A Propensity for Nonsense

Guernsey McPearson

“I’ll come no more behind your scenes, David; for the silk stockings and white bosoms of your actresses excite my amorous propensities.”

Dr Samuel Johnson

“I’ll have no more to do with epidemiologists because their obsessions with propensities excite my sarcastic tendencies.”

Dr Guernsey McPearson

What is the point of our personnel department? They keep on sending me these invitations by email to go on non-courses. For example

Hi Guernsey,

We note that you have not yet enrolled for one of our gender-awareness courses. There are several opportunities coming up soon that are too good to miss. Just click on the link below and enroll. It’s that easy. Enjoy!

Bestest

Lindsay

Human Resources

Dear Miss or Mrs Bestest,

I have a passable acquaintance with German and French and know that the former has three genders but that the latter has two. Apart from French, I cannot claim any knowledge of Romance languages but I understand from Mrs McPearson that the situation in Italian is very similar but that nouns of the masculine gender are further divided. On the other hand, I have decided that the details of genders of nouns and their declensions in the Slavonic languages must forever remain a closed book to me. I have thus decided that I have achieved as much awareness of genders as is necessary to function in everyday life and, indeed, to discharge my duties at Pannostrum Pharmaceuticals for the foreseeable future. Therefore, in order to maximise the use of my very personal human resources, I shall not be signing up for any of these courses. Should the situation change in the future I shall certainly let the personnel department know.

Yours sincerely

Dr G McPearson

Biostatistics

As you can tell from this example, and might in any case guess, I am a dab hand at declining these invitations tactfully, so that however irritating they are, their impact on me personally is minimal. Unfortunately, however, this does not mean that personnel are harmless. They also handle our system of ‘personal development profiles’ (PDPs). That’s fine for me. I resolutely refuse to stick anything in them as goals for the year that has not to do with learning more statistics or attending conferences or possibly advanced courses. However, others with whom I come into contact also have PDPs and, unfortunately, Harvey Puffer has put, ‘learning more about statistics,’ as a personal goal.

I have tried to persuade Personnel that we should never send medics on external statistics courses but instead have them attend the rather fine, though I say so myself, in-house course that I have given from time to time at Pannostrum, enlivened as it is with a sprinkling of, witty remarks. Example:

Q. Why is medical education like making butter? A. Because you take the cream and make it thick.

However, it seems that, personnel have had the odd complaint about my sarcasm and attitude by physicians attending these courses and more and more are being sent elsewhere. Anyway, this year Harvey has been sent on a statistics course and not just a one day course but one for a whole week! And I am certainly suffering.

‘Ah Guernsey. Fascinating course I just went on. Had a lecture about a technique we could use in clinical trials. Some score or other…pro…pro, what was it ah yes, proclivity score. Have you heard of it?’

‘Not quite in those terms, Harvey, but I think I know what you are talking about and I like the name. Between you and me, Harvey, let it forever be known as the proclivity score.’

Harvey looked a bit taken aback by this. ‘Well,’ he continued after a while, ‘this proclivity thing is a much better way of dealing with demographics than analysis of covariance, or whatever it is you are always promoting. Apparently epidemiologists are always using it.’

‘Confound all epidemiologists is one of my mottos. A whole cohort of epidemiologists couldn’t convince me that there was a case for preferring the proclivity score to analysis of covariance. Let’s not forget, Harvey, that these are people who think that relative risks are preferable to odds ratios.’

Harvey looked puzzled again but came back, ‘There you go again, Guernsey. You are always so negative.’

‘I accept the compliment, Harvey. In the words of Artemus Ward, “It ain’t the things we don’t know that hurt us. It’s the things we know that ain’t so.” Negative thinking is a speciality of mine. It’s one of the ways that I know, thank goodness, that I am a statistician. I leave positive thinking to marketing. Analysis of covariance uses covariates that are predictive of outcome, the proclivity score if they are predictive of assignment. The former is logical, the latter is not.’

‘Whoa whoa. Wait a minute, Guernsey, you’ll have to explain that to me.’

‘Well, Harvey. Let’s imagine that we have run a clinical trial in asthma with equal numbers of patient under active treatment and placebo and we are measuring FEV₁ at outcome.’ Harvey perked up at this mention of his personal discipline. ‘Now suppose that we measure the mean difference between active and placebo at outcome.’

‘Got, that Guernsey.’

‘Now, suppose that we observed some demographics as you call them at baseline and decide to adjust for them. Under what circumstances would you expect it to make no difference to the estimate if you adjusted for a given demographic variable. To make it easy let’s suppose it was a binary demographic variable.’

Harvey’s brow furrowed. He thought for a while. ‘Well,’ he said after a while, ‘if it was balanced of course.’

‘Quite right,’ I said ‘and if this binary covariate were balanced, the proportion of patients under active and under placebo would be identically 0.5 whatever the value of the binary covariate.’

Harvey started to look distinctly stressed but after a pause he said, ‘Yes, OK. It’s a funny way of putting it but that’s correct.’

‘Well this proportion is the probability that a randomly drawn patient of a given type will be found to be on active treatment and the proclivity score approach is to stratify by this probability. So in this case, since every patient has a proclivity score of 0.5 there is just one stratum and effectively you can ignore the covariate.’

‘Well that makes sense. If the covariate is balanced we don’t need to adjust for it.’

‘Au contraire,’ I said, thus implicitly using the fact that the gender of contraire is masculine. ‘We will come back to that. But what about the second of my conditions? Under what other circumstance would it make no difference to the treatment estimate if I adjusted or not? Just to help you, Harvey, a very obvious method of adjustment would be to calculate the treatment effects in both strata and then average the two estimates appropriately’

Harvey’s brow furrowed again. ‘I suppose,’ he said, ‘if the effects in each of the two strata were the same as they were in the trial as a whole then it would make no difference.’

‘Excellent, Harvey,’ I said, ‘you are absolutely right. But if the first condition does not apply so that numbers given active treatment and placebo are unbalanced within strata as a whole but balanced for the trial as a whole but the within stratum mean differences are the same as the overall difference then this implies that the demographic covariate has no effect on outcome.’

‘You lost me there somewhere, Guernsey. However, are you trying to say in that convoluted way of yours that if a covariate is not prognostic we don’t need to adjust for it. If so, why didn’t you say so.’

‘Yes, I was trying to say that, Harvey. So it boils down to this. If you adjust for things because they are predictive of outcome, that’s the analysis of covariance strategy but if you adjust for the probability of assignment to active treatment (as opposed to placebo) as a function of the covariates, then that’s the proclivity score approach.’

‘OK. But I can’t see what your objection to this proclivity thing is in that case. Surely you don’t need to adjust for something that is perfectly balanced.’

‘Well, imagine we have a placebo-controlled parallel group design in which we think there will be a great difference between centres and we can only have two patients per centre. How would you design this?’

‘Well I would have one patient per centre randomised to active treatment and one to placebo.’

‘Good choice, Harvey. Now we agree that every patient has a fifty percent chance of getting active treatment or placebo. So that means that there is a single value of the proclivity score of 50% for everybody and that we can analyse patients in a single stratum.’

‘Well, hang on a minute Guernsey, I thought you said that there was an important difference between centres and I remember you showing me that when that is the case it makes a big difference if you put centre in the model. In fact, haven’t we got a matched pair design?’

‘My point exactly. However, there is nothing in the proclivity score approach that requires us to put centre in the model because centre does not affect the probability of assignment. On the other hand centre does affect outcome and therefore it has to be in the model from the ANCOVA point of view.’

‘I begin to see your point but I think that there is something wrong. I’ll report back.’

He was as good as his word.

‘It seems that we were talking at cross-purposes, Guernsey. This proclivity score you were mentioning (can’t think where you got the name) must be something quite different. It was the propensity score I was talking about and I have it on very good authority that it is a brilliant approach to dealing with demographics.’

‘This authority wouldn’t be an epidemiologist?’

‘Yes, how did you guess?’

‘Just a hunch.’