{"id":301,"date":"2014-08-05T16:01:05","date_gmt":"2014-08-05T16:01:05","guid":{"rendered":"https:\/\/www.transplantevidence.com\/blog\/?p=301"},"modified":"2014-08-05T16:01:05","modified_gmt":"2014-08-05T16:01:05","slug":"meta-analysis-in-r-part-2-binary-data","status":"publish","type":"post","link":"https:\/\/www.transplantevidence.com\/news\/2014\/08\/05\/meta-analysis-in-r-part-2-binary-data\/","title":{"rendered":"Meta-analysis in R: Part 2 – Binary data"},"content":{"rendered":"

In part 1<\/a>, I discussed how to get set up for meta-analysis in R, by installing the necessary software and libraries.<\/p>\n

In this post, I will take the reader through the steps for performing meta-analysis of binary data in R.<\/p>\n

<\/p>\n

Required data format<\/strong><\/p>\n

Binary outcomes are those in which study participants either experience an outcome, or do not. Examples are acute rejection and delayed graft function. The data required for meta-analysis is as follows:<\/p>\n

[table th=0]
\n\u00a0n.s<\/strong>, The total number of participants in the study group
\n\u00a0n.c<\/strong>, The total number of participants in the control group
\n\u00a0event.s<\/strong>, The number of participants experiencing the outcome in the study group
\n\u00a0event.c<\/strong>, The number of participants experiencing the outcome in the control group
\n[\/table]<\/p>\n

In order to label the studies, it is recommended that a study name and year of publication are used.<\/p>\n

An example spreadsheet looking at the incidence of hypercholesterolaemia in patients withdrawn from or avoiding steroids is shown below:<\/p>\n

[table]
\nname,year,event.s,n.s,event.c,n.c
\nVincenti,2008,101,227,57,109
\nLaftavi,2005,4,14,11,16
\nPonticelli,1997,86,114,102,115
\nMontagnino,2005,43,65,48,68
\nVitko,2005,18,143,25,134
\nWoodle,2008,97,156,112,152
\nBurke,2001,6,20,13,20
\nPark,1994,8,22,35,46
\nCristinelli,1986,7,35,13,31
\nVanrenterghem,2005,39,235,62,237
\nSmak Gregoor,2002,14,76,11,73
\nSola,2002,5,46,6,46
\nHollander,1997,9,42,23,41
\n[\/table]<\/p>\n

Loading the dataset<\/strong><\/p>\n

In R, a spreadsheet of data is termed a \u201cdataset\u201d. Datasets can either be entered manually, or imported from an excel spreadsheet. The latter can be performed from the command-line, or using the RStudio GUI.<\/p>\n

Loading data using the GUI<\/em><\/p>\n

This is the easiest method to load your dataset into R. From the \u201cEnvironment\u201d tab in the top right pane, click the \u201cImport Dataset\u201d button, and select \u201cFrom Text File…\u201d:<\/p>\n

\"Load<\/a><\/p>\n

Select your .csv file that you created in excel, and click \u201cOpen\u201d.<\/p>\n

You will then be given the option to describe your data format. Use the settings shown below:<\/p>\n

\"Import<\/a><\/p>\n

The data frame on the bottom left previews what you data will look like once imported. Click \u201cImport\u201d, and a new panel will open at the top left of the screen showing your data frame. The dataset will also appear in your environment in the top right pane:<\/p>\n

\"Data<\/a><\/p>\n

Loading data from the command-line<\/em><\/p>\n

If the above step does not work, or you are using a different GUI\/platform, you can load your file from the command-line. First of all, R needs to know where to find your files. From the \u201cSession\u201d menu, select \u201cSet Working Directory > Choose Directory…\u201d. Navigate to the directory containing your data, and click \u201cSubmit\u201d. Alternatively, you can type in the console:<\/p>\n

setwd(\"C:\/Documents and Settings\/User\/My Documents\")<\/pre>\n
Replace the directory in the quotes with your working directory.<\/p>\n
To see the files in the current directory, type:<\/p>\n
dir()<\/pre>\n
To load a CSV file (as prepared above), type the following:<\/p>\n
read.table(\"cholesterol.csv\", sep = \",\", header=TRUE)<\/pre>\n
This tells R the file name and extension, that the data is separated by commas, and that the first row of data is the column headings. It should output something like this:<\/p>\n
\"data\"<\/a><\/p>\n
In order to be able to use this data, it must be stored as a variable. Run the following command:<\/p>\n
cholesterol.data <- read.table(\"cholesterol.csv\", sep = \",\", header=TRUE)<\/pre>\n
This stores the dataset above as a variable called \u201ccholesterol.data<\/span>\u201d. The dataset can be viewed by typing it’s name:<\/p>\n
cholesterol.data<\/pre>\n
The output should be the same as the table above. To access an individual column from the data, use the $ operator. For example:<\/p>\n
cholesterol.data$name<\/pre>\n
Should output:<\/p>\n
[1] Vincenti      Laftavi       Ponticelli    Montagnino    Vitko        \n[6] Woodle        Burke         Park          Cristinelli   Vanrenterghem\n[11] Smak Gregoor  Sola          Hollander    <\/pre>\n
Performing the meta-analysis<\/strong><\/p>\n
There are two steps to performing the meta-analysis. Firstly, an effect size must be calculated for each study. In the case of discrete data this can be a Relative Risk (RR), Odds Ratio (OR) or Risk Difference (RD). Then these effect sizes much be combined in a meta-analytical model to create a summary effect size, along with confidence intervals and measures of heterogeneity.<\/p>\n
Fortunately, the metafor <\/span> package contains functions that can perform these steps individually, or more conveniently combine these steps automatically giving all of the required data. The function for meta-analysis is the\u00a0rma.uni()<\/span> function. In the case of binary meta-analysis, it takes data in the form of a 2×2 table:<\/p>\n
[table]
\nGroup, Outcome 1, Outcome 2, Total
\nStudy Group, ai, bi, n1i
\nControl Group, ci, di, n2i
\n[\/table]<\/p>\n
So looking at our cholesterol data from section 3.2, we have values for ai, ci, n1i<\/span> and n2i<\/span>. Try the following:<\/p>\n
rma.uni(ai=event.s, n1i=n.s, ci=event.c, n2i= n.c, data=cholesterol.data, slab=paste(name, year), measure=\"RR\")<\/pre>\n
In brackets, we are telling the function the names of the columns containing the data (event.s, n.s, event.c, n.c<\/span>) and the name of the dataset (data=cholesterol.data<\/span>). The argument (slab=paste(name, year)<\/span>) provides a label for each study by combining the name and year columns, separated by a space. The final argument tells the function that we wish to use the relative risk. The command should produce the following output:<\/p>\n
Random-Effects Model (k = 13; tau^2 estimator: REML)\n\ntau^2 (estimate of total amount of heterogeneity): 0.0225 (SE = 0.0225)\ntau (sqrt of the estimate of total heterogeneity): 0.1499\nI^2 (% of total variability due to heterogeneity): 47.93%\nH^2 (total variability \/ within-study variance):   1.92\n\nTest for Heterogeneity: \nQ(df = 12) = 20.6639, p-val = 0.0555\n\nModel Results:\n\nestimate       se     zval     pval    ci.lb    ci.ub          \n -0.2854   0.0712  -4.0083   <.0001  -0.4249  -0.1458      *** \n\n---\nSignif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1<\/pre>\n
The default here is a random-effects model.  Below this, there is an assessment of heterogeneity including the I^2 value and Chi-squared p-value.  Finally, the results of the model are given, with the log relative risk, SE, p-value and borders for the 95% confidence interval.  The log values can be converted to the true relative risk using the exp()<\/span> function.  For example:<\/p>\n
exp(-0.2854)\n[1] 0.7517135<\/pre>\n
This tells us that the relative risk from the random-effects model is 0.75. The same can be done for the borders of the confidence interval (giving 0.65-0.86).<\/p>\n
Other rma.uni<\/span> options<\/strong><\/p>\n
By default, the rma.uni<\/span> function uses the restricted maximum-likelihood estimator (REML) random-effects model.  By adding more options to our command, we can modify these defaults.  Some useful options are:<\/p>\n
[table th=0]
\nmethod<\/span>,\"The meta-analysis model used.  This can be 'REML', 'DL' (DeSimonian-Laird),  or \t\t\t'FE' (fixed effects).  Other models are available.\"
\nmeasure<\/span>, \"The summary method used.  This can be 'RR', 'OR' or 'RD' for binary data, 'MD' \t\t\tor 'SMD' for continuous data.\"
\nsubset<\/span>,\t\"A subset of studies from the dataset to meta-analyse.  This will be described in a later post.\"
\nmods<\/span>, \"Moderator variables for a mixed-effects analysis.  This will be described in a later post.\"
\n[\/table]<\/p>\n
To give another example, try the following command:<\/p>\n
rma.uni(ai=event.s, n1i=n.s, ci=event.c, n2i= n.c, data=cholesterol.data, slab=paste(name, year), measure=\"OR\", method=\"FE\")<\/pre>\n
This gives:<\/p>\n
Fixed-Effects Model (k = 13)\n\nTest for Heterogeneity: \nQ(df = 12) = 19.6044, p-val = 0.0750\n\nModel Results:\n\nestimate       se     zval     pval    ci.lb    ci.ub          \n -0.5898   0.1005  -5.8685   <.0001  -0.7868  -0.3928      *** \n\n---\nSignif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1 <\/pre>\n
Now a fixed-effects model is used, with results reported as the log odds-ratio.  Exp(-0.5898)<\/span> tells us that the combined odds ratio from the fixed-effects model is 0.55.<\/p>\n
In the next post, I will deal with the meta-analysis of continuous data.<\/p>\n","protected":false},"excerpt":{"rendered":"
In part 1, I discussed how to get set up for meta-analysis in R, by installing the necessary software and libraries. In this post, I will take the reader through the steps for performing meta-analysis of binary data in R.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[169],"tags":[249,250,273,292],"class_list":["post-301","post","type-post","status-publish","format-standard","hentry","category-meta-analysis-in-r","tag-meta-analysis","tag-methodology","tag-r","tag-systematic-review"],"_links":{"self":[{"href":"https:\/\/www.transplantevidence.com\/news\/wp-json\/wp\/v2\/posts\/301","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.transplantevidence.com\/news\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.transplantevidence.com\/news\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.transplantevidence.com\/news\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.transplantevidence.com\/news\/wp-json\/wp\/v2\/comments?post=301"}],"version-history":[{"count":0,"href":"https:\/\/www.transplantevidence.com\/news\/wp-json\/wp\/v2\/posts\/301\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.transplantevidence.com\/news\/wp-json\/wp\/v2\/media?parent=301"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.transplantevidence.com\/news\/wp-json\/wp\/v2\/categories?post=301"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.transplantevidence.com\/news\/wp-json\/wp\/v2\/tags?post=301"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}