meta (version 0.5)

metabin: Meta-analysis of binary outcome data

Description

Calculation of fixed and random effects estimates (relative risk, odds ratio or risk difference) for meta-analyses with binary outcome data. Mantel-Haenszel, inverse variance and Peto method are available for pooling.

Usage

metabin(event.e, n.e, event.c, n.c, studlab,
        data = NULL, subset = NULL, method = "MH",
        sm = ifelse(!is.na(charmatch(method, c("Peto", "peto"), nomatch = NA)), "OR", "RR"),
        incr = 0.5, allincr = FALSE, addincr = FALSE, allstudies = FALSE,
        MH.exact = FALSE, RR.cochrane = FALSE, warn = TRUE)

Arguments

event.e

Number of events in experimental group.

n.e

Number of observations in experimental group.

event.c

Number of events in control group.

n.c

Number of observations in control group.

studlab

An optional vector with study labels.

data

An optional data frame containing the study information, i.e., event.e, n.e, event.c, and n.c.

subset

An optional vector specifying a subset of studies to be used.

method

A character string indicating which method is to be used for pooling of studies. One of "Inverse", "MH", or "Peto", can be abbreviated.

sm

A character string indicating which summary measure ("RD", "RR", or "OR") is to be used for pooling of studies.

incr

Numerical value added to each cell frequency for studies with a zero cell count.

allincr

A logical indicating if incr is added to each cell frequency of all studies if at least one study has a zero cell count. If false, incr is added only to each cell frequency of studies with a zero cell count.

addincr

A logical indicating if incr is added to each cell frequency of all studies irrespective of zero cell counts.

allstudies

A logical indicating if studies with zero or all events in both groups are to be included in the meta-analysis (applies only if sm = "RR" or "OR").

MH.exact

A logical indicating if incr is not to be added to all cell frequencies for studies with a zero cell count to calculate the pooled estimate based on the Mantel-Haenszel method.

RR.cochrane

A logical indicating if 2*incr instead of 1*incr is to be added to n.e and n.c in the calculation of the relative risk (i.e., sm="RR") for studies with a zero cell count.

warn

A logical indicating whether the addition of incr to studies with zero cell frequencies should result in a warning.

Value

• An object of class c("metabin", "meta") with corresponding print, summary, plot function. The object is a list containing the following components:
• event.e, n.e, event.c, n.c, studlab,
• sm, method, incr, allincr, addincr,
  As defined above.
• allstudies, MH.exact, RR.cochrane, warn
• TE, seTE
  Estimated treatment effect and standard error of individual studies.
• w.fixed, w.random
  Weight of individual studies (in fixed and random effects model).
• TE.fixed, seTE.fixed
  Estimated overall treatment effect and standard error (fixed effect model).
• TE.random, seTE.random
  Estimated overall treatment effect and standard error (random effects model).
• k
  Number of studies combined in meta-analysis.
• Q
  Heterogeneity statistic Q.
• tau
  Square-root of between-study variance (moment estimator of DerSimonian-Laird).
• Q.CMH
  Cochrane-Mantel-Haenszel heterogeneity statistic.
• sparse
  Logical flag indicating if any study included in meta-analysis has any zero cell frequencies.
• call
  Function call.

Details

Treatment estimates and standard errors are calculated for each study. For studies with a zero cell count, by default, 0.5 is added to all cell frequencies of these studies. Treatment estimates and standard errors are only calculated for studies with zero or all events in both groups if allstudies is TRUE. Both fixed and random effects estimates are calculated. If method is "MH" (default), the Mantel-Haenszel method is used to calculate the fixed effects estimate; if method is "Inverse", inverse variance weighting is used for pooling; finally, if method is "Peto", the Peto method is used for pooling. The DerSimonian-Laird estimate is used in the random effects model. For the Mantel-Haenszel method, by default (if MH.exact is FALSE), 0.5 is added to all cell frequencies of a study with a zero cell count in the calculation of the pooled estimate. This approach is also used in other software, e.g. RevMan 4.1 and the Stata procedure metan. According to Fleiss (in Cooper & Hedges, 1994), there is no need to add 0.5 to a cell frequency of zero to calculate the Mantel-Haenszel estimate and he advocates the exact method (MH.exact=TRUE). Note, the estimate based on the exact method is not defined if the number of events is zero in all studies either in the experimental or control group.

References

Cooper H & Hedges LV (1994), The Handbook of Research Synthesis. Newbury Park, CA: Russell Sage Foundation.

DerSimonian R & Laird N (1986), Meta-analysis in clinical trials. Controlled Clinical Trials, 7, 177--188.

Fleiss JL (1993), The statistical basis of meta-analysis. Statistical Methods in Medical Research, 2, 121--145.

Greenland S & Robins JM (1985), Estimation of a common effect parameter from sparse follow-up data. Biometrics, 41, 55--68.

Review Manager (RevMan) [Computer program]. Version 4.1 for Windows. Oxford, England: The Cochrane Collaboration, 2000.

StataCorp. 2001. Stata Statistical Software: Release 7.0. College Station, TX: Stata Corporation.

See Also

funnel, metabias, metacont, metagen, print.meta

Examples

metabin(10, 20, 15, 20, sm="OR")

##
## Different results:
##
metabin(0, 10, 0, 10, sm="OR")
metabin(0, 10, 0, 10, sm="OR", allstudies=TRUE)


data(Olkin95)

meta1 <- metabin(event.e, n.e, event.c, n.c,
                 data=Olkin95, subset=c(41,47,51,59),
                 sm="RR", meth="I")
summary(meta1)
funnel(meta1)

meta2 <- metabin(event.e, n.e, event.c, n.c,
                 data=Olkin95, subset=Olkin95$year<1970,
                 sm="RR", meth="I")
summary(meta2)