brief intro on what is meta-analysis, since the same study hypothesis will be tested over and over again by different researchers over the world, meta analysis is a method to collect all those similar studies, and end up with a single results.

so these are the packages im going to load for just once,

#install.packages("remotes")
#remotes::install_github("MathiasHarrer/dmetar", force = T)

library(metafor) # install.packages("metafor")
library(dmetar) # install.packages("dmetar")

Let’s see the data.

data("DepressionMortality")
DepressionMortality
##                   author event.e  n.e event.c   n.c     country
## 1    Aaroma et al., 1994      25  215     171  3088     Finland
## 2     Black et al., 1998      65  588     120  1901         USA
## 3     Bruce et al., 1989       5   46     107  2479         USA
## 4     Bruce et al., 1994      26   67    1168  3493         USA
## 5    Enzell et al., 1984      32  407     269  6256      Sweden
## 6   Fredman et al., 1989       1   44      87  1520         USA
## 7    Murphy et al., 1987      24   60     200   882      Canada
## 8   Penninx et al., 1999      15   61     437  2603 Netherlands
## 9    Pulska et al., 1998      15   29     227   853     Finland
## 10  Roberts et al., 1990     173 1015     250  3375         USA
## 11      Saz et al., 1999      37  105      66   409       Spain
## 12   Sharma et al., 1998      41  120       9    54          UK
## 13  Takeida et al., 1997      29  258      24  1490       Japan
## 14  Takeida et al., 1999      61  388      34  1257       Japan
## 15   Thomas et al., 1992      15  211      73  1366         USA
## 16   Thomas et al., 1992      21  237      67  1340         USA
## 17 Weissman et al., 1986      10   48      36   216         USA
## 18    Zheng et al., 1997      31  615    1468 57674         USA

the columns are =>event.e n.e event.c n.c it include the source to calculate Risk Ratio. => Risk Ratio(RR) So we decide to use RR as our measurement.

library(metafor)
res = rma(measure = "RR", ai = event.e, bi = n.e-event.e , ci = event.c , di =n.c-event.c ,
          data = DepressionMortality, slab = paste(author ))
forest(res,header = T)

So by the forest plot, we can see there is a lot of squares in diff sizes, bigger the size higher the weight, and the weight is related to the research sample size, which means, if the research have a greater study population, it will leads to more stable and precise result, and ends up weighting higher to the final estimation for all the studies.and the width reflects the 95% confidence interval, wider means less precision. now we look at the last row RE model, it means over all these study, since the log risk ratio is above 0 and the CI doesn’t cross through 0, we can confidently says that the depression group is associated with an increased risk of the event, which is death in this case. since we’re not familiar with the log scale, you can take exponential of 0.7, e^0.7 =2.014, which means exposre group comparing to control group’s RR is 2 times.

funnel(res)

the x axis is log risk ratio, 0 means no effect, for this case the middle point is around 0.7,which means increased risk. y axis is standard error, greater the sample, more precise and stable, and lower the se, and there are a bunch of study’s se is near 0 in this case, which means most of the researches are reliable. the assumption of the funnel plot is, as a scatter plot, it should be symmetrical, if not, youmay consider publication bias. publication bias is a systematic bias due to the lazy researchers, they don’t have enough time and resources to publish every findings, which leads that the published paper we see are all “successful” publish.