We know that LD50 is the dose of a chemical able to kill 50% population of an organism. I wonder if the same concept may be used for a growth speed. In particular, I would like to know if a LD50 can be defined as the dose of a chemical able to slow down by 50% the growth of a fungus in vitro.
This question implies also a statistical aspect: LD50 is calculated with a logistic regression, which uses counts as a response variable; could logistic regression be forced to calculate LD50 for a growth speed variable?
I think in this case, you should try to find a LT50, which is a time where 50 % of a population is killed. Trough proc NLIN of SAS you can obtain this results or you may consider to work with Survival analysis, using Kapplan-Meyer, but for growth inhibition, when usually we measure weight as an explanatory variable, PROC NLIN, may works better. I particularly work with insects, so I don't know which factor or parameter you relate with fungus growth inhibition. Hope it helped a little.
Thanks Matheus. The parameter that I measure is the diameter of fungal colony in a agar-plate. At present I don't know if growth speed is linear or non-linear (I mean relation between growth and time). Actually I think that in SAS I could use the best-fitting model and 'estimate' the 50% speed reduction (LD50) with the ESTIMATE statement. However, every suggestions are welcome from you.
It is not necessary to assume any kind of functional form for the sigmoid you are trying to investigate.
The only thing you have to do is to find the inflection point of the curve. This point is the desired 50% point.
Two methods for identifying the inflection point of any sigmoid curve can be found in the link posted at this answer.
If you are not familiar with mathematical analysis, you can send me the (xi,yi) data to examine it with those methods.
http://arxiv.org/abs/1206.5478
Hi Giovanni,
The question you ask has a two-part answer. You are interested in finding the concentration of a substance that slows fungal colony growth rate by 50%. To get at that quantity you need to know the response function of the Rate to concentration. In other words you need to know how the rate changes in response to changing concentration. To find that out you first need to estimate the rate of growth at different concentrations, which is, as you know, found by looking at the change in colony diameter with time. Change in colony diameter with time might take on any one of a number of forms: linear, exponential, sigmoidal etc., depending on (among other things); the relative size of the inoculum used to initiate your colonies and the plates, the availability of nutrients, the effect of the compound and the timescale over which you make observations. Whatever the details you need to extract from the data for colony growth over time a rate parameter which has the same functional form at all concentrations. Then you need to estimate the response relationship between the rate parameter and concentration (again this may be any one of a range of forms, but the most likely are (linear, exponential or sigmoidal). Once you have estimated the statistical relationship (response function) you'll be able to calculate the concentration at which 50% inhibition occurs quite readily.
I agree with Neil, but you can also work with proportion in fungal growth reduction relative to control treatment and use this values as raw data to compare your treatments. All in all, assuming that the mutation rates among microorganisms is high, I strongly believe that population (fungi) will respond non-linearly to your treatments, but it is just my guess.
Hi Giovanni, I realized I didn't say anything about the second part of your question. In general, the answer would be no. It could be done, but the response and explanatory variables in your experiment are not really of the appropriate form for logistic regression. Matheus Ribeiro suggested a simple approach that would probably be more appropriate. What you're really trying to examine is the response surface of fungal growth to time and inhibitor concentration.
LD50 is the dose that kill 50% of the test organism. the dose that slows down the growth is inhibition. So the concentration of the chemical that can slow down the growth of your test organisms is the 50%inhibition concentration.
Aminu, I'm not sure that you are right. Perhaps, you would be right in case of a linear relationship.
I think that you can proceed as follows.
1. Fit a suitable functional relationship between growth rate Y as a function of dose X.
2. Invert the fitted relationship for a predicted value of Y (say Y50) at which the growth rate is 50% of usual.
This general approach would work for a wide variety of problems. See attached example. Most of this (the middle) has to do with illustrating statistical ideas of fitting (maximum likelihood and so forth) and is irrelevant. It is the start and the end that are important.
Your data is simply concave, so the methods proposed by me are not applicable, since there is not an inflection point to be computed, for your specific data.
Only if you had a sigmoid shape data, you could solve the problem with those methods.
If your data was first concave, then convex and your LD50 was the inflection point, then my analysis could be applicable.
Of course you should perform them separately for every (xi,yi) set and compute an inflection point every time, thus you could find 3 such points, if your specific uploaded data was concave/convex.
In radiation biology and toxicology more broadly, LD50s are calculated all the time. Often these calculations involve dose-response models. The key is whether the dose (growth rate of fungus) is continuous and you can quantify when 10%, 20% etc. of the growth is achieved. With radiation, you know the dose. With chemicals, you know the concentration. So, with growth you must know the rate. In principal, it seems like an LD50 approach could be implemented.
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