8.1 Importing dataset in R

There are many ways to import a dataset in R. The way I prefer is to have the data in a csv file created using microsoft excel or any spreadsheet software and use the following command to import the dataset and assign it a name. Let’s call it abc.

abc <- read.csv(file.choose())

It will open a window for you to choose file.

Just so that you can copy what I am mentioning here, just copy the following code into R, and run it and it will generate the dataset for you.

abc <- structure(list(Study = c("Study 1", "Study 2", "Study 3", "Study 4", 
                                "Study 5", "Study 6", "Study 7", "Study 8", 
                                "Study 9", "Study 10", "Study 11", "Study 12",
                                "Study 13", "Study 14", "Study 15", "Study 16"), 
                      event.e = c(1L, 4L, 6L, 20L, 69L, 22L, 19L, 26L, 13L, 2L, 7L, 2L, 29L, 6L, 11L, 4L), 
                      n.e = c(12L, 21L, 43L, 83L, 373L, 219L, 164L, 264L, 102L, 14L, 53L, 60L, 172L, 55L, 49L, 14L)), 
                       class = "data.frame", row.names = c(NA, -16L))

Now you can explore the dataset and see it’s structure.

head(abc) #If the dataset is large, it only shows first few rows. 

summary(abc) #For the summary of the dataset.

##     Study              event.e           n.e       
##  Length:16          Min.   : 1.00   Min.   : 12.0  
##  Class :character   1st Qu.: 4.00   1st Qu.: 37.5  
##  Mode  :character   Median : 9.00   Median : 57.5  
##                     Mean   :15.06   Mean   :106.1  
##                     3rd Qu.:20.50   3rd Qu.:166.0  
##                     Max.   :69.00   Max.   :373.0

As you can see, our data set consists of 16 studies and it includes the number of events event.e and total population n.e in each study.

8.2 Metaprop Function

Metaprop is a function in the meta package which can be used to pool the effect sizes of proportions from a single arm study. You will find more information about other functions from the meta documentation.

8.3 Code for meta-analysis

The code for meta-analysis using metaprop function taking into account various important arguments is below and we will assign the results of our meta-analysis to another variable, let’s call it def.

def <- metaprop(event = event.e, 
                n= n.e, 
                data=abc,
                studlab = Study,
                sm="Plogit",
                level = 0.95,
                comb.fixed=TRUE, comb.random=TRUE,
                hakn=F,
                method.tau="DL")

Now, if we take a look at the code, let me explain it. We have fed metaprop function a bunch of data which is necessary to carry out this meta-analysis. You can also find the details of all these arguments in the meta documentation. But I will briefly write them here.

Firstly we have assigned the appropriate column from our dummy dataset abc we created in the previous step so that it can get the data. event=event.e means that for the event, the data is in the column event.e of our dataset, and the dataset is abc. And the study labels are in column Study. sm indicates which summary measure should be used to pool effect sizes. Here we have used Plogit which is uses logit transformation. Some other commonly used measures like Freeman-Tukey Double Arscine Transformation (PFT) are written along with their respective codes in documentation of meta. Level stands for confidence level which we have set to 95%. comb.fixed and comb.random stands for fixed and random effects meta-analysis which we have set to true as we want to see the results from both of them. method.tau is the method used to calculate between study variance and the most commonly used is DerSimonian-Laird estimator which we have used.

There are a ton of other arguments but for the beginning, we will only use these ones and leave others to the default.

Now, in order to take a look at the results of the meta-analysis, just write the value which you have assigned to the results of the meta-anlaysis and run it using ctrl+enter. And it will give the details of meta-analysis including various statistical results. The command and its output would be this:

def

##          proportion           95%-CI %W(fixed) %W(random)
## Study 1      0.0833 [0.0021; 0.3848]       0.5        1.2
## Study 2      0.1905 [0.0545; 0.4191]       1.6        3.4
## Study 3      0.1395 [0.0530; 0.2793]       2.5        4.7
## Study 4      0.2410 [0.1538; 0.3473]       7.5        8.6
## Study 5      0.1850 [0.1469; 0.2282]      27.7       12.2
## Study 6      0.1005 [0.0640; 0.1481]       9.8        9.5
## Study 7      0.1159 [0.0712; 0.1750]       8.3        8.9
## Study 8      0.0985 [0.0653; 0.1410]      11.6       10.0
## Study 9      0.1275 [0.0696; 0.2081]       5.6        7.5
## Study 10     0.1429 [0.0178; 0.4281]       0.8        2.0
## Study 11     0.1321 [0.0548; 0.2534]       3.0        5.3
## Study 12     0.0333 [0.0041; 0.1153]       1.0        2.2
## Study 13     0.1686 [0.1159; 0.2331]      11.9       10.1
## Study 14     0.1091 [0.0411; 0.2225]       2.6        4.9
## Study 15     0.2245 [0.1177; 0.3662]       4.2        6.5
## Study 16     0.2857 [0.0839; 0.5810]       1.4        3.1
## 
## Number of studies combined: k = 16
## 
##                      proportion           95%-CI
## Fixed effect model       0.1496 [0.1329; 0.1679]
## Random effects model     0.1444 [0.1183; 0.1750]
## 
## Quantifying heterogeneity:
##  tau^2 = 0.0935 [0.0000; 0.4335]; tau = 0.3058 [0.0000; 0.6584];
##  I^2 = 52.2% [15.5%; 73.0%]; H = 1.45 [1.09; 1.92]
## 
## Test of heterogeneity:
##      Q d.f. p-value
##  31.41   15  0.0077
## 
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
## - Jackson method for confidence interval of tau^2 and tau
## - Logit transformation
## - Clopper-Pearson confidence interval for individual studies

In this result, you will find the quantitative summary of the studies as well as various measures of heterogeneity.

8.4 Forest Plot

We can create a default forest plot quite easily using the forest function in R. For the time being, let’s create only a default plot in this paper. Forest function has numerous arguments, but we are not going into its detail in this article.

The command and the output is as under:

forest(def)

8.5 Conclusion

We have successfully generated the forest plot of our studies. Although a single arm meta-analysis is not commonly used, but we have used it to orient ourselves to the workings of R and the basic methodology for a meta-analysis in this language.

There are various other things to account for in meta-analysis which are beyond the scope of this paper. So, we will conclude here for now.

Do try to replicate it. It will help you get comfortable with R and RStudio.