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Subject:

Re: The individual patient and Bayesian statistics

From:

Matt Williams <[log in to unmask]>

Reply-To:

Matt Williams <[log in to unmask]>

Date:

Tue, 14 Aug 2007 12:30:20 +0100

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 ```Dear All, Some quick comments. Apologies if they seem a little grumpy, but I really thought that this was a very poor set of comments. For me, the giveaway is "One technique which answers all these problems is the Bayesian approach to statistics". This isn't science - its salesmanship. For the record, although I have some issues with Bayesian approaches, I generally think that they are interesting, and have some real potential, both in clinical decision-making (which I am assuming the readers of this list are familiar with) and also in clinical trials. Those interested might want to read: Bayesian Approaches to Clinical Trials and Health-care Evaluation (Statistics in Practice) by Spiegelhalter (or   see his page at http://www.mrc-bsu.cam.ac.uk/BSUsite/AboutUs/People/davids/davids_Research.shtml) > The major limitation of the "frequentist" statistical approaches is that > they makes assumptions on the nature of the data rather than on the > processes that are being studied. Bayesian approaches make assumptions about the processes (e.g. that they are conditionally independent). In addition, techniques used > frequentist statistics are based on asymptotic principles and are > applicable to normally distributed data. > The only data I know which is truly /normalI/ is measurement error. No > real world data is normal. The techniques work because when there are > large numbers, the results asymptotically approach that of truly normal > data. Which means that for large samples, we can treat them as normally distributed. The issue of no real world data fitting a theoretical distribution is not unique to the normal distribution - it is a feature of real-world data vs. theoretical distributions. > Such techniques therefore are not suitable when our interest is centred > on the sample size of one that you are talking about. > To make predictions at the individual level, one needs to create models > which realistically capture all the sources of variation at the > individual level. Which is going to be impossible; From the frequentist POV because we can never do enough studies to get the data; from the bayesian because we can't guarantee the independence of variables. In reality, therefore, we   use a smaller subset of the variables and hope that they are suitable as a surrogate for what we want to measure. > One technique which answers all these problems is the Bayesian approach > to statistics. Individuals when they make decisions (including > physicians) use Bayesian techniques. No they don't; Some people would say that they /should/ but there is ample work (Kaheman & Tversky) which shows that humans don't apply bayesian reasoning. > Unlike frequentist statistics, all estimates in Bayesian statistics are > arrived by Monte Carlo simulation. I do hope not; Monte Carlo simulations are nice, and interesting, but since one can apply bayes theorem, they are also a little unnecessary for many situations (but not all). I quick flick through Sackett et al.s   Clinical Epidemology book will show you how to use Bayes without Monte Carlo simulation. [Most real world data are gamma distributed]. I'd like to see a reference for this; I suspect it is very heavily dependent on the domain. > When the numbers are large, conventional statistics and Bayesian > statistics give generally equivalent results ( when they differ, > Bayesian results are more correct under equivalent assumptions). I have no idea what this means - correct WRT what? > One example. Suppose you are studying the prevalence of lupus in a > district in Malaysia. You have surveyed 10,000 individuals and found none. > Can you give an upper limit on the prevalence of lupus from the above data. > Frequentist statistics fail because you will encounter infinite variance > (which is far from the truith). You can give a valid confidence limit > (only the upper limit is valid) using Bayesian statistics. See other post for comments on this. > I have been working on it for more than an year now. I'll let this speak for itself. Matt ```

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