  A typical random effects meta-analysis of odds-ratios assumes binomially
distributed numbers of events in a treatment and control group and requires the
proportion of deaths to be extracted from published papers. This data is often
not available in the publications due to loss to follow-up. When the Kaplan
Meier survival plot is available, it is common practice to manually measure the
needed information from the plot and infer the probability of survival and then
to infer a best-guess of the number of deaths. Uncertainty introduced from
theses guesses is not accounted for in current models. This naive approach
leads to over-certain results and potentially inaccurate conclusions. We
propose the Uncertain Reading-Estimated Events model to construct each study's
contribution to the meta-analysis separately using the data available for
extraction in the publications. We use real and simulated data to illustrate
our methods. Meta-analysis based on the observed number of deaths lead to
biased estimates while our proposed model does not. Our results show increases
in the standard deviation of the log-odds as compared to a naive meta-analysis
that assumes ideal extracted data, equivalent to a reduction of the overall
sample size of 43% in our example.
