How to calculate EC50 (Half maximum growth)

[ram320]

Dear community,

I am a PhD student. I am doing some experiment of chemical sensitivity on fungi and I have some data I require to have some help from the community. 

I have 6 concentration with 1 control for each isolate of fungi and the concentration is {0.000(is control), 0.001, 0.01, 0.10, 1, 10}

kindly find attached data below.

Thank you

Warm regards

Ram Kumar

[ballardw]

For those of us that are not PHD's or candidates in your field, what is the process for calculating EC50?

From the values you show I suspect we would use some form of regression involving logs to get parameters for a general equation and the plug the result into the formula plus some algebra (maybe). But that is a guess purely because you show "concentration" values that are exponents of 10.

[ed_sas_member]

Hi @ram320 

Maybe you could check this paper: http://onbiostatistics.blogspot.com/2015/12/dose-response-modeling-calculating-ec50.html

Best,

[StatDave]

The EC50 statistic (also known as the ED50 or LD50) is typically applied to assay data in which the response is binary (such as died or survived). This statistic is an estimate of the predictor (typically, dose of a drug or chemical) that causes the event (such as death) 50% of the time. In this context, the EC50 can be estimated by fitting a model in PROC PROBIT using the INVERSECL option as shown in the list of Frequently Asked-for Statistics which can be accessed from the Important Links on this Communities front page. In this case, you could consider using the maximum growth as the denominator (number of trials) variable and the observed growth as the numerator variable, then fit the model to the proportion thus defined. However, I would be skeptical of any tests or confidence intervals from such an analysis since your growth values are not actually counts and the standard errors from the analysis could be made arbitrarily small by multiplying the values by any constant.

[ram320]

Hello,
I am a beginner for SAS programing.
Can please provide some example for my data which I have mentioned in the question.
I will help me a lot to get EC50 value from the rest of the data.
I will really appreciate your help.
Thank you in advance.
Warm regards
Ram

[StatDave]

See the example titled "Dosage Levels" in the Examples section of the PROC PROBIT documentation. 

[SteveDenham]

If that does not suffice, search the internet for "four parameter logistic growth model."  This is "logistic" only in the sense that the response is S shaped when plotted in the original units.  There are several papers that used PROC NLIN to fit these data, and from the fit calculate ED/LD/EC/IC50 values. Here are some papers:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2586183/ 

http://webpages.math.luc.edu/~tobrien/courses/old_ab/E-Spring-2006/hwk05.html  (follow the link in example 3)

https://www.researchgate.net/publication/21215173_Use_of_a_Four-Parameter_Logistic_Equation_to_Evalu...  (I happened to have some input on this one - it's down there in the Acknowledgements)

SteveDenham

[StatDave]

Steve's post reminded me of this note which shows how to fit the fractional logit and 4- or 5-parameter logit models for modeling continuous response data. It discusses and illustrated the estimation of the ED50 using these models.

[PGStats]

Your data shows the following feature:

Isolate 	Min / Control Growth
280 	0.441905
281 	0.731581
284 	0.652847

i.e. the half growth is barely or not at all present in the tested range. From experience, I wouldn't expect reliable EC50 estimates from such data. Moreover EC50 estimates would be very sensitive to the choice of the growth curve function, and any estimate would be disproportionnately influenced by the growth measured at the highest concentration.

If you have other data exibiting lower Min/Max ratios, use them as test cases to develop your estimation method. Because with the data above, you are going to run into all kinds of problems.