This may be a rudimentary question, but I'm trying to find a way to combine z statistics (per observation) from 10 MI datasets into a composite z statistic value or composite p value for each observation. The z statistic value comes from calculation of a logit model interaction effect (Ai and Norton), plotted against probability of the outcome, where each observation has a separate value for interaction effect, z statistic, and prob(outcome) (n = 25,000). While I plan to average the estimates for interaction effect and prob(outcome) across MI sets, I'm struggling with a method for combining the z statistic values (or approximating a composite z stat value) on an individual observation level for a large dataset that appropriately accounts for the MI process. Any suggestions are greatly appreciated. Many thanks.
Craig Craig D. Newgard, MD, MPH Assistant Professor Department of Emergency Medicine Department of Public Health & Preventive Medicine Oregon Health & Science University 3181 Sam Jackson Park Road Mail Code CR-114 Portland, OR 97239-3098 (503) 494-1668 (Office) (503) 494-4640 (Fax) [email protected] -------------- next part -------------- An HTML attachment was scrubbed... URL: http://lists.utsouthwestern.edu/pipermail/impute/attachments/20051017/2338512a/attachment.htm From junedsiddique <@t> gmail.com Tue Oct 25 18:11:37 2005 From: junedsiddique <@t> gmail.com (Juned Siddique) Date: Tue Oct 25 18:11:46 2005 Subject: [Impute] Re: the PE statistic with imputed data Message-ID: <[email protected]> Hi Bill, I would be interested in any responses you received to this posting. One comment I have is to look at Don Rubin's response to an earlier question posed to this listserv (Volume 18, issue 4) concerning combining estimates of R-squared. Rubin noted that: Because the standard combining rules rely on asymptotic normality, and R-squared is a proportion of variance, asymptotic normality will be better approximated with a transformation, like log (R-squared). Then the standard rules can be used with the corresponding asymptotic variance for it. I believe this response is relevant to your question since you are also estimating a proportion. As far as which of your two methods is correct, I would appreciate any comments you or others might have. Thanks. -Juned Today's Topics: > > 1. the PE statistic with imputed data (Howells, William) > > > ---------------------------------------------------------------------- > > Message: 1 > Date: Tue, 27 Sep 2005 10:35:38 -0500 > From: "Howells, William" < [email protected]> > Subject: [Impute] the PE statistic with imputed data > To: <[email protected]> > Message-ID: > < 2ada428b6944da4b8f8a2fdf4e60e52a197...@exchange.wusm-pcf.wustl.edu> > Content-Type: text/plain; charset="US-ASCII" > > I'm interested in calculating what some have referred to as the > "proportion explained" statistic from two regression models with imputed > data. This statistic comes up in the analysis of indirect effects (or > surrogate variables, or mediation effects, depending on the literature, > eg. Freedman and Schatzkin, Am J Epi 1992). PE = (C-C')/C where C = the > unadjusted effect of some independent variable and C' = the same effect > adjusted by the putative mediator. PE quantifies the proportion > reduction in the independent variable due to mediation. If PE = 1 there > is complete mediation. If PE = 0, there is no mediation. > > Calculation of standard errors for PE is controversial, depending on the > outcome, in my case a time to event outcome. I'm using the method due > to Lin, Fleming, and DeGruttola (Stats in Medicine 1997). But with 50 > imputed datasets. My question is whether I am combining the imputations > correctly. I first impute my 50 datasets, n=600 each. I run the two > regression models within each imputed dataset and obtain C and C', and > apply the Lin et al formula to obtain both PE and se(PE). Then I use > the usual formulas as implemented in SAS PROC MIANALYZE to obtain the > combined PE over the m=50 imputations and the combined variance using > the within and between imputation variance. All seems well. I think > this is the right approach. > > The other way of doing it is to first calculate C and C' separately by > averaging over the imputations and then find PE from these C and C'. > Note that mathematically this produces a different result than the above > method. For example, with m=2 imputations that produced (C,C') = (6,4) > and (3,1) then PE_1 = (6-4)/6 = 1/3 and PE_2 = (3-1)/3 = 2/3. The first > method produces (1/3 + 2/3)/2 = 1/2. The second method produces > [(6+3)/2 - (4+1)/2] / [(6+3)/2] = (9/2-5/2)/ 9/2 = 4/9. I'm just > looking for confirmation that the second method is incorrect. Thanks. > > Bill Howells, MS > Wash U Med School, St Louis > > <br/>The materials in this message are private and may contain Protected > Healthcare Information. If you are not the intended recipient, be advised > that any unauthorized use, disclosure, copying or the taking of any action > in reliance on the contents of this information is strictly prohibited. If > you have received this email in error, please immediately notify the sender > via telephone or return mail. > > > > ------------------------------ > > _______________________________________________ > Impute mailing list > [email protected] > http://lists.utsouthwestern.edu/mailman/listinfo/impute > > > End of Impute Digest, Vol 18, Issue 6 > ************************************* > -------------- next part -------------- An HTML attachment was scrubbed... URL: http://lists.utsouthwestern.edu/pipermail/impute/attachments/20051025/635da55c/attachment.htm
