Normalizing Plate-to-Plate Measurements Using Bracketed Positive and Negative ControlsI'm stumped on how to best analyze a common experimental design for microtiter plate laboratory workflows for our users.
A common need is to run experimental measurements across a large number of treatments (bacterial strains, for instance), with more treatments in the analysis than will fit on a 96-well microtiter plate. My general approach to this is to use the Custom Design platform to use a blocking factor with 96 runs per block and randomize across all of the necessary plates to fit everything and use a REML model to compare across plates. However, many of the scientists I support use what seems like an intuitive approach to handling the potential plate-to-plate differences, and I can't find a method to analyze this approach.
The intuitive approach to this design is to include a "positive" and "negative" control on each plate, so that, say, a bacterial strain that is known to perform well and a bacterial strain that is known to perform poorly is included on every plate (usually in triplicate, as are all the other treatments on the plate. Biologists love triplicates).
^ Like that. All the blues are experimental treatments in triplicate, with the plate location of individual samples randomized in subsequent plates.
The idea is that we should be able to use these controls to "bracket" the performance of the experimental treatments and understand where they fall between the + and - on their respective plates. Intuitively, the +/- bracket forms a sliding "window" of normalization across plates, representing the plate-to-plate variation not just in overall mean but the effect of good strain performance.
When it comes to analysis, though, I can't think of or find a method that uses this bracketing approach without losing the available information about the controls. Typically, the scientist will take the negative-control mean, the positive-control mean, and the range between them and use that information to calculate a value per non-control well representing the well's position along that range (between 0 and 1 if between the two, >1 if outperforming the positive control, <0 if underperforming the negative control). The controls are then excluded from further analyses. This "works" in the sense that we can run a regression model or means comparison that doesn't include "plate" as a factor and get a comparison of all bacterial strains across all plates, but it feels like cheating to me.
Is this the best way to handle this kind of design? Is there any literature/JMP methodologies that are more valid for this analysis?
Thanks in advance for any expertise from the community!
AnalyticsDOERe: Normalizing Plate-to-Plate Measurements Using Bracketed Positive and Negative ControlsI think this question can be divided into two parts.
1. Normalizing samples to a control
2. Experimental designs for microtiter plates
Taking a stab at the intuitive normalizing to a bracket based on 3 replicates.
I'm a molecular biologist, so I kind of get the historical desire for n=3 to be the right number. I'm also an applied statistician, and I laugh while gesturing rudely at n=3. Depending on the variation in the control measurement, n=3 provides a poor estimate of the mean. This is biological in nature so a CV of 10% might be pretty good, but it's likely higher. I also spent some time in cGMP world, so setting acceptance criteria for the controls is probably pretty important too. e.g. if the CV for a control is higher than n%, throw out the plate and try again. Note I didn't say how hight the control n should be. That's up to you, but DOE>Design Diagnostics>Sample Size is a good place to start. And you probably already get this, but communicating it to those dense biologists is going to have to include pictures.
As an example imagine you were measuring something that has a mean of about 100 and a standard deviation of about 10. With n=3 the difference you can detect is about 189, but with n=25 we can detect a difference just under 12.
In the microtiter experiment case. If I want to say my sample strain is higher or lower than a positive or negative control, either the precision of the replicates needs to be phenomenal or the sample size needs to be bigger, because in reality, unless the differences are on a log scale they aren't actually capable of detecting a nearly 2 fold change, if it actually exists.
I can imagine they might take the mean of the positive and the mean of the negative control and scale all the rest of the measurement to a 0 to 1 range to compare plates. The zinger with n=3 is that now we have just compounded the control measurement twice and added that to the test article measurement. Variance components add, right, so now the error on the estimate of the strain effect is likely 3 times higher. Reporting percent of negative and percent of positive separately, helps a little.
I'll come back later and talk about design and analysis.
