Hello,
I am trying to analyze some pilot data with the following setup: I basically have three different types of drugs which were administered to my cells at 3 different doses (9 conditions, if you will). I repeated this experiment 4 times (biological replicates) and each experiment contained duplicate wells for each condition (technical replicates - so basically I'm getting 18 data points each experiment - not counting controls). I am trying to assess viability of the cells 24 hours after treatment. I expect the three different drugs to differ in terms of cell viability after 24 hours of exposure (the question I'm really interested in). I would technically expect the dose of drug to also affect viability, but I am less concerned with this variable (but fine with including it in the statistical analyses).
My question has to do with the "weight" or importance of each data point and how this factors into the statistical analysis. Is it fair to say that I basically have 8 total data points for each condition across all experiments (and treat them the same when doing statistics), or do I have to consider the duplicates in one experiment to be different from the duplicates in another experiment for one condition, i.e. biological and technical replicates must be factored in differently in statistical analysis. I am not sure what I am supposed to do.
Also, I suppose the best analysis would just be to do two-way ANOVA with post-hoc tests. But I'm not sure if I should consider it all one single analysis, or maybe do separate ANOVAs comparing the drugs WITHIN the different doses. I have read that sometimes it is not always best to do a lot of multiple comparisons because it can weaken the power of the test overall. Please advise.
I hope I explained that okay. Thank you very much for your help!
Have you heard about linear mixed effect (LME) model? The n-way ANOVA is considered outdated technique, and scientists tend to shift from using ANOVA to LME. After the LME model, you can use estimated marginal means with post-hoc comparisons (I recommend you to use Bejamini-Hochberg). Using LME, you can compare within-, between-group differences. Here's an easy-to-read article that I recommend to my students: Article Categorical Data Analysis: Away from ANOVAs (transformation ...
LME can be easily applied in any statistical packages, but I use R's 'nlme' and 'emmeans' packages.
As for the replication issues, that's the decision that the researcher must make. The best way would be that your decision is based on the published article from similar studies. There are different scenarios I can think of; however, whatever decision I make, I should make sure that I am not making a strong (implausible) assumption, and if possible, find a reference to support my decision. Good luck.
LMEs will be applicable in your case, but they may not be required. They are particularily useful if you have missing data, or if you used different doses for the different drug types, and if you are interested in the contribution of each level of replication to the total variance. I think neither is the case in your experiment, so using LMEs may be "over the top".
I your case it will be sufficient to average the data from the duplicate wells and include a fixed intercept for the plate.
And don't forget to log-transform your raw data (e.g. the fluorescence reading) before analysis.
I am not sure if a two-way ANOVA is the best approach. You would do this if you were interestedin the drug x dose interactions. Are you?
In an experimantally controlled context as yours, I think you can run an ANOVA with a 3 Between (Drugs) x 3 Within (Doses) subjects design, with 8 replicated. If this design is correct, you would have 24 'subjects' or replicates (3 x 8 data points). If this is correct, you can run a repeated measures ANOVA with post hoc comparisons (e.g., indeed with Benjamin-Hogberg corrections). Be sure to check the distributions and equality of variances with histograms, Shapiro and Levene tests. If the distributions are clearly 'not normal' try a rank transformed test such as the ARTool or one of the nparLD tests.
ARTool: http://depts.washington.edu/acelab/proj/art/index.html
nparLD: file:///C:/Users/josfe/AppData/Local/Temp/v50i12.pdf
If you only have 8 replicates (datapoints), you probably have a 3 (Drugs) Within x 3 (Doses) Within subjects design. A nonparametric equivalent for such a repeated measures ANOVA would then be the 'ld.f2' test from the nparLD R package. In attachment an R script for such a design.
Hello Cinnamon L. Hardee ,
I will be the one that gives the answer that will be disappointing for this project, but hopefully improve the next one.
As D. Eastern Kang Sim mentioned, this design fits nicely the modern linear mixed effects models (or Generalized Mixed Effects Model with a binomial distribution, since the response is survival). The issue however, is that there are only 4 biological replicates (groups). The random effect in mixed effects models assumes differences among groups are random differences drawn from a normal distribution, and the model tries to estimate its variance. Estimating the mean of anything with 4 measurements is challenging, estimating its variance is even harder...
See "Should I treat factor xxx as fixed or random?" on GLMM FAQ and references therein (http://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#should-i-treat-factor-xxx-as-fixed-or-random).
* For future projects, having 10 or more biological replicates (very minimum 6) will avoid this issue.
Thanks a lot, everyone, for all of your thoughtful answers. I will have to think about them quite a bit more since they are rather over my head in terms of my statistical knowledge. I am rather surprised, though, that 4 experiments (or up to 8 data points per condition) is not enough to draw at least some sort of conclusion, though. I certainly would have no problem with adding more replicates/experiments, but the funding does not always permit. I see many experiments repeated far fewer than 6 times (let alone 10) pretty often. Of course, perhaps it's a widespread mistake!
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