Simple imputation method for meta-analysis of survival rates when precision information is missing

In meta-analyses of survival rates, precision information (i.e., standard errors (SEs) or confidence intervals) are often missing in clinical studies. In current practice, such studies are often excluded from the synthesis analyses. However, the naïve deletion of these incomplete data can produce serious biases and loss of precision in pooled estimators. To address these issues, we developed a simple but effective method to impute precision information using commonly available statistics from individual studies, such as sample size, number of events, and risk set size at a time point of interest. By applying this new method, we can effectively circumvent the deletion of incomplete data, resultant biases, and losses of precision. Based on extensive simulation studies, the developed method markedly improves the accuracy and precision of the pooled estimators compared to those of naïve analyses that delete studies with missing precision. Furthermore, the performance of the proposed method was not significantly inferior to the ideal case, where there was no missing precision information. However, for studies for which the risk set size at the time of interest was not available, the proposed method runs the risk of overestimating the SE. Although the proposed method is a single-imputation method, the simulations show that there is no underestimation bias of the SE, even though the proposed method does not consider the uncertainty of missing values. To demonstrate the robustness of our proposed methods, they were applied in a systematic review of radiotherapy data. An R package was developed to implement the proposed procedure.