estimated proportion of 2 percent although all events were zero in single arm meta-analysis using meta package I am trying to do single arm meta-analysis using meta and metafor packages in R; however, although all events were 0, I got estimated proportion of 0.02 (0.01-0.06).
I just want to confirm that this makes sense as I thought it should be 0 as well.
Here is my code:
library(meta); library(metafor)

data<- read.table(text = "
studlab Number.of.patients  Procedure   events
Lee 2015    15  SPT 0
Wang 2019   44  SPT 0
chira 2018  12  SPT 0
Zhang 2020  20  SPT 0
Lee 2017    48  SPT 0
Weiping Hu 2018 28  SPT 0
Zhu 2021    19  SPM 0
", sep="\t",header=T)

mp<-metaprop(events,Number.of.patients, data=data, studlab=studlab,  method = "Inverse",method.tau = "DL");mp


### Results#
# Number of studies combined: k = 7
# Number of observations: o = 186
# Number of events: e = 0
# 
# proportion           95%-CI
# Common effect model      0.0202 [0.0071; 0.0562]
# Random effects model     0.0202 [0.0071; 0.0562]
# 
# Quantifying heterogeneity:
#   tau^2 = 0; tau = 0; I^2 = 0.0% [0.0%; 70.8%]; H = 1.00 [1.00; 1.85]
#   
#   Test of heterogeneity:
#     Q d.f. p-value
#   0.78    6  0.9927
#   
#   Details on meta-analytical method:
#     - Inverse variance method
#   - DerSimonian-Laird estimator for tau^2
#   - Logit transformation
#   - Continuity correction of 0.5 in studies with zero cell frequencies


Any advice will be greatly appreciated

Under the assumption of homogeneity, the sum of independent binomial counts also follows a binomial distribution. Hence, there are then 0 events out of sum(data$Number.of.patients) (i.e., 186) patients. One could then use the 'rule of 3' to compute a CI (see here for details) or simply compute the Clopper-Pearson CI with binom.test(0, sum(data$Number.of.patients)), which yields the bounds 0 to 0.0196.
