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The meta Package
Title Meta-Analysis
Version 0.5
Author Guido Schwarzer <sc@imbi.uni-freiburg.de>
Maintainer Matthias Wangler <mw@imbi.uni-freiburg.de>
Date 2005-02-23
Description Fixed and random effects meta-analysis. Functions for tests of bias, forest and funnel plot.
License GPL version 2 or later
R topics documented:
Fleiss93 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fleiss93cont . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Olkin95 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
funnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
metabias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
metabin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
metacont . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . metacum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . metagen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . metainf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . print.meta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . read.mtv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aspirin after Myocardial Infarction Description
Meta-analysis on Aspirin in Preventing Death after Myocardial Infarction study study label
year year of publication
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
Fleiss JL (1993), The statistical basis of meta-analysis. Statistical Methods in Medical Research, 2,
121–145.
Examples
metabin(event.e, n.e, event.c, n.c, data=Fleiss93) Description
Meta-analysis on the Effect of Mental Health Treatment on Medical Utilisation study study label
year year of publication
n.e number of observations in experimental group
mean.e estimated mean in experimental group
sd.e standard deviation in experimental group
n.c number of observations in control group
mean.c estimated mean in control group
sd.c standard deviation in control group
Fleiss JL (1993), The statistical basis of meta-analysis. Statistical Methods in Medical Research, 2,
121–145.
Examples
Thrombolytic Therapy after Acute Myocardial Infarction Description
Meta-analysis on Thrombolytic Therapy after Acute Myocardial Infarction author first author
year year of publication
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
Olkin I (1995), Statistical and theoretical considerations in meta-analysis. Journal of Clinical Epi-
demiology
, 48, 133–146.
Examples
summary(metabin(event.e, n.e, event.c, n.c, data=Olkin95)) Calculation of confidence intervals (normal approximation) Description
Calculation of confidence intervals; based on normal approximation.
Arguments
Standard error of treatment estimate.
Standard error of treatment estimate.
P-value of test with null hypothesis TE=0.
This function is primarily called from other functions of the library meta, e.g. plot.meta,summary.meta.
Author(s)
Examples
Plot to assess funnel plot asymmetry Description
Draw a funnel or radial plot to assess funnel plot asymmetry in the active graphics window.
funnel(x, y, xlim=NULL, ylim=NULL, xlab=NULL, ylab=NULL, comb.f=FALSE, axes=TRUE, labels=NULL, cex.lab=0.8, log="", yaxis="se", sm=NULL, .) xlab="Inverse of standard error", ylab="Standardised treatment effect (z-score)", comb.f=TRUE, axes=TRUE, labels=NULL, cex.lab=0.8, Arguments
An object of class meta, or estimated treatment effect in individual studies.
Standard error of estimated treatment effect (mandatory if x not of class meta).
A logical indicating whether the pooled fixed effects estimate should be plotted.
A logical indicating whether axes should be drawn on the plot.
A character string specifying the text to be used as plotting symbol.
The magnification to be used for x and y labels.
A character string which contains "x" if the x axis is to be logarithmic, "y"if the y axis is to be logarithmic and "xy" or "yx" if both axes are to belogarithmic (applies only to function funnel).
A character string indicating which type of weights are to be used. Either "se","inv", or "size" (applies only to function funnel).
A character string indicating underlying summary measure, e.g., "RD", "RR","OR", "WMD", "SMD" (applies only to function funnel).
The confidence level utilised in the plot (applies only to function radial).
Graphical parameters as in par may also be passed as arguments.
A funnel plot or radial plot, also called Galbraith plot, is drawn in the active graphics window. Ifcomb.f is TRUE, the pooled estimate of the fixed effects model is plotted. If level is not NULL,the corresponding confidence limits are drawn.
In the funnel plot, if yaxis is "se", the standard error of the treatment estimates is plotted onthe y axis which is likely to be the best choice (Sterne & Egger, 2001). Other possible choices foryaxis are "inv" (inverse of the variance) and "size" (study size).
Author(s)
References
Galbraith RF (1988a), Graphical display of estimates having differing standard errors. Technomet-
rics
, 30, 271–281.
Galbraith RF (1988b), A note on graphical presentation of estimated odds ratios from several clini-
cal trials. Statistics in Medicine, 7, 889–894.
Light RJ & Pillemer DB (1984), Summing Up. The Science of Reviewing Research. Cambridge:Havard University Press.
Sterne JAC & Egger M (2001), Funnel plots for detecting bias in meta-analysis: Guidelines on
choice of axis. Journal of Clinical Epidemiology, 54, 1046–1055.
Examples
meta1 <- metabin(event.e, n.e, event.c, n.c, funnel(meta1$TE, meta1$seTE, sm="RR") funnel(meta1, comb.f=TRUE, xlim=c(0.1, 10), axes=FALSE) Description
Test for funnel plot asymmetry, based on rank correlation or linear regression method.
Arguments
An object of class meta, or estimated treatment effect in individual studies.
Standard error of estimated treatment effect (mandatory if x not of class meta).
Overall treatment estimate (mandatory if x not of class meta and method ="rank").
Standard error of overall treatment estimate (mandatory if x not of class metaand method = "rank").
A character string indicating which test is to be used. Either "rank", "linreg","mm" or "count", can be abbreviated.
A logical indicating whether a plot should be produced for method "rank","linreg" or "mm".
A logical indicating whether a continuity corrected statistic is used for rank cor-relation methods "rank" and "count".
If method is "rank", the test statistic is based on the rank correlation between standardisedtreatment estimates and variance estimates of estimated treatment effects; Kendall’s tau is usedas correlation measure (Begg & Mazumdar, 1994). The test statistic follows a standard normaldistribution. By default (if correct is FALSE), no continuity correction is utilised (Kendall &Gibbons, 1990).
If method is "linreg", the test statistic is based on a linear regression of the standardised treat-ment effect (standard normal deviate) on the inverse of the standard error of the treatment estimate(Egger et al., 1997). The test statistic follows a t distribution with number of studies - 2degrees of freedom.
If method is "mm", the test statistic is based on a weighted linear regression using the method ofmoments estimator of the additive between-study variance component (method 3a in Thompson,Sharp, 1999). The test statistic follows a t distribution with number of studies - 2 degreesof freedom.
If method is "count", the test statistic is based on the rank correlation between a standardisedcell frequency and the inverse of the variance of the cell frequency; Kendall’s tau is used as cor-relation measure (Schwarzer, 2003). The test statistic follows a standard normal distribution. Bydefault (if correct is FALSE), no continuity correction is utilised (Kendall & Gibbons, 1990).
A list with class "htest" containing the following components: the estimated degree of funnel plot asymmetry, with name "ks" or "bias"corresponding to the method employed, i.e., rank correlation or regression method.
The degrees of freedom of the test statistic in the case that it follows a t distri-bution.
The value of test statistic under the null hypothesis, always 0.
A character string describing the alternative hypothesis.
A character string indicating what type of test was used.
A character string giving the names of the data.
Author(s)
References
Begg CB & Berlin JA (1994), Operating characteristics of a rank correlation test for publication
bias. Biometrics, 50, 1088–1101.
Kendall M & Gibbons JD (1990), Rank Correlation Methods. London: Edward Arnold.
Egger M, Smith GD, Schneider M & Minder C (1997), Bias in meta-analysis detected by a simple,
graphical test. British Medical Journal, 315, 629–634.
Schwarzer G (2003), Statistical Tests for Bias in Meta-Analysis with Binary Outcomes, PhD thesis,University of Dortmund, Germany, http://eldorado.uni-dortmund.de Thompson SG, Sharp, SJ (1999), Explaining heterogeneity in meta-analysis: A comparison of
methods, Statistics in Medicine, 18, 2693–2708.
Examples
meta1 <- metabin(event.e, n.e, event.c, n.c, metabias(meta1, method="linreg", plotit=TRUE) metabias(meta1, method="linreg")$p.value metabias(meta1$TE, meta1$seTE, method="linreg")$p.value Meta-analysis of binary outcome data Description
Calculation of fixed and random effects estimates (relative risk, odds ratio or risk difference) formeta-analyses with binary outcome data. Mantel-Haenszel, inverse variance and Peto method areavailable for pooling.
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
Number of events in experimental group.
Number of observations in experimental group.
Number of observations in control group.
An optional vector with study labels.
An optional data frame containing the study information, i.e., event.e, n.e, event.c,and n.c.
An optional vector specifying a subset of studies to be used.
A character string indicating which method is to be used for pooling of studies.
One of "Inverse", "MH", or "Peto", can be abbreviated.
A character string indicating which summary measure ("RD", "RR", or "OR")is to be used for pooling of studies.
Numerical value added to each cell frequency for studies with a zero cell count.
A logical indicating if incr is added to each cell frequency of all studies if atleast one study has a zero cell count. If false, incr is added only to each cellfrequency of studies with a zero cell count.
A logical indicating if incr is added to each cell frequency of all studies irre-spective of zero cell counts.
A logical indicating if studies with zero or all events in both groups are to beincluded in the meta-analysis (applies only if sm = "RR" or "OR").
A logical indicating if incr is not to be added to all cell frequencies for studieswith a zero cell count to calculate the pooled estimate based on the Mantel-Haenszel method.
A logical indicating if 2*incr instead of 1*incr is to be added to n.e andn.c in the calculation of the relative risk (i.e., sm="RR") for studies with azero cell count.
A logical indicating whether the addition of incr to studies with zero cell fre-quencies should result in a warning.
Treatment estimates and standard errors are calculated for each study. For studies with a zerocell count, by default, 0.5 is added to all cell frequencies of these studies. Treatment estimates andstandard errors are only calculated for studies with zero or all events in both groups if allstudiesis 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", inversevariance weighting is used for pooling; finally, if method is "Peto", the Peto method is used forpooling. 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 cellfrequencies of a study with a zero cell count in the calculation of the pooled estimate. This approachis 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 calculatethe Mantel-Haenszel estimate and he advocates the exact method (MH.exact=TRUE). Note, theestimate based on the exact method is not defined if the number of events is zero in all studies eitherin the experimental or control group.
An object of class c("metabin", "meta") with corresponding print, summary, plotfunction. The object is a list containing the following components: Estimated treatment effect and standard error of individual studies.
Weight of individual studies (in fixed and random effects model).
Estimated overall treatment effect and standard error (fixed effect model).
Estimated overall treatment effect and standard error (random effects model).
Number of studies combined in meta-analysis.
Square-root of between-study variance (moment estimator of DerSimonian-Laird).
Cochrane-Mantel-Haenszel heterogeneity statistic.
Logical flag indicating if any study included in meta-analysis has any zero cellfrequencies.
Author(s)
References
Cooper H & Hedges LV (1994), The Handbook of Research Synthesis. Newbury Park, CA: RussellSage 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: TheCochrane Collaboration, 2000.
StataCorp. 2001. Stata Statistical Software: Release 7.0. College Station, TX: Stata Corporation.
Examples
metabin(0, 10, 0, 10, sm="OR", allstudies=TRUE) meta1 <- metabin(event.e, n.e, event.c, n.c, meta2 <- metabin(event.e, n.e, event.c, n.c, data=Olkin95, subset=Olkin95$year<1970, Meta-analysis of continuous outcome data Description
Calculation of fixed and random effects estimates for meta-analyses with continuous outcome data;inverse variance weighting is used for pooling.
metacont(n.e, mean.e, sd.e, n.c, mean.c, sd.c, studlab, data=NULL, subset=NULL, sm="WMD") Arguments
Number of observations in experimental group.
Estimated mean in experimental group.
Standard deviation in experimental group.
Number of observations in control group.
Standard deviation in control group.
An optional vector with study labels.
An optional data frame containing the study information, i.e., n.e, mean.e, sd.e,n.c, mean.c, and n.c.
An optional vector specifying a subset of studies to be used.
A character string indicating which summary measure ("WMD" or "SMD") is tobe used for pooling of studies.
Calculation of fixed and random effects estimates for meta-analyses with continuous outcome data;inverse variance weighting is used for pooling. The DerSimonian-Laird estimate is used in therandom effects model. For the summary measure "SMD", Hedges’ adjusted g is utilised for pooling.
The function metagen is called internally to calculate individual and overall treatment estimatesand standard errors.
An object of class c("metacont", "meta") with corresponding print, summary, plotfunction. The object is a list containing the following components: Estimated treatment effect and standard error of individual studies.
Weight of indiviudal studies (in fixed and random effects model).
Estimated overall treatment effect and standard error (fixed effect model).
Estimated overall treatment effect and standard error (random effects model).
Number of studies combined in meta-analysis.
Square-root of between-study variance (moment estimator of DerSimonian-Laird).
Author(s)
References
Cooper H & Hedges LV (1994), The Handbook of Research Synthesis. Newbury Park, CA: RussellSage Foundation.
Examples
meta1 <- metacont(n.e, mean.e, sd.e, n.c, mean.c, sd.c, data=Fleiss93cont, sm="SMD") meta2 <- metacont(Fleiss93cont$n.e, Fleiss93cont$mean.e, Description
Performs a cumulative meta-analysis.
metacum(x, pooled="fixed", sortvar) Arguments
A character string indicating whether a fixed or random effects model is usedfor pooling. Either "fixed" or "random", can be abbreviated.
An optional vector used to sort the individual studies (must be of same length asx$TE).
A cumulative meta-analysis is performed. Studies are included sequentially as defined by sortvar.
An object of class c("metacum", "meta") with corresponding print, plot function. Theobject is a list containing the following components: Estimated treatment effect and standard error of pooled estimate in cumulativemeta-analyses.
Study label describing addition of studies.
Number of studies combined in meta-analysis.
Author(s)
References
Cooper H & Hedges LV (1994), The Handbook of Research Synthesis. Newbury Park, CA: RussellSage Foundation.
Examples
meta1 <- metabin(event.e, n.e, event.c, n.c, plot(metacum(meta1, pooled="random")) Generic inverse variance meta-analysis Description
Fixed and random effects meta-analysis based on estimates and their standard errors; inverse vari-ance weighting is used for pooling.
metagen(TE, seTE, studlab, data=NULL, subset=NULL, sm="") Arguments
Standard error of treatment estimate.
An optional vector with study labels.
An optional data frame containing the study information.
An optional vector specifying a subset of studies to be used.
A character string indicating underlying summary measure, e.g., "RD", "RR","OR", "WMD", "SMD".
Generic method for meta-analysis, only treatment estimates and their standard error are needed.
The method is useful, e.g., for pooling of log hazard ratios. The inverse variance method is used forpooling. Random effects estimate is based on the DerSimonian-Laird method.
An object of class c("metagen", "meta") with corresponding print, summary, plotfunction. The object is a list containing the following components: Weight of individual studies (in fixed and random effects model).
Estimated overall treatment effect and standard error (fixed effect model).
Estimated overall treatment effect and standard error (random effects model).
Number of studies combined in meta-analysis.
Square-root of between-study variance (moment estimator of DerSimonian-Laird).
Author(s)
References
Cooper H & Hedges LV (1994), The Handbook of Research Synthesis. Newbury Park, CA: RussellSage Foundation.
Examples
meta1 <- metabin(event.e, n.e, event.c, n.c, data=Fleiss93, sm="RR", meth="I") ## Identical results by using the following commands: metagen(meta1$TE, meta1$seTE, sm="RR") Influence analysis in meta-analysis Description
Performs a influence analysis. Poooled estimates are calculated omitting one study at a time.
metainf(x, pooled="fixed", sortvar) Arguments
A character string indicating whether a fixed or random effects model is usedfor pooling. Either "fixed" or "random", can be abbreviated.
An optional vector used to sort the individual studies (must be of same length asx$TE).
Performs a influence analysis; poooled estimates are calculated omitting one study at a time. Studiesare sorted according to sortvar.
An object of class c("metainf", "meta") with corresponding print, plot function. Theobject is a list containing the following components: Estimated treatment effect and standard error of pooled estimate in influenceanalysis.
Study label describing omision of studies.
Number of studies combined in meta-analysis.
Author(s)
References
Cooper H & Hedges LV (1994), The Handbook of Research Synthesis. Newbury Park, CA: RussellSage Foundation.
Examples
meta1 <- metabin(event.e, n.e, event.c, n.c, plot(metainf(meta1, pooled="random")) Plot function for objects of class meta Description
Draws a forest plot in the active graphics window.
plot.meta(x, byvar, bylab, sortvar, studlab = TRUE, level = 0.95, level.comb = level, comb.f = FALSE, comb.r = FALSE, text.f = "Fixed effect model", text.r = "Random effects model", lty.f = 2, lty.r = 3, xlab, xlim, ylim, lwd = 1, cex = 1, log = ifelse(x$sm == "RR" | x$sm == "OR" | x$sm == "HR", "x", ""), axes = TRUE, allstudies = TRUE, weight = "fixed", scale.diamond = 1, Arguments
An optional vector containing grouping information (must be of same length asx$TE).
A character string with a label for the grouping variable.
An optional vector used to sort the individual studies (must be of same length asx$TE).
A logical indicating whether study labels should be printed in the graph.
The level used to calculate confidence intervals for individual studies.
The level used to calculate confidence intervals for pooled estimates.
A logical indicating whether the pooled fixed effect estimate should be plotted.
A logical indicating whether the pooled random effects estimate should be plot-ted.
A character string used in the plot to label the pooled fixed effects estimate.
A character string used in the plot to label the pooled random effects estimate.
Line type (pooled fixed effect estimate).
Line type (pooled random effects estimate).
A numerical value giving the amount by which plotting text and symbols shouldbe scaled relative to the default.
A numerical value giving the amount by which plotting text and symbols forpooled fixed and random effects estimates should be scaled.
A character string which contains "x" if the x axis is to be logarithmic (othervalues for log are not reasonable).
A logical indicating whether the x axis should be drawn on the plot.
A logical indicating whether studies with inestimable treatment effects shouldbe plotted.
A character string indicating which type of plotting symbols is to be used forindividual treatment estimates. One of "same" and "fixed", i.e., plot sym-bols have the same size for all studies or represent the weight of the study in thefixed effect model.
A numerical value giving the amount by which the diamond representing pooledtreatment effects should be scaled relative to the default.
scale.square A numerical value giving the amount by which the square representing treatment effects in individual studies should be scaled relative to the default.
Graphical parameters as in par may also be passed as arguments.
The color for individual study results and confidence limits.
A forest plot, also called confidence interval plot, is drawn in the active graphics window. Sub-groupanalyses are conducted and displayed in the plot if byvar is not missing.
Author(s)
Examples
meta1 <- metabin(event.e, n.e, event.c, n.c, plot(meta1, byvar=c(1,2,1,2), bylab="label") Print and summary method for objects of class meta Description
Print and summary method for objects of class meta.
print.meta(x, sortvar, level=0.95, level.comb=level, details=FALSE, ma=TRUE, digits=max(4, .Options$digits - 3), .) summary.meta(object, byvar, bylab, bystud=FALSE, level.comb=0.95, .) print.summary.meta(x, digits = max(3, .Options$digits - 3), Arguments
An object of class meta or summary.meta.
An optional vector used to sort the individual studies (must be of same length asx$TE).
The level used to calculate confidence intervals for individual studies.
The level used to calculate confidence intervals for pooled estimates.
A logical indicating whether further details of individual studies should be printed.
A logical indicating whether the summary results of the meta-analysis should beprinted.
An optional vector containing grouping information (must be of same length asx$TE).
A character string with a label for the grouping variable.
A logical indicating whether results of individual studies should be printed bygrouping variable.
Minimal number of significant digits, see print.default.
A logical indicating whether the name of the grouping variable should be printedin front of the group labels.
A list is returned by the function summary.meta with the following elements: Results for fixed effect model (a list with elements TE, seTE, lower, upper, z, p,level).
Results for random effects model (a list with elements TE, seTE, lower, upper,z, p, level).
A list with elements TE, lower, upper, seTE, z, p, level, scale.
Number of studies combined in meta-analysis.
Square-root of between-study variance (moment estimator of DerSimonian-Laird).
Heterogeneity statistic H (a list with elements TE, lower, upper).
Heterogeneity statistic I2 (a list with elements TE, lower, upper).
Cochrane-Mantel-Haenszel heterogeneity statistic.
A character string indicating underlying summary measure.
A character string with the pooling method.
Results within groups (a list with elements TE, seTE, lower, upper, z, p, level) -if byvar is not missing.
Number of studies combined within groups - if byvar is not missing.
Heterogeneity statistic Q within groups - if byvar is not missing.
Label for grouping variable - if byvar is not missing.
Levels of grouping variable - if byvar is not missing.
Author(s)
References
Cooper H & Hedges LV (1994), The Handbook of Research Synthesis. Newbury Park, CA: RussellSage Foundation.
Examples
meta1 <- metacont(n.e, mean.e, sd.e, n.c, mean.c, sd.c, data=Fleiss93cont, sm="SMD") summary(meta1, byvar=c(1,2,1,1,2), bylab="label") Description
Reads a file created with RevMan 4.1 and creates a data frame from it.
Arguments
The name of the file which the data are to be read from.
The field separator character. Values on each line of the file are separated by thischaracter.
Reads a file created with RevMan 4.1 (Menu: "File" - "Export" - "Analysis data file.") and createsa data frame from it.
A data frame containing the following components: Number of events in experimental group.
Number of observations in experimental group.
Number of observations in control group.
Estimated mean in experimental group.
Standard deviation in experimental group.
Standard deviation in control group.
Observed minus expected (IPD analysis).
Concealment of treatment allocation.
Type of outcome. D = dichotomous, C = continuous, P = IPD.
Author(s)
Examples
## Locate MTV-data file "FLEISS93.MTV" in sub-directory of package "meta" filename <- paste(searchpaths()[seq(along=search())[search()== "package:meta"]], "/data/FLEISS93.MTV", sep="") ∗Topic datagen
∗Topic datasets
∗Topic hplot
∗Topic htest
ci, metabias, metabin, metacont, metacum, metagen, metainf, ∗Topic print
Fleiss93, Fleiss93cont, funnel, 8, 10 metabias, 5, 10metabin, 5, 8, 12, 13, 15, 16, 18, 20, 21metacont, 8, 10, 13, 15, 16, 18, 20, 21metacum, metagen, 5, 8, 10, 12, 18, 20, 21metainf, plot.meta, print.meta, 10, 13, 15, 16, print.summary.meta (print.meta),

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Nuclides Analysis Result of the Radioactive Materials in the Seawater< Coast, Fukushima Daiichi Nuclear Power Station >North of Unit 5-6 Discharge Channel at FukushimaAround South Discharge Channel of Fukushima(Approx. 30m North of Unit 5-6 Discharge Channel) (Appox. 1.3km South of Unit 1-4 Discharge Channel) the Reactor Regulation (Bq/L)* The density specified by the Reactor Regulation

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