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<p class="MsoNormal">Dear list members,<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">I apologize for the length of this request but this is an issue raised by a reviewer for which I have no definite answer.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">In <a href="http://www.metafor-project.org/doku.php/tips:comp_two_independent_estimates">
http://www.metafor-project.org/doku.php/tips:comp_two_independent_estimates</a>, Dr. Viechtbauer describes how to compare
<span lang="EN">summary estimates obtained from 3 independent subgroups of studies. In the example, the categorical variable “alloc” is dichotomized into “random” and “other” and RR from each category are compared using 1) a procedure similar to conducting
a Wald test, and the rma.mv function allowing the residual heterogeneity to differ in random and other studies.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN">In animal science, the data set often include studies in which the levels of a categorical variable of interest are not evaluated in the same study. For example, a subgroup of studies could have been conducted in Ayrshire
cows and another subgroup of studies could have used Holstein cows. Ayrshire and Holstein cows are 2 different breeds of dairy cows which may respond differently to a dietary treatment: the infusion of casein may increase milk yield (MY) to a greater extent
in Holstein cows versus Ayrshire cows. My first question is about the validity of comparing the slopes of casein between breed (MY = casein * breed), even if no study used the 2 breeds to test the effect of casein; and how to do it?.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN"><o:p> </o:p></span></p>
<p class="MsoNormal">Can I use the approach in <a href="http://www.metafor-project.org/doku.php/tips:comp_two_independent_estimates">
http://www.metafor-project.org/doku.php/tips:comp_two_independent_estimates</a> , and compare “year” according to “alloc” (i.e., year*alloc)?.<span lang="EN"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN">library(metafor)<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN">dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg)<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN">dat$alloc <- ifelse(dat$alloc == "random", "random", "other")<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN">dat<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN"><o:p> </o:p></span></p>
<p class="MsoNormal"><u><span lang="EN">### I added moderator year in the model</span></u><span lang="EN">:<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN">res1 <- rma(yi, vi, mods = ~ year, data=dat, subset=alloc=="random")<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN">res2 <- rma(yi, vi, mods = ~ year, data=dat, subset=alloc=="other")<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN"><o:p> </o:p></span></p>
<p class="MsoNormal"><u><span lang="EN">### The following script needs to be fixed in order to compare the estimates of year:<o:p></o:p></span></u></p>
<p class="MsoNormal"><span lang="FR-CA">dat.comp <- data.frame(estimate = c(coef(res1), coef(res2)), stderror = c(res1$se, res2$se),<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="FR-CA"> </span><span lang="EN">meta = c("random","other"), tau2 = round(c(res1$tau2, res2$tau2),3))<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN">dat.comp<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN">rma(estimate, sei=stderror, mods = ~ meta, method="FE", data=dat.comp, digits=3)<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN">with(dat.comp, round(c(zval = (estimate[1] - estimate[2])/sqrt(stderror[1]^2 + stderror[2]^2)), 3))<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN"><o:p> </o:p></span></p>
<p class="MsoNormal"><u><span lang="EN">### The final model could be:<o:p></o:p></span></u></p>
<p class="MsoNormal"><span lang="EN">rma.mv(yi, vi, mods = ~ year * alloc, random = ~ alloc | trial, struct="DIAG", data=dat, digits=3)<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN">rma.mv(yi, vi, mods = ~ alloc-1 + year : alloc, random = ~ alloc | trial, struct="DIAG", data=dat, digits=3)<o:p></o:p></span></p>
<p class="MsoNormal"><u><span lang="EN">### The slopes of year do not differ (P = 0.552) between random and other.<o:p></o:p></span></u></p>
<p class="MsoNormal"><span lang="EN"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN">Finally, I cannot use this approach for a multilevel model because we get this error message:<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height:11.25pt;background:white;word-break:break-all">
<span style="font-size:10.0pt;font-family:"Lucida Console";color:#C5060B;mso-fareast-language:EN-CA">Cannot use '~ inner | outer1/outer2' type terms in the 'random' argument.
</span><span style="font-size:10.0pt;font-family:"Lucida Console";mso-fareast-language:EN-CA">C</span>an this be fixed ?<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Best regards,<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Roger <span style="font-family:"Segoe UI Symbol","sans-serif"">
☺<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:13.5pt;font-family:"Kaufmann Bd BT";color:navy;mso-fareast-language:FR-CA"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="FR-CA" style="font-size:13.5pt;font-family:"Kaufmann Bd BT";color:navy;mso-fareast-language:FR-CA">Roger Martineau, mv Ph.D.</span><span lang="FR-CA" style="mso-fareast-language:FR-CA"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="FR-CA" style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy;mso-fareast-language:FR-CA">Nutrition et Métabolisme des ruminants<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="FR-CA" style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy;mso-fareast-language:FR-CA">Centre de recherche et de développement</span><span lang="FR-CA" style="mso-fareast-language:FR-CA"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="FR-CA" style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy;mso-fareast-language:FR-CA">sur le bovin laitier et le porc</span><span lang="FR-CA" style="mso-fareast-language:FR-CA"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="FR-CA" style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy;mso-fareast-language:FR-CA">Agriculture et agroalimentaire Canada/Agriculture and Agri-Food Canada</span><span lang="FR-CA" style="mso-fareast-language:FR-CA"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="FR-CA" style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy;mso-fareast-language:FR-CA">Téléphone/Telephone: 819-780-7319</span><span lang="FR-CA" style="mso-fareast-language:FR-CA"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="FR-CA" style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy;mso-fareast-language:FR-CA">Télécopieur/Facsimile: 819-564-5507</span><span lang="FR-CA" style="mso-fareast-language:FR-CA"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy;mso-fareast-language:FR-CA">2000, Rue Collège / 2000, College Street</span><span lang="EN-US" style="mso-fareast-language:FR-CA"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy;mso-fareast-language:FR-CA">Sherbrooke (Québec) J1M 0C8</span><span lang="EN-US" style="mso-fareast-language:FR-CA"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy;mso-fareast-language:FR-CA">Canada</span><span lang="EN-US" style="mso-fareast-language:FR-CA"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-CA"><a href="mailto:roger.martineau@canada.ca"><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:blue;mso-fareast-language:FR-CA">roger.martineau@canada.ca</span></a></span><span lang="EN-US" style="mso-fareast-language:FR-CA"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-CA"> <o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D;mso-fareast-language:EN-CA"><img border="0" width="154" height="31" id="Image_x0020_3" src="cid:image001.jpg@01D4AA5B.F62A2510" alt="cid:image001.jpg@01D4679E.125DD520"></span><span style="mso-fareast-language:EN-CA"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-CA"> <o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
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