Meta-analyses of survival rates: improving the extraction of the standard errors from reported 95% confidence intervals

In clinical research, meta-analyses are widely used to synthesize results from various studies. The advantage is to generalize a result to a larger population and to allow a more accurate data analysis by increasing the sample size. These objectives are achieved by assigning weights to different and sometimes contradictory studies, then combining their results by a weighted average of the estimates of interest, i.e. proportions, differences in risk or in mean between study arms, etc. The weight assigned to each study is derived from the variance of its estimate of interest (Shadish & Haddock, 1994). One issue in conducting a meta-analysis is the extraction of the needed data from the published articles. Indeed, data are sometimes reported graphically, incompletely, or not in a directly analyzable format (for instance, the median is reported while the mean is meant to be meta-analyzed). In studies reporting survival analyses, results are often communicated in the form of the Kaplan-Meier survival curves (Kaplan & Meier, 1958) or survival rates at specific time points in the text of the manuscript or in a table. For the meta-analysis of survival data, various approaches have been proposed to extract the needed information from articles. Most of them focused on the extraction of the hazard ratio since meta-analyses of randomized clinical trials are frequent in clinical research (Parmar et al. 1998; Williamson et al. 2002; Tierney et al. 2007). Some approaches have also been proposed to reconstruct individual data from published survival curves (Guyot et al. 2012; Wei & Royston 2017; Liu et al. 2021). However, when the purpose of a meta-analysis is to combine, across studies, the survival rates of patients with a specific disease condition and, those studies report survival only at specific time points, the previously mentioned approaches are not suitable. In these cases, since the needed data are the survival rates and their standard errors, the common approach is to assume the normality of the survival estimator and extract the standard error from its reported 95% confidence interval. However, this can be problematic because there are several methods to compute the 95% confidence interval of survival. In scientific medical articles, the transformation used is rarely clarified and the default method is not the same in all statistical software. Therefore, the meta-analyst needs to make an assumption about the transformation used by the authors of the article from which the standard error has to be extracted. This Master's thesis aims at assessing the impact of a wrong assumption about the method used to compute the 95% confidence interval of the survival on the results of the meta-analyses. It also aims at proposing an innovative approach to identify the method used to compute the 95% confidence interval of a survival rate thus and to correctly extract the standard error of the survival estimate from its 95% confidence interval.