Category "Me"
Category "PhD Process"
Category "Scientific interpretation"
August 26, 2005
Daily affirmation: "Matrix algebra is my friend!"
Non-negative definite matrices are also called "positive semi-definite" matrices...
I've been reading a bit about matrix algebra lately. Notice I said reading and not learning. There's a lot in mathematics that I just don't grok. I definitely feel like a non-native speaker. I wonder if people who are really good in mathematics have trouble understanding other things - things that I may be fairly good at - and if they feel as completely disoriented as I do when I'm trying to understand terms like determinant, orthogonal, and classical adjoint.
The reason for this self-flagellation is not so much directly related to my dissertation, but to improve myself as a methodologist. You see, matrix algebra is the foundation for regression analysis. Regression is used a lot in epidemiology to predict associations between exposures and outcomes or diseases. My problem is that I have a growing concern that methods like regression are misused - that they are applied in the wrong instances and leave the epidemiologist with a false confidence in the results.
So, I'm going back and reviewing regression from scratch. I'm reading a new book by David Freedman, a well-known statistics professor at UC Berkeley, and someone whom I've heard to be critical of how certain statistical tools are used in practice. I was heartened to read in the book's preface:
Much of the discussion [in this book] is organized around published studies... Some may find the tone of the discussion too skeptical. If you are among them, I would make an unusual request: suspend belief until you finish reading the book. (Suspension of disbelief is all too easily obtained, but that is a topic for another day.) [Emphasis added]
I'm looking forward to reading what he has to say. For now, it's back to
If G is non-negative definite rather than positive definite, that is, x'Gx = 0 for some x ≠ 0, then G is not invertible...
Posted by rigd0003 at 3:30 PM | Comments (1) | Me | PhD Process | Scientific interpretation
Category "PhD Process"
Category "Scientific interpretation"
June 15, 2005
I'm just guessing here...
I just realized something about my dissertation project: I'm just guessing. I'm working on something that I know will not give me one true, definitive answer. When you get down to it, isn't that what all probability models are? Sure you have weights and likelihoods for the different outcomes in different situations, but you're just guessing. It may be an educated guess; it may be a guess that's come out of a very sophisticated algorithm or model. But it's still just a guess.
It's not that this 'revelation' has freaked me out or anything. It's just made me realize the simplicity of the truth. Guessing is okay (said in my best Stuart Smalley "Daily Affirmation" voice*). And acknowledging that I'm guessing leads to some good questions: What is the benefit of guessing? What is the harm? What would I need to know to improve my guess? What is the ideal that I'm working towards? It's actually kind of nice. It gets away from that 'know-it-all' posturing and gets down to the heart of it -- seeking answers that will help us improve.
Look for my best guess at Salmonella attribution to be published this winter! (Do you think the journal editors will be as opened minded to the whole 'guessing' thing?)
*Wikipedia rocks! I can't believe they have a minor pop culture reference like Stuart Smalley!
Posted by rigd0003 at 10:23 AM | Comments (0) | PhD Process | Scientific interpretation
Category "News"
Category "Scientific interpretation"
April 25, 2005
More of Merck's murky waters
Another article about Merck pharmaceutical company and trouble over how it handled clinical trials of its painkiller, Vioxx. This one was in yesterday's New York Times: "Evidence in Vioxx Suits Shows Intervention by Merck Officials".
Two disturbing points jump out at me:
| (1) | A Merck scientist urged one of the clinical trial researchers to list the cause of death for a patient as "unknown" rather than heart-related. And the researcher seemed to be a willing participant, since he said in an e-mail communication, "If it is easier to call this an unknown cause of death, I could be persuaded to say that as well." It seems to me that "unknown" should no be acceptable as a cause of death for a patient participating in a clinical trial since it may be connected to the drug or procedure exposure. At the very least a contributing cause should be indicated and by an impartial doctor. |
| (2) | The doctor listed as first author for the published trial results, Dr. Jeffrey Lisse, didn't write the paper. Merck wrote the paper and he edited it. And it doesn't sound like he was overly questioning of the data because he accepted it at face value, telling the Times reporter, "Basically, I went with the cardiovascular data that was presented to me." |
Clinical trials are a great asset to public health and medicine. When conducted correctly, we are able to make some reasonably good assumptions like random assignment of the exposure (drug, procedure) among the groups, exchangeability of the groups--outcomes in each group is a good substitute for the outcomes of the other, etc. that make interpretation of the data more robust. I guess it never occurred to Dr. Lisse to question the assumption that the data were accurate and not deliberately skewed.
Putting obvious duplicity aside, this reminds me of a more general point. You've probably heard the line about "letting the data speak for themselves." This is totally wrong--data don't speak, we speak! We look at the data and make assumptions about what it represents, what we think it is telling us. Everyone understands that art is all about interpretation; it's about time that we realize it is similar for science, as well. And no, I don't think this will horribly muddle the waters. In fact, I think we scientists will be better able to reach consensus once we make it common practice to state our assumptions along with our data and conclusions. Then all the cards will be on the table, and we can call a spade a spade.
Posted by rigd0003 at 11:00 AM | Comments (0) | News | Scientific interpretation