Dealing with studies with no cases in meta-analysis I am meta-analysising the following data by age range:
    Case  Sample   age range     study
1      0   44818    40-49       A
2      9   57368    50-59       A
3     23   54932    60-69       A
4     55   64087    70-79       A
5     31   34912      80+       A
6      9    4339    70-79       B
7      2    2303      80+       B
8      4   85042    40-49       C
9      5   72216    50-59       C
10    14   53293    60-69       C
11    40   42480    70-79       C
12    22   27867      80+       C

Case is the number of cases of the condition.
Sample is the size of sample. Study is the Study name.
I use package metaphor and first calculate effect size by:
 escalc(measure = "PLN", xi = Case, ni = Sample, data = data, append = TRUE)

then use package  meta to do meta analysis
ma.cd.all.1year = metagen(
  TE = yi,
  seTE = sei,
  studlab = study,
  data = data,
  sm = "PLN",
  comb.fixed = FALSE,
 byvar = as.vector(agerange),
)

Then do a forest plot.
But I don't know how to deal with the one with 0 case number. Should I exclude it? If I include it, the confidence interval seems to be not reasonable. How to show the confidence interval properly?
Thanks 
 A: According to Cochrane:

The standard practice in meta-analysis of odds ratios and risk ratios
  is to exclude studies from the meta-analysis where there are no events
  in both arms. This is because such studies do not provide any
  indication of either the direction or magnitude of the relative
  treatment effect.

(See 16.9.3, Studies with no events)
A: Let's start with the outcome measure. You used measure="PLN", so this gives you log-transformed proportions. Is this really what you meant to use? It is more common to apply a logit transformation when analyzing proportions (that would be measure="PLO").
In either case, the outcome cannot be computed when there are no events/cases (in which case the proportion is equal to 0). The common approach to deal with this is to add a constant to the counts when this happens, the default being 1/2. So, really, what is being computed is log((x+1/2)/(n+1)) in that first case, where x=0 and n=44818.
However, the number of events/cases is overall quite low compared to the sample sizes. Therefore, the underlying true proportions are likely to be very small. In that case, you really shouldn't be analyzing these data using a model that uses normal distributions to approximate the sampling distributions of the outcomes. Instead, it would be better to use a proper (random-effects) logistic model (also called binomial-normal model in the meta-analytic literature). See, for example: 
Stijnen, T., Hamza, T. H., & Ozdemir, P. (2010). Random effects meta-analysis of event outcome in the framework of the generalized linear mixed model with applications in sparse data. Statistics in Medicine, 29, 3046–3067.
Such a model can be easily fitted with the metafor package. The syntax would be:
res <- rma.glmm(measure="PLO", xi=Case, ni=Sample, data=data)
res

An added advantage is that no ad-hoc adjustment to the counts is necessary. For plotting purposes of the individual studies, the 1/2 is still used (otherwise the logit-transformed proportion for that first case would not be available). So, if you then use
forest(res)

you will still get a value for that first case. But the actual meta-analysis is based on unadjusted counts.
You may also want to take a look at:
http://www.metafor-project.org/doku.php/analyses:stijnen2010
where I replicate the analyses from Stijnen et al. (2010).
