Extracting standard error from the 95% confidence interval of a survival.

Abstract

Extracting the standard error of survival from published 95% confidence intervals (95%CI) may be needed for meta-analyses. For the extraction, the transformation used to compute the 95%CI must be known. When that transformation is not stated in publications, an assumption must be made about it. However, an assessment of the impact of an incorrect assumption and a procedure to identify the correct transformation are lacking. To address this, we propose an approach aiming at identifying the transformation used to compute the 95%CI of the survival and enhancing the extraction of the standard error. This approach, named "Logarithm of the Relative Asymmetry" (LRA), is based on the asymmetry of the reported 95%CI. In this study, we assess the extraction error, which is the difference between extracted and true standard errors, and the performance of the LRA approach. The impact of the extraction error and the LRA approach on meta-analyses is also assessed. This study shows that an incorrect assumption about the transformation used to compute the 95%CI of the survival causes, in most cases, an overestimation of the standard error. This overestimation worsens as the survival approaches 0 or 1 or as the sample size decreases, and it propagates into the meta-analysis results. The LRA approach correctly identifies the transformation, yet its performance may be negatively impacted by the number of decimal places used to report the survival and its 95%CI or when the lower or upper bound of the reported 95%CI is exactly 0 or 1 respectively. Overall, the LRA approach is suitable for avoiding important extraction errors and mitigates their impact on meta-analyses results. Thus, we recommend this approach to identify the transformation used to compute the 95%CI of the survival.