I hope for you that Jochen Wilhelm will pick up your question.

He is the most active biostatiscian in the RG community.

I strongly advice you to contact directly Jochen.

Best regards

Robert

Thank you very much Robert,

best Luci

Hi,

I did not well understand the design of the experiment yet: 6 different donors, each one was treated with all the substances? Each treatment per donor was replicated in 6 wells?

6 donors x 6 wells = 36 wells (per substand/treatment). Just to confirm: 96 is not a multiple of 36. With 8 substances you would get an experiment that would fill 3 96-well plates... so how were donors and treatments distributed over the plates and how many different treatments were applied? The background of this question is to find out if donor or treatment could be confounded with a plate. And if so: do you have some control, experience or good arguments that there are no relevant differences between plates?

Given there is no problem with confounding, you have several hierarchic and crossed levels of replication:

- treatment within donor (if each donor recieved each teatment)

- well within treatment:donor (6)

- well:treatment:donor within experiment (3)

From an academic analysis-perspective this would indicate a hierarchical (multilevel) model to account for the different correlations withing the replication levels. Such an analysis would be helpful to see how much the replication levels contribute to the overall variance of the data. This would be good to know if further experiments are to be planned, so that the replications can be concentrated at the level introducing the larges variance.

But I think this is not your problem here. So you may favour a more pragmatic solution. What you likely want to know is what one can expect (=estimates of the treatment effects) when this study would be replicated with different donors. This can be achieved by reducing the measurements to a single value per donor (and treatment). This is done in fact by averaging. To get the stats work properly, the values that are averaged should scatter (more or less) symmetrically around a center value. This is likely not the case for fold-changes, but for log fold-changes.

The simplest way to do all the calculations is by using the logarithms of your response (cell density; If the measurement itself gives you a read-out that is already proportional to the logarithm of the cell-density, no further transformation is required!). You can then proceed using only plain differences and averages. A difference would have the meaning of a log ratio, and averages are the logarithms of the geometric means.

To prepare the final data for the analysis of the treatment effects simply average the (log values of the) replicate wells per donor and treatment. You can include all plates and all experiments. Given you have k treatments (like controls, substance A, substance B,...) you will now have 6*k values (k values for each of your 6 donors).

Now (if I got your design correctly) the treatment is replicated within donor ("paired data", so to say). To account for this you should best use an appropriate model. You can use a mixed model with "donor" as random factor (1) or a two-factorial model with "donor" as fixed factor. (2)

It does not matter much (because you have a balanced design and no missing values). From an academic point-of-view, the mixed model is a bit more appropriate. The models can be standard models (general linear models) with Gaussian errors. They will give you the estimates for the treatment effects. Any statistical software should be able to do this (it it a quite standard analysis).

If you use a treatment-coding with "control" as the reference, the coefficients ("betas") of the model estimate the treatment effects. These estimates are log-ratios. You will get these estimates, their standard errors, confidence intervals, and p-values.

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symbolic model representations:

(1) log(RESPONSE) ~ TREATMENT + (1|DONOR)

(2) log(RESPONSE) ~ TREATMENT + DONOR

log(RESPONSE) is distributed as N( µ(predictors), s²),

TREATMENT is a factor (categorical variable) coding the k different treatments,

DONOR is a factor (categorical variable) coding the donor ID.

Hi Jochen,

Thank you so much for you fast and long reply.

First the experimental Setup in details. See attached

In this outlined experiment (one day ) 3 donors (littermate controls), each +/+ and -/-

1x 96 well plate for nontreated

1x 96 well plate for each treatments (6 different treatments)

And you are right, there could also be differences between plates!!!!

I've just calculated the log values and will go through the analysis.

I think we will discuss tomorrow how we are dealing with normalization and statistics. But I assume we will stick on the mixed model.

Thank you very much.

Best Luci

You see Luci: I was right!!

Robert