if you moving the cut off to higher or lower values.

Now Mr. Youden came and added both for the Youden index (Y = Sp + Se -1). So you get only one line in your graph (see figure 2a in the attached paper) and this line will show you an optimum = it means the best discrimination point between the real positives and the real negatives.

There is another opportunity to give this all in one graph: the ROC (figure 2b). The threat of this graph is that you didn’t see any dependency on the cut off.

By using the Youden graph, you can describe also the grey zone. There is also an opportunity to weight Sp and Se. E.g. in HIV, you would have a very high sensitivity. For checking the specificity, you can use a confirmatory assay like a western blot. In other diseases (e.g. tumor markers), you don’t like to startle your patients when they have low values. So you can modify the term:

                Y = (a*Sp + b*Se)-1 (condition: a + b = 1).

It’s a quite simple procedure. Use your training test population, move the cut off (it’s can be the OD, it’s can be also a titer, a concentration etc.) and recalculate the Sp & Se & Y. So can see directly where the best cut off could be.

How to calculate the LoD: use the ICH Q2R: http://www.ich.org/fileadmin/Public_Web_Site/ICH_Products/Guidelines/Quality/Q2_R1/Step4/Q2_R1__Guideline.pdf

It’s also quite simple: measure your zero sample 20 times. So you get an average and a standard deviation (SD) us a calibration curve as well. Now add the 3fold (2,96fold) SD to your average. Read out at the calibration curve the LoD. 

http://onlinelibrary.wiley.com/doi/10.1002/1097-0142(1950)3:13.0.CO;2-3/pdf

Pl. go through attached publication.

I would use the blank with antigen but without sera, not the other one. I would consider the titre as the last dilution giving values above the cut-off level, that could be twice the mean value of the blank wells. There are several variations about the cut-off, but if you always consider the same criteria, your analysis should be correct. 

Another way to express ELISA titers is to use the half maximal effective concentration (EC50). EC50. The EC50 refers to the concentration of a drug, antibody or toxicant which induces a response halfway between the baseline and maximum after a specified exposure time. The ELISA titer of an antibody/serum is the concentration (dilution) in which we observe half maximal effect (generally O.D.)

In general, in antibody detection assay both, the affinity and the concentrations generates the signal. Therefore, standardization is always difficult. The easy way: create your own “arbitrary units”. The best way is to compare affinities (but it is no common to do this). Since microbiologist are detecting antibody concentration, the use of dilution series is common and the dilution with the last detectable reaction was used to define the titer. This method has one major threat. For one sample you need to detect several dilutions. This will limit the throughput of your assay and will increase the costs.

Therefore methods using a single dilution only are in favor. There are several principal solution available. The easy way is to use a standard (if available). For many specific antibodies standards are available via http://www.nibsc.org/standardisation/international_standards.aspx . Other way are describe below.

The only issue which have to be solve is names above. You have to find assay conditions which fulfill the requirements of the ICH guidelines: http://www.ich.org/fileadmin/Public_Web_Site/ICH_Products/Guidelines/Quality/Q2_R1/Step4/Q2_R1__Guideline.pdf in a way that only the antibody concentration and not the affinity is reflected in the test signal. Tzhe wax to modify this is the adaption of the dilution buffer. In most cases, I was successful using PBS pH 7.2, 0.3 mol/L NaCl (the increased salt concentration will inhibit low affinity unspecific antibody bindings), 0.05 … 0.1% v/v Tween, 20, 3% hydrolyzed gelatin. BSA can replace this, but don’t use milk proteins. They are often recognized by antibodies in patients with a cow milk allergy (which his often not known even by the patient).

Now the ways for an standardization allowing you to use only a single sample dilution (which have to optimized before). By using a standard, you can apply a calibration curve:

1. you can use a defined monoclonal with a known concentration to compare your samples with.

Pro: easy to use

Con: a monoclonal has one affinity, the polyclonal has many and you will detect an “average”

2. you can purify from a polyclonal Antiserum via positive affinity chromatography the specific antibodies. They can be quantifies in µg/mL … . Those should be used as a primary standard to quantify a secondary standard (e.i. antiserum, etc.).

Pro: a lot of work

Con: you will lose the low affinity antibodies (they would not bind to the affinity column) and the high affinity as well (they could not eluted). And again, the polyclonal samples has many and you will detect an “average”

3. you can work with different species, a murine monoclonal and a human antiserum. The specific antibodies can compete for the binding. You need to have only species specific labelled antibodies which are able to differentiate between both species.

Pro: a lot of work

Con: you will lose the low affinity antibodies (they would not bind to the affinity column) and the high affinity as well (they could not eluted). And again, the polyclonal samples has many and you will detect an “average”

4. You can make your assay more “independent” from affinities. To get this, use for the sample incubation a buffer with higher salt concentrations (0,3 mol/L … 0,45 mol/L NaCl)

5. An easy estimation of the affinity is the incubation of constant dilutions with increasing salt concentrations (0.15 mol/L up to 3 mol/L NaCl, Urea up to 7 mol/L, ….) Low affinity antibodies will lose their binding to the antigen at lower concentration, high affinity antibodies much later.

Comments: The solid phase antigen is difficult to quantify. The binding is realized via hydrophobic interactions (hydrophobic amino acids à polystyrene rings) at concentrations between 1 – 10 µg/mL. The average bound is at 100 - 200 ng/cm². The antigen-antibody reaction is never 1:1. You cannot compare the antigen-antibody reaction in liquid phases (Heidelberger precipitation curve) with solid phase reactions. The antigen at the solid phase in present in Excess.

and now something about the cut off: 

The cout off value should be the optimal value for a differentiation between positive and negative samples. Also here only a singel dilution of the sample is required.  

You know how to determine specificity and sensitivity. Normally you can change display the change of the sensitivity or specificity in a graph (Y= Sp, Se, X = cut off value). You can see here, that the specificity will decrease when you are using a lower cut off. In contrast to this, the sensitivity is getting higher the lower the cut off value will be.

Simplified: Let‘s say the cut off is „0“, you will have only positive results, so you could oversee any real positive patient (Se = 100% or 1). But, at this point the specificity is 0% (or 0). At the end, you are searching for an optimum, where you have most of the real positives found as positive (above the cut off) and most of the real negatives as negative (below the cut off). By using your training populations, you can see what will happen, if you moving the cut off to higher or lower values.

Now Mr. Youden came and added both for the Youden index (Y = Sp + Se -1). So you get only one line in your graph (see figure 2a in the attached paper) and this line will show you an optimum = it means the best discrimination point between the real positives and the real negatives.

There is another opportunity to give this all in one graph: the ROC (figure 2b). The threat of this graph is that you didn’t see any dependency on the cut off.

By using the Youden graph, you can describe also the grey zone. There is also an opportunity to weight Sp and Se. E.g. in HIV, you would have a very high sensitivity. For checking the specificity, you can use a confirmatory assay like a western blot. In other diseases (e.g. tumor markers), you don’t like to startle your patients when they have low values. So you can modify the term:

                Y = (a*Sp + b*Se)-1 (condition: a + b = 1).

It’s a quite simple procedure. Use your training test population, move the cut off (it’s can be the OD, it’s can be also a titer, a concentration etc.) and recalculate the Sp & Se & Y. So can see directly where the best cut off could be.

How to calculate the LoD: use the ICH Q2R: http://www.ich.org/fileadmin/Public_Web_Site/ICH_Products/Guidelines/Quality/Q2_R1/Step4/Q2_R1__Guideline.pdf

It’s also quite simple: measure your zero sample 20 times. So you get an average and a standard deviation (SD) us a calibration curve as well. Now add the 3fold (2,96fold) SD to your average. Read out at the calibration curve the LoD. 

http://onlinelibrary.wiley.com/doi/10.1002/1097-0142(1950)3:13.0.CO;2-3/pdf

Thank you everyone.i am readaing and considering all the suggestions.

in serial dilution, ELISA titer=the last dilution with twice OD of the blank well,

Reciprocal of the last dilution that give the positive result

Hi to you all.

I do agree with all other comments and can only add two things:

1) Check other papers in the field you're doing your experimental analysis to see a peer-wise standard for you (Besides other people's comments, check a paper from Andreas Frey Article A statistically defined endpoint titer determination method ...

2) If you're not familiar with ELISA standardization, you can refer to other people at your institution (with expertise on it), other institutions nearby you or to many of the guidelines existent in the web or important books in this area.

I will list a few company guides you can read about it.

https://www.corning.com/worldwide/en/products/life-sciences/resource-library/search.html?productsSearchState=&resourcesSearchState=fq%3D%257B!tag%253Dresource_types_en_us_s%257Dresource_types_en_us_s%253A%2528%2522Application%2520Notes%2522%252BOR%252B%2522Technical%2520Papers%2522%2529%26&relatedContentSearchState=&initialResultType=resources (at this website, write ELISA and you will get nice guides on this subject).

https://www.cusabio.com/m-225.html (Standard Curve using GraphPad Prism)

https://www.rndsystems.com/resources/how-to-analyze-elisa-data (Standard Curve)

https://www.bosterbio.com/elisa-data-analysis-instructions (Standard Curve)

https://www.mybiosource.com/elisa-results (Standard Curve)

https://www.thermofisher.com/br/en/home/life-science/protein-biology/protein-biology-learning-center/protein-biology-resource-library/pierce-protein-methods/overview-elisa/elisa-data-analysis.html (Standard Curve)

http://go.myabcam.com/ELISA-guide?utm_source=Eloqua&utm_medium=Email&utm_campaign=ELISA%20conversion%7cContent%7c43132%7cKITS/QPA%7cN%2FA%7cEng%7cNewsletter&utm_content=ELISA%20guide%7c&_ga=2.140904370.1440906948.1584316581-1764917632.1584316581 (Standard Curve)

https://www.bio-rad-antibodies.com/elisa-results-quantitative-semi-qualitative.html (Standard Curve)

https://www.elisagenie.com/content/Calculating%20%26%20Analyzing%20ELISA%20Data.pdf

https://www.elisaanalysis.com/app (Online applet)

Hope it helps.