Dear AllStaters, Regarding my query on how to do metaanalysis of proportions, I got the following answers. Thanks indeed to: Bharat Thakrar, Robert G. Newcombe, Paul T Seed, David W. Smith and Jonathan Sterne ____________________________________________________________________________ On way forward is to do something like: For each study estimate Log(prevelance) ie: LPi=Log(Pi), The variance of Log(Pi) is: vi= Lpi(1-Lpi)/ni (where pi is the prevelence for the i study, ni is the sample in the i study) Do this for each study. For each study define the inverse of the variance ie: wi=1/vi Now add the wi and call it W ie: W=w1+w2 +...wn Now define the weight for the i study as: ki= wi/W define the pooled weighted log(prevelence) as: k1*LP1 + k2*LP2 + ....kn*LPn This is the overall estimate of prevelence. The variance of this quantity is 1/W. You can define 95% CI in the usual way, take the antilogs and you are there. Regards, Bharat ____________________________________________________________________________ The variance imputed to an estimated proportion depends on two things, the sample size and the observed proportion. It is maximal when the proportion is 0.5, and is zero when p=0 or 1. This suggests there may be problems with weighting with the inverse of the variance. The proportion estimated from each individual study should have a confidence interval attached, calculated using a good method. The signature file that will attach to the foot of this message contains a pointer to my website, from which you can access SPSS and minitab macros to do so. The next step is to carry out some sort of analysis of the degree of heterogeneity of the p's between the various studies. This could simply be a chi-square test on a 2 by k table, comparing the k observed proportions, with k-1 df. If numbers positive in some of the series are low, then you'll need something more sophisticated, for example from StatXact. If the heterogeneity analysis suggests it is meaningful to pool the series together, then I suggest that you simply merge the k series together, so that your pooled proportion is sigma r / sigma n, where sigma denotes summation over series 1 to k. Then get a CI for the pooled proportion, again preferably using a good method, not just using the asymptotic variance. Hope this helps. Best wishes. Robert Newcombe. .......................................... Robert G. Newcombe, PhD, CStat, Hon MFPHM Senior Lecturer in Medical Statistics University of Wales College of Medicine Heath Park Cardiff CF14 4XN, UK. Phone 01222 742329 or 742311 Fax 01222 743664 Email [log in to unmask] Macros for good methods for confidence intervals for proportions and their differences available at http://www.uwcm.ac.uk/uwcm/ms/Robert.html ____________________________________________________________________________ Sounds OK to me. The usual points about fixed vs random effects apply. In particular, of there is evidence of heterogeneity, he should look for the likely causes - major differences between the studies either in method of measurement or in population. Paul T Seed ([log in to unmask]) Department of Public Health Sciences, Guy's Kings and St. Thomas' School of Medicine, King's College London, 5th Floor, Capital House 42 Weston Street, London SE1 3QD tel (44) (0) 171 955 5000 x 6223 fax (44) (0) 171 955 4877 ____________________________________________________________________________ A transformation of each proportion, such as to stabilize the variance, is likely to work better. The arcsin-square root transformation is traditional. A logit transformation might also be appropriate for prevalence data. Use p' = arcsin [ sqrt {p} ]. If all the variation is binomial (an unlikely fact) then the variance of p' is about 821/n. This doesn't depend on p or p', so it is a variance-stabilizing transformation. In order for this to work well, the values of p should vary over a range of 0% to 30%. If they vary from about 30% to 70%, there probably isn't any point in using it. I got all this from Snedecor and Cochran, Statistical Methods, eighth edition, page 289. I don't have a meta-analysis reference handy. Snedecor and Cochran seem to imply that the user would be combining proportions from different sources in their discussion. Cordially Yours, David Smith Associate Professor Biostatistics and Epidemiology College of Public Health - CHB 323 University of Oklahoma Health Sciences Center PO Box 26901 Oklahoma City, OK 73190 ____________________________________________________________________________ The short answer is that yes, you can use the meta command to make a meta-analysis of proportions if you only have p and V(p). The basic syntax is: meta p varp, var However you could run into problems if some studies had small number and therefore the approximation for V(p) was poor. Peter Sasieni ([log in to unmask]) presented a program, partly based on meta, at the 5th Stata UK users' group meeting which was designed to analyse such data directly using (if I remember correctly) exact binomial probabilities. Jonathan Sterne %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%