Re: [Fwd: CLIN PHAR STAT: Mixed Vs Fixed]

From: Stephen Senn <stephens@public-health.ucl.ac.uk> Date: Wed, 9 Aug 2000 11:46:26 GMT0 Subject: Re: [Fwd: CLIN PHAR STAT: Mixed Vs Fixed] Nick, It is interesting to compare meta-analysis to the general linear model A. In a general linear model analysis of a data set consisting of two treatments and many strata you (usually) impose the assumption that the within-cell variances are constant. This then weights the contribution from the respective strata according to the design information: it depends only on the number of observations and their distribution between treatment and control. The danger is that if heteroscedasticty applies this will be inefficient. B. In a meta-analysis you use the calculated (and hence estimated) variances for each within-stratum estimate as the means of combining them. The danger is that differences in the weights reflect random differences rather than true differences. Because we often have little information in clinical work the dangers inherent in B are often more serious than those in A. Hence a constrained common variance is often preferable. Typically, frequentist solutions end up at one of two extremes. A Bayesian approach permits compromises between these two. Now, turning to PK/PD work. Here you have non-linear models. This means that evn if you constrain a residual variance to be equal the estimated variances of parameters will not be fixed by the design alone. It depends on the response as well. The fact that you have a hierarchy on the parameters may help with this problem but I suspect that in any case it means that approach A veres towards approach B (but I am guessing). However, I would also guess that freeing the variances will make this problem worse rather than better. Regards Stephen