8: Fixed & Random Summaries with Preferred Binary Input Fixed and random-effects overall or summary effects for odds and risk Meta-analysis in R with Metafor

Overall Summary The Metafor program uses inverse variance weights to combine study ES into an overall or summary effect size You can specify Fixed (common) effects analysis or Random (varying) effects analysis If RE, you can choose from several methods for estimating the random effects variance component (REVC). Different REVC, weight, summary. The method statement specifies both fixed or random and which REVC estimator you want The effect sizes input to metafor may be transformed in various ways The measure option tells metafor what transformation you want If you use preferred input format, you can use measure ; otherwise use generic input

Binary Data Most outcome studies in medicine and epidemiology compare success and failure (number of events and non-events) in two conditions, which results in a two-by-two table. The number of cases should be counted and recorded for each cell (A, B, C, D) of the design. The labels that Metafor uses are shown in the table below. Note that n1i = ai+bi and n2i = ci+di. EventNon-eventTotals Treatment group aibin1i Control groupcidin2i

measure= If you input sample sizes for ai, bi, ci, and di; or if you input ai and n1i, ci and n2i, then you can instruct Metafor to compute the following using measure=: “RR” – Risk ratio = log[(ai/n1i)/(ci/n2i)] “OR” – Odds ratio = log[(ai/bi)/(ci/di)] “RD” – Risk difference = (ai/n1i) – (ci/n2i) “AS” – arcsine transformed risk difference = asin(sqrt(ai/n1i)) – asin(sqrt(ci/n2i)) “PETO” – log odds ratio estimated with Peto’s method

Empty Cells For studies with small samples or rare events, some of the cell frequencies (ai, bi, ci, di) may be zero. This presents a problem for the analysis. Your choices in Metafor are to leave it alone, to add a small number to every cell in the analysis, or to add a small number to tables that contain one or more cells with zero frequency. The add command. You may input add=number, e.g., add =.5. Metafor will add the number you specify to cells specified by the to command. The to command. You may specify either to = “all”, which add the value of add to every cell in every table in the analysis, or to = “only0”, which adds the value of add to very cell in any table that contains at least one zero entry. If you leave it alone, and there is table where there is division by zero, the result is missing for that table.

R code: Mindfulness study – manufactured data 1 Measure=“OR”, method = “DL” 2 Measure=“RR”, method=“DL” 3 Measure=“OR”, method=“DL”, add=.5, to = “all” 4 Measure=“OR”, method=“DL”, add=.5, to = “only0” 5 Measure=“OR”, method=“REML”, add=.5, to=“only0” 6 Measure=“OR”, method=“FE”, add=.5, to=“only0”