It seems like such a simple question. If you stimulate with two drugs at once, is the response what you would expect (the drugs are additive) or more than you expect (the drugs are synergistic)? But this is a very confusing area. Just defining what it means for drugs to be "additive" is way more complicated than you'd guess.

Greco and colleagues likened the situation to Dorothy and the ruby slippers. They say that the huge number of studies, with conflicting definitions of interaction terms, and different conclusions from the same data... reminds them of a dream or fantasy like "Wizard of Oz". Additionally, many assume that proper and easy synergy assessment is possible if only some wizard could tell us the secret.

But it really is pretty complicated. What seems like a simple question "Do these two drugs act in a synergistic manner?" is not so simple.

I've completed a new page in the GraphPad library with links to some interesting articles, and to an article I wrote explaining how to use Prism to test for additivity (in one simple case). As always, I'd appreciate comments.

Nonlinear regression fits a curve through your data. The idea is to find the values of the parameters (rate constants, etc.) that make your curve come as close as possible to your data. More precisely, the goal is to find the values of the parameters that are most likely to be correct. The nonlinear (and linear) regression methods used by Prism (and other programs) assumes that the scatter of data around the idea model follows a bell-shaped Gaussian distribution. This assumption (with some mathematical wrangling) leads to the goal of nonlinear regression: To minimize the sum of squares of the distances of the points from the curve.

But what if the scatter is not all Gaussian? What if one (or a few) points are outliers, far from the rest? Standard regression techniques may be overwhelmed by this one point (depending on how many other points there are, and depending on where in the dataset the outlier appears). This is a problem that anyone who has analyzed data has encountered.

Ron Brown from AISN software and I have been working to develop a method for robust nonlinear regression. "Robust" means the method is not greatly influenced by outliers. Basically, the method works by assuming a different distribution of the scatter. Instead of assuming a Gaussian distribution, we assume instead a Lorentzian (also called Cauchy) distribution, which has much wider tails (making outliers more common). We also found a way to gradually ramp in the robustness of the method, which is essential to avoid getting trapped by declaring the wrong points to be outliers.

We've just about completed development of this method, and plan to put it into a future version of Prism. But first, we'd appreciate feedback. I presented this method at FASEB (April 2004), and have posted the PowerPoint slides. These slides include a sound track, so you can listen to the entire presentation. InternetExplorer 5.0 or later is needed to view/hear this presentation.

We'd appreciate feedback on robust fitting (and also on the usefulness of posting complete lectures on the web site).

What do you do when all your data and analyses and graphs are in Prism, but your colleagues don't (yet) use Prism? One solution is to suggest that they download the free Prism demo. But the demo expires after 30 days. Now we provide a better solution. Email your colleagues your Prism .PZM or .PZF files, and tell then to open the files using the free Prism viewer. This free utility (which doesn't expire) lets anyone examine and print all parts of a Prism file (version 2, 3, or 4) -– including data, analysis results and choices, notes, info constants, graphs and layouts. Of course, the Prism viewer cannot be used to enter or edit data, or to create or modify analyses or graphs. Your colleagues will be able to use the Prism viewer right away with no learning curve.

The viewer is only available for Windows right now, but the Mac version will come out soon (along with Prism 4.0b).

One of our goals of our software has always been to help people understand which statistical tests to use and how to make sense of the results. But I always focused on graduate students, post-docs, and researchers. So it was a surprise to get this nice email from a long-time user of Prism who helped get Prism established in undergraduate science labs at his university:

"One of my colleagues who teaches a lab course came in a couple of days ago to tell me his undergraduate students. When they go off and do a class experiment, they come back routinely with a good choice set of statistics and a reasonable writeup. This was completely unheard of in his previous university, and I think Prism and Intuitive Biostatistics can take a lot of the credit."

I often get asked whether Prism can help figure out whether two drugs work synergically. The usual approach used by workers in this field is to create an isobologram, but this seems clumbsy to me. I wondered whether global curve fitting couldn't be used, figured it out. This article explains how to fit three dose-response curve to a model that assumes that the third curve is the sum of the first two.

What is needed next are explicit models of drug synergism, so we can compare an additive with synergistic model. Any ideas for how to construct a synergistic dose-response model?

Many scientists are confused by power and sample size calculations. So we created GraphPad StatMate 2, which is now in the final stages of beta testing. It helps you performs sample size calculations while designing studies, and also lets you compute the power of completed experiments that result in nonsignificant P values. (The other parts of StatMate 1 have been removed from StatMate but are part of the GraphPad free web-based QuickCalcs.

Let me know if you'd like to beta test StatMate 2. It is ready to be released quite soon, so at this point we just want to know about bugs or typos. But I would also appreciate suggestions for future versions or programs.

Many scientists are confused by power and sample size calculations. So we created GraphPad StatMate 2, which is now in the final stages of beta testing. It helps you performs sample size calculations while designing studies, and also lets you compute the power of completed experiments that result in nonsignificant P values. (The other parts of StatMate 1 have been removed from StatMate but are part of the GraphPad free web-based QuickCalcs.

Let me know if you'd like to beta test StatMate 2. It is ready to be released quite soon, so at this point we just want to know about bugs or typos. But I would also appreciate suggestions for future versions or programs.

We fixed a bunch of minor bugs. Let me know if you'd like to beta test. Also note that if you are using Prism 4.00, the update to 4.01 is available on our support page.

I'll be giving two back-to-back talks on Monday April 19 in room 102a, starting at 4Pm.

4PM. Nonlinear regression with a family of data sets. Nonlinear regression is usually done one data set at a time. But many experiments are designed to collect a family of data sets at once. Fitting the entire family of curves at once, using global nonlinear regression, is a better way to analyze these experiments. Global fitting is helpful in two general situations. The first is fitting a family of curves when the information you want comes from the relationship between the curves. Examples include fitting total and nonspecific binding at one time to determine the Bmax and Kd of specific binding, and fitting a family of dose-response curves in the presence of antagonist to determine antagonist affinity (easier and more accurate that a Schild plot). The second use of global fitting is to compare curves or compare best-fit parameters. I'll show how to analyze the examples listed above using GraphPad Prism 4, but will focus on general principles rather than the details of using Prism.

5PM. Robust nonlinear regression. Nonlinear (and linear) regression is based on the assumption that all scatter around the curve (or line) follows a Gaussian bell-shaped distribution. But experimental data often includes outliers, and these can have a huge impact on the results. While this is a common problem in science, the existing solutions are not very good. Most scientists deal with outliers informally (erase the “bad” data points). Others use published methods for robust nonlinear regression, but these don't always work reliably (especially if the initial estimated values for the parameters are not very good). For this reason, I've been working with Ron Brown of AISN Software to create a new method for robust nonlinear regression that reliably fits curves in the presence of outliers. It works great, better than we hoped for. But we aren't quite done, and this method is not yet a part of GraphPad Prism. I'm giving this talk to elicit feedback.

If you can't attend these talks, check the Resource Library section of graphpad.com where we will post the PowerPoint slides of both presentations. These slides are not yet posted.

The Fisher's test is called an "exact" test, so you'd think there is exactly one way to compute the P value. Not so. While everyone agrees on how to compute one-sided (one-tailed) P value, there are actually three (or maybe four) methods to compute "exact" two-sided (two-tailed) P value from Fisher's test. Who would have guessed?

Prism and InStat compute the two-sided P value using the method called "summing small P values". Most statisticians seem to recommend this approach, but some programs use a different approach. Until today, the GraphPad free web-based QuickCalc used the "mid-P" method, which almost always gives a different P value. I changed the code so QuickCalc now uses the same, recommended, method as Prism and InStat.

If you want to learn more, SISA provides a detailed discussion with references. Also see the section on Fisher's test in Categorical Data Analysis by Alan Agresti. It is a very confusing topic, which explains why different statististicians (and so different software companies) use different methods.

Paige and I will be at booth 532 at the Experimental Biology meeting in Washington April 18-22. Drop by to see a demonstration of Prism 4, the forthcoming StatMate 2, or just to say Hi.