At Loggerheads

Guernsey McPearson

A riddle for you.

Question What’s the difference between lumberjacks and physicians?

Answer. The former have no problem with log transformations.

So I have to be thankful for small mercies. At least I have escaped Pannostrum’s Zombie Division: medicine for the brain-dead, and that’s just the “scientists”. No more Hamilton scores or Activities of Daily Living for me, thank goodness. I am back in asthma working with Dr Harvey Puffer. However, every silver lining has its cloud and this time it is the strange sense of déjà-vu I’m having all over again or should that be déjà-blew, since it has to do with forced expiratory volume in one second (FEV₁)? I sorted out the way we analysed these trials years ago and even wrote a lengthy internal guidance document on the subject but it is just as if I had never been in the division.

“So run this past me again, Harvey”, I said, “the people in the other place are saying that we can’t use log-transformations because they can’t understand them”. (I should explain here that by the other place, I meant our company research and development facility an ocean away at Medicine Springs.)

“Now, now, Guernsey. Let’s be collegial about this and not think negatively. We are supposed to be a global company. Nobody is implying that log-transformations are too difficult; why a child could understand them, although,” and here he frowned momentarily, “ I do think myself that it’s all very well calling for log-transformations but the question is ‘which one?’. You statisticians are always obsessed with these natural logs, which seem rather unnatural to me, but what about logs to base ten and I understand you could have them to base two as well and perhaps there are other possibilities. Why, the results could be quite different. It all seems rather arbitrary. Don’t you ever worry about that?”

“Oh yes”, I said, “I spend exactly as much time agonising over that as I do worrying about whether we should measure FEV₁ in litres, millilitres, gills, gallons, British standard bathtubs or jeroboams. It could have exactly the same crucial impact on the interpretation of the trial.”

Puffer looked baffled and began, “I don’t…” and then thought better of it. “Well, I merely offer it as a technical consideration. Perhaps you could get one of these MSc students we are sponsoring at great expense in these wonderful universities we have links with to look into the matter as a student project.”

The prospect filled me with gloom. I wish I could believe that I couldn’t find a student of statistics with a freshly minted 2(i) who after several months of simulations would come up with the astonishing and unexpected result that it made hardly any difference at all to the P-value, really only in the third or fourth significant figure, which base you used for your log-transformation.

Puffer brought me back to the point. “No, the real reason they are opposing log-transformations is that they have reliable information that the Agency doesn’t like them and let’s face it, at Medicine Springs they know the Agency better than we do.”

“Oh that’s certainly true,” I replied, “in fact, based on my many frequent interactions with Agency statisticians over the years, many of whom appear quite lucid and sensible, I can say that our colleagues in the Springs know things about the Agency the Agency doesn’t know itself. Certainly there are many Agency practices of which they have informed me of which my Agency contacts have denied all knowledge.”

“Hm. I see that you are being sarcastic. However, I am not referring to the statisticians. It is the physicians in Respiratory who are telling me that. Furthermore, they have had some very negative experiences using log-transformations on change from baseline. Apparently the transformation sometimes fails altogether and very frequently so in the placebo group.”

“Yes,” I replied, “these would be negative experiences. Have they considered that they ought to be transforming the raw values and not the change from baseline values?”

Puffer was quite taken aback. “Not use the change from baseline values!?. What sense would that make? You see, Guernsey, asthma is a very variable disease. We must use the baseline values.”

“No problem”, I replied, “the way it works is like this. We log-transform the FEV₁ values at outcome and baseline and use the log-transformed values at baseline as a covariate in an analysis of covariance.”

“Whoa! Hold on there! This is all a bit radical isn’t it? Who said we could use analysis of covariance? In any case, there is no arguing with this. I have it here in black and white from our new division head, Dr Zapper. It shall be the policy of respiratory division to use only untransformed values in statistical analyses.”

“Let me understand this policy. I can use airways resistance, RAW, but not its reciprocal? I can use airways conductance, GAW, but not its reciprocal?”

“Yes, that’s right.”

“And when it comes to FEV₁ measures collected over twelve hours, can I calculate the area under the curve.?”

“No, AUCs are out”

“Does that mean that FEV₁ itself is out?”

“How do you mean?”

“Well it’s often calculated using flow spirometers as the area under the expiratory flow curve up to one second.”

“Now you’re being silly. That’s quite different. The machine does that automatically.”

“How stupid of me. I can see that this is a crucial difference. Well this truly has the mark of genius”, I continued. “Still, at least we can see the back of these damn QTc measurements in our safety analyses.”

“How do you mean?”

“Well”, I said. “If log-transforming an FEV₁ is a sin against the glorious principle of natural measurement, then taking the square root of the RR interval, let alone the cube root must be an abomination and dividing it into the QT interval an unspeakable crime.”

“I think that you will admit that the case is quite different there?”

“Oh yes. It’s quite different from a log transformation. Dividing the QT interval in milliseconds by the antilog of half the logarithm of the RR interval, or taking the antilog of the log of QT minus one-third the log of RR. What could be more natural than that? On the other hand taking the log transformation of FEV₁ would only make sense if we believed the effect of treatment was more reasonably approximately constant in percentage terms rather than absolute terms, a preposterous idea if there was one.” I fear I had lost Harvey somewhere along the way there. There was a long pause and I followed up with a further question, “and when the data are really badly skewed, will rank transformations also be forbidden?”

“I assume so but I will check for you.”

He was as good as his word and only a few days later reported back as follows.

“Yes, Guernsey. Rank transformations are also out. For badly skewed data the new divisional head at Medicine Springs favours a radically different approach.”

“Nonparametric analyses,” I said.

“Yes! How do you know?”

“Long, long years of study,” I replied.

“Of statistics?”

“No. Of physicians.”

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