Hi all
I am having some troubles with the statistics in comparing dose-response curves. Hope you can help me out, for I am quite the statistics-noob.
I have plotted the toxicity of a drug on a cell line against a range of 6 ascending concentrations and fitted the curve using five parameter non-linear regression (Graphpad) (n=4 per concentration). I have done this for different cell-lines and different formulations of the drug
I would like to compare for all of them whether the curves are significantly different and preferably whether the LD50 values are significantly different.
To specify my question:
1. How can you compare the complete curves (two-way ANOVA is often suggested, but my independent variable is not categorical (concentration).
2. How can you compare values derived from a fit?
For one is never quite sure how well your model fits your data, and the fit already has its own 95% confidence interval for each point. If one then performs an independent t-test on the LD50 value of e.g. 2 different cell-lines, wouldn't that be multiple testing with an increased type 1 error?
3. Am I even allowed to use a t-test with a sample-size this small? Or should I go for the Mann Whitney U test?
4. How many degrees of freedom should I use for these tests?
(n=4 for each concentration. 6 concentrations were used to make the curves.) For the LD50 is derived from the curve, I gather the df is computed differently?
Thanks in advance!
Els
Every statistic has error. It can be difficult to measure this error. Here are two options:
1) Perform a stratified randomization test. Take your data and randomize all values within a dose. Reanalyze the data, save the regression coefficients (or fit statistics, or whatever you want), and calculate the difference between treatment A and treatment B. Then re-randomize the data. Do this 20,000 to 100,000 times, saving the result. you can now generate a distribution of typical values and see how unusual your observed value is relative to the random values.
2) Take the means and standard errors for the regression coefficients. Put these into a random number generator and then generate a data that can then be analyzed. Do this 20,000 to 100,000 times and estimate the probabilities.
How easy these solutions are for you to use will depend on what program you use to run statistics. They will be easiest in R, if you already know R.
Formulate the model so that it fits curves for several groups using a coefficient representing the difference in LD50 between groups. Not sure if or how this is possible in Prism, but one can do this in R.
http://www.hiercourse.com/docs/Rnotes_nonlinear.pdf
You can use the ANOVA as a method of comparing the results to the different concentrations, since the basic idea of ANOVA is to compare the means of 3 or more populations, the fact that the concentration is a continuous quantitative variable and not categorical does not preclude the Application of the statistical tool, it is undoubtedly the most appropriate tool, but first we have to prove the ANOVA assumptions (data normality, homoscedasticity of variances and independence of samples), if these are not met, a test of Comparison of medians (for example Kruskal - Wallis).
- Badges
- Science topic
- Similar topics
- Mathematics
- Statistics